jumps, cojumps and macro announcements - duke university

Research Division Federal Reserve Bank of St. Louis Working Paper Series

Jumps, Cojumps and Macro Announcements

Jérôme Lahaye Sébastien Laurent

and Christopher J. Neely

Working Paper 2007-032A http://research.stlouisfed.org/wp/2007/2007-032.pdf

August 2007

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P.O. Box 442 St. Louis, MO 63166

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Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

Jumps, Cojumps and Macro Announcements∗

Jerome LAHAYE† Sebastien LAURENT‡ Christopher J. NEELY§

First Version: October 2006

This Version: August 2007

Abstract

We analyze and assess the impact of macroeconomic announcements on the discontinuities in

many assets: stock index futures, bond futures, exchange rates, and gold. We use bi-power variation

and the recently proposed non-parametric techniques of Lee and Mykland (2006) to extract jumps.

Beyond characterizing the jump and cojump dynamics of many assets, we analyze how news arrival

causes jumps and cojumps and estimate limited-dependent-variable models to quantify the impact of

surprises. We confirm previous findings that some surprises create jumps. However, many announce-

ments do not create jumps and many jumps are not related to announcements. The propensity of

surprises to create jumps differs across asset classes, i.e., exchange rates, bonds, stock index. Payroll

announcements are most important on stocks and bonds futures markets. Trade related news often

creates cojumps on exchange rate markets.

Keywords: exchange rate, futures, bonds, realized volatility, bipower variation, jumps, macroeconomic

announcement.

JEL Codes: G14, G15, F31, C22

∗The authors would like to thank participants at the Economic Department Doctoral Workshop (University of Namur,

29th of March 2006), CORE Econometrics Seminar (University of Louvain-la-Neuve, 30th of March 2006), 2nd Research

Day of the METEOR “Money and Banking Group” (University of Maastricht, 28th of June2006), 7th Missouri Economic

Conference (University of Missouri at Columbia, 30th of March 2007), GREQAM summer school/workshop on “New

Microstructure of Financial Markets” (Aix en Provence, 25th to 29th of June 2007) for helpful comments and discussions.

We would like to thank in particular Mardi Dungey, Cumur Ekinci, Woon K. Wong, Jesper Pedersen. This text presents

research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime

Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.

†CeReFiM, University of Namur and CORE; [email protected] (corresponding author)‡CeReFiM, University of Namur and CORE; [email protected]§Assistant Vice President, Research Department, Federal Reserve Bank of St. Louis; [email protected]

1 Introduction

How markets process information and what determines asset return distributions are central issues

in economics. Our study focuses on two important aspects of financial time series to which the

literature has recently devoted attention: jumps and simultaneous jumps in multiple markets

(cojumps). How big and frequent are jumps across asset classes and over time? Do jumps cluster

in time? Do jumps tend to occur simultaneously on several markets? That is, are there more

“cojumps” than one would expect if asset prices jumped independently? What causes (co)jumps?

Do scheduled macroeconomic announcement create (co)jumps or do these releases affect only the

continuous part of volatility? Our study answers these questions.

We thus re-investigate the central question of how asset prices are related to fundamentals.

Andersen, Bollerslev, Diebold, and Vega (2003, 2007) have studied this issue in great detail but

we focus on discontinuous price changes, not on returns in general. Moreover, as Lee and Myk-

land (2006) and Tauchen and Zhou (2005) explain, characterizing the distribution and causes of

jumps can improve and simplify asset pricing models.1 So—beyond scientific curiosity—we have

a practical interest in understanding how news affects discontinuities. Our paper illuminates the

relations between scheduled macroeconomic news, jumps and cojumps.

We extract jumps and cojumps of many important asset series—exchange rates, stock index

futures, U.S. bond futures and gold prices—and relate them to macroeconomic news. We use the

non-parametric statistic of Lee and Mykland (2006) to estimate jumps on high-frequency data.

The Lee-Mykland estimation technique is simple and parsimonious: Compare returns to a local

volatility measure to find returns that a diffusion is very unlikely to produce—discontinuities. To

measure local volatility, Lee and Mykland (2006) use the jump-robust bi-power variation (RBV)

estimator, defined as the sum of the product intra-daily adjacent returns over the considered

horizon (Barndorff-Nielsen and Shephard, 2004, 2006a).

The Lee-Mykland procedure identifies intraday jumps, which makes it especially useful in

studying if and how announcements cause jumps. We also use this statistic to investigate mul-

tivariate issues and test whether macroeconomic announcements cause cojumps. Though a fully

consistent cojump characterization should compare returns, or a combination of returns to local co-

variation measures, the literature has not yet extended the technique to a multivariate procedure.2

1In general, the impact of jumps on financial management is non-negligible. See for example Duffie, Pan, and

Singleton (2000), Liu, Longstaff, and Pan (2003) , Eraker, Johannes, and Polson (2003), and Piazzesi (2005).2To the best of our knowledge, Barndorff-Nielsen and Shephard (2006b), generalizing their univariate results,

2

It seems very reasonable to assume, however, that highly significant, simultaneous individual jumps

provide insights for understanding cojump processes. This is a conservative approach—analogous

to using OLS rather than SUR to estimate a system of equations—as a multivariate procedure

would surely be more efficient. We show that exchange rate cojumps are relatively frequent and

macroeconomic announcements appear to cause many of them.

Researchers have evaluated the impact of macroeconomic news on assets returns in many

ways.3 The works of Andersen, Bollerslev, Diebold, and Vega (2003, 2007) show that jumps in

exchange rates, stocks and bonds are linked to fundamentals.4 However, recent developments

in jump estimation have revived studies about news and economic events’ impact on financial

markets. The fact that these techniques precisely define jumps enables researchers to analyze such

discontinuites more easily. The recent literature using non-parametric tools to estimate jumps

provides some evidence that news creates jumps. Barndorff-Nielsen and Shephard (2006a) apply

their bipower variation technique on a 10-year exchange rate data set (USD/DEM and USD/JPY),

relating macroeconomic news releases to jump days. Lee and Mykland (2006) also examine the

relation between announcements and jumps on individual equities and the S&P 500 index returns

with three months of high frequency data. They relate jumps to news found with the Factiva

search tool: Jumps on individual equities correspond to scheduled and unscheduled firm level

news while jumps on the S&P index correspond to macroeconomic announcements. Jumps on

individual equities are also much larger and more frequent than those on the stock index. Beine,

Lahaye, Laurent, Neely, and Palm (2007) study the link between central bank interventions and

jumps with the Barndorff-Nielsen and Shephard (2004, 2006a) statistic and find that interventions

can cause rare but especially large discontinuities. To the best of our knowledge, two simultaneous

and building on ideas of Hendry (1995), is the only theoretical paper in the field. While an estimator that accounts

for multivariate behavior is likely to be more efficient in finding jumps, it is very reasonable to define cojumps as

simultaneous individual jumps.3In general, the huge amount of studies in the field are differentiated according to several dimensions: the

moments of the returns’ distribution under study (level or volatility), returns’ frequency (intra-daily or lower

frequency), type of assets (exchange rates, stocks, bonds, ...), type of news (scheduled or unscheduled), etc. For

example, the literature on the effect of news on volatility dates back at least to 1984 and include inter alia Patell

and Wolfson (1984), Harvey and Huang (1991), Ederington and Lee (1993), Andersen and Bollerslev (1998b), Li

and Engle (1998), Jones, Lamont, and Lumsdaine (1998), or Bauwens, Ben Omrane, and Giot (2005). On the other

hand, the literature on the effect of news on the return’s conditional mean includes notably the works of Andersen,

Bollerslev, Diebold, and Vega (2003, 2007), Evans and Lyons (2007), or Veredas (2005).4See Goodhart, Hall, Henry, and Pesaran (1993), Almeida, Goodhart, and Payne (1998), and Dominguez (2003)

about exchange rates.

3

and concurrent papers study the link between non-parametric jumps and news besides the present

paper. Huang (2006) estimates daily jumps with bi-power variation on 10 years of S&P 500 and

U.S. T-bonds 5-minute futures to measure the response of volatility and jumps to macro news.

Analyzing conditional distributions of jumps, and regressing continuous and jump components on

measures of disagreement and uncertainty concerning future macroecnomic states, Huang (2006)

finds a major role for payroll news and a relatively more responsive bond market. This is consistent

with our findings. On the other hand, Dungey, McKenzie, and Smith (2007) focus on the treasury

market, estimating jumps and cojumps using bi-power variation and examining “simultaneous”

jumps across the term structure of interest rates. Dungey, McKenzie, and Smith (2007) find that

the middle of the yield curve often cojumps with one of the ends, while the ends of the curve exhibit

a greater tendency for idiosyncratic jumps. Macro news is strongly associated with cojumps in

the term structure.

Our paper differs from the existing literature in several respects, however:

• We estimate jumps at a very high frequency with the Lee/Mykland technique. These

estimates are better suited than daily (bipower variation) measures of jumps for studying

the link between jumps and scheduled macro news.

• Our approach considers a broad set of financial assets including exchange rates, stocks,

bonds, gold.

• We define simultaneous occurrences of high frequency jumps, which provides precise insights

into cojumping dynamics.

• We estimate Tobit-probit models on the time-series of jumps and cojumps to assess the

impact of surprises on these discontinuities.

The rest of the paper proceeds as follows: After explaining the theory of jump estimation in

Section 2, we characterize (co)jump dynamics and intensity in Section 3. In Section 4, we address

a central issue of asset return distribution: What is the link between macroeconomic news and

(co)jumps? We initially compare jump size distributions on days with and without announcements

and then study what types of announcements cause jumps. We finally evaluate the surprise impact

of news on jumps and cojumps with probit-Tobit models. Finally, Section 5 concludes.

4

2 Theoretical background

This section describes the two estimators used for volatility and jump measurement. We first

describe the more familiar bi-power variation estimator before presenting the Lee and Mykland

(2006) statistic, used throughout this paper.

The idea behind bi-power variation is the following: Realized volatility (RV) is the sum of

squared returns over an interval. This sum consistently estimates the sum of integrated volatility

(the diffusion variance) plus the sum of squared jumps within a period. Bipower variation (BV),

however, is the sum of the products of absolute adjacent returns. This quantity consistently

estimates only integrated volatility even in the presence of jumps. Therefore the difference between

RV and BV consistently estimates the sum of squared jumps within a period.

More formally, let p(t) be a logarithmic asset price at time t. Consider the continuous-time

jump diffusion process defined by the following equation:

dp(t) = µ(t)dt + σ(t)dW (t) + κ(t)dq(t), 0 ≤ t ≤, T (1)

where µ(t) is a continuous and locally bounded variation process, σ(t) is a strictly positive

stochastic volatility process with a sample path that is right continuous and has well defined

limits, W (t) is a standard Brownian motion, and q(t) is a counting process with intensity λ(t)

(P [dq(t) = 1] = λ(t)dt and κ(t) = p(t)− p(t−) is the size of the jump in question). The quadratic

variation for the cumulative process r(t) ≡ p(t)− p(0), denoted [r, r]t, is the integrated volatility

of the continuous sample path component plus the sum of the q(t) squared jumps that occurred

between time 0 and time t:

[r, r]t =∫ t

0

σ2(s)ds +∑

0<s≤t

κ2(s). (2)

The empirical counterpart to daily quadratic variation is daily realized volatility, denoted

RVt+1(∆), which is the sum of the intraday squared returns:

RVt+1(∆) ≡1/∆∑

j=1

r2t+j∆,∆, (3)

where rt,∆ ≡ p(t)− p(t−∆) is the discretely sampled ∆-period return.5

As Andersen, Bollerslev, and Diebold (2006) explain, realized volatility converges uniformly in

probability to the daily increment of the quadratic variation process as the sampling frequency of5We use the same notation as in Andersen, Bollerslev, and Diebold (2006) and normalize the daily time interval

to unity.

5

the returns increases (∆ → 0):6

RVt+1(∆) →∫ t+1

t

σ2(s)ds +∑

t<s≤t+1

κ2(s). (4)

That is, realized volatility consistently estimates integrated volatility plus the sum of the squared

jumps.

In order to disentangle the continuous and the jump component of realized volatility, we need

to consistently estimate the integrated volatility, even in the presence of jumps in the process.

This is done using the asymptotic results of Barndorff-Nielsen and Shephard (2004, 2006a). The

realized bipower variation, denoted BVt+1(∆), is defined as the sum of the product of adjacent

absolute intradaily returns standardized by a constant:

BVt+1(∆) ≡ µ−21

1/∆∑

j=2

|rt+j∆,∆||rt+(j−1)∆,∆|, (5)

where µ1 ≡√

2/π ' 0.79788 is the expected absolute value of a standard normal random variable.

It can be shown that bipower variation converges to integrated volatility, even in the presence of

jumps:

BVt+1(∆) →∫ t+1

t

σ2(s)ds. (6)

Barndorff-Nielsen and Shephard use the difference between realized volatility and bipower

variation to estimate the sum of jumps within a day. This difference does not, however, show how

many jumps there are, their individual size or when they occur within the day. To avoid these

deficiencies, we use the Lee and Mykland (2006) statistics to estimate jumps for each intraday

period.7

To test whether a jump occurred in a small interval, the Lee and Mykland (2006) statistic

quantifies the intuition that a “jump” is too big to come plausibly from a pure diffusion. Because

a “big” price change depends on the volatility conditions prevailing at the time, the Lee and

Mykland (2006) statistic compares the price change to a local robust-to-jumps volatility estimator

6See also, for example, Andersen and Bollerslev (1998a), Andersen, Bollerslev, Diebold, and Labys (2001),

Barndorff-Nielsen and Shephard (2002a), Barndorff-Nielsen and Shephard (2002b), Comte and Renault (1998).7In the Lee-Mykland setting, q(t) is a counting process that may be non homogenous, independent of W (t), and

κ(t) is independent from q(t) and W (t). Moreover, the drift and diffusion coefficients are not allowed to change

dramatically over short period of time. Formally, that is expressed as supj supt+(j−1)∆≤u≤t+j∆ |µ(u)− µ(t + (j −1)∆)| = Op(∆1/2−ε) and supj supt+(j−1)∆≤u≤t+j∆ |σ(u) − σ(t + (j − 1)∆)| = Op(∆1/2−ε), for any ε > 0. That

means that, for any δ > 0, there exists a finite constant Mδ such that the probability that the mentioned supreme

is greater than Mδ∆1/2−ε is smaller than δ.

6

(bipower variation). During periods of “high” volatility, for example, price changes must be even

larger than the average critical value to be considered “jumps.”

The statistic Lµ tests whether a jump occurred between any intradaily time periods t+(j−1)∆

and t+j∆, for an integer j. It is defined as the normalized return—the return, less its local mean,

divided by the local standard deviation:

Lµ(t + j∆) ≡ rt+j∆,∆ − m(t + j∆)σ(t + j∆)

, (7)

where m(t+j∆) is the mean local return and σ(t+j∆) is the realized bipower variation multiplied

by µ21/K−2. They are computed over a K-length window immediately preceding the tested return

and are defined as follows:8

m(t + j∆) =1

K − 1

j−1∑

l=j−K+1

rt+l∆,∆, (8)

σ(t + j∆)2 ≡ 1K − 2

j−1∑

l=j−K+2

|rt+l∆,∆||rt+(l−1)∆,∆|. (9)

Under the null of no jumps at the testing time, the stated assumptions and a suitable choice

of the window size for local volatility K (i.e. we must have K = Op(∆α), with −1 < α < −0.5),

the statistic Lµ asymptotically follows a zero mean normal distribution with variance 1/c2, where

c =√

2/π.

There is a tradeoff in choosing the window size, K. While larger values impose a greater

computational burden, K must be large enough to retain the advantage of bipower variation as

a robust-to-jump estimator. A range of values satisfy the condition for K (K = Op(∆α), with

−1 < α < −0.5). Lee and Mykland (2006) recommend the smallest possible window size within the

range given by α, as their simulations show that greater windows only increase the computational

burden. So K is chosen as ∆−0.5. For example, suppose ∆ = 1252×nobs , nobs being the number

of observations per day, then the integers between 15.87 and 252 are within the required range.

More specifically, they recommend the following window sizes for sampling at frequencies of one

week, one day, one hour, 30 minutes, 15 minutes and 5 minutes: 7, 16, 78, 110, 156, and 270,

respectively.

Finally, Lee and Mykland (2006) propose a rejection region using the distribution of their

statistics’ maximums. Under the stated assumptions and no jumps in (t + (j − 1)∆, t + j∆], then

when ∆ → 0,max |Lµ(t + j∆)| − Cn

Sn→ ψ, (10)

8The term m(t + j∆) reduces to zero in the case of no drift. In that case, the statistic is denoted by L(t + j∆).

7

where ψ has a cumulative distribution function P (ψ ≤ x) = exp(−e−x), Cn = (2 log n)0.5

c −log(π)+log(log n)

2c(2 log n)0.5 and Sn = 1c(2 log n)0.5 , n being the number of observations. So if we choose a signifi-

cance level α = 0.0001, we reject the null of no jump at testing time if |Lµ(t+j∆)|−Cn

Sn> β∗ with the

threshold β∗ such that P (ψ ≤ β∗) = exp(−e−β∗) = 0.9999, i.e. β∗ = −log(−log(0.9999)) = 9.21.

In the remainder of the text, Jt+j∆ denotes significant jumps. It is equal to the tested return

rt+j∆ when the statistic Lµ(t+j∆) detects a significant jump according to the described rejection

region. It is equal to 0 otherwise. Moreover, we use the notation P (jump) for P (Jt+j∆ 6= 0).

We can now move on in the next section to a description of the data used in our analysis before

turning to the empirical results.

3 Data description

3.1 Asset price data

We use a long span of high frequency time series data on 15 assets from 4 asset classes: four

exchange rates involving the dollar (USD/EUR, USD/GBP, JPY/USD, CHF/USD), three stock

index futures (Nasdaq, Dow Jones, S&P 500, for which we use the acronyms ND, DJ, and SP,

respectively), 30-year U.S. Treasury bonds futures (with the acronym US), as well as gold prices

(with acronym XAU). From the four exchange rate series, we recover the implied non-dollar

exchange rates (GBP/EUR, CHF/EUR, JPY/EUR, CHF/GBP, JPY/GBP and CHF/JPY), as-

suming no triangular arbitrage. All the original series were provided at a 5-minute frequency.

We re-sampled them at 15-minute intervals (30-minute for Tobit-probit estimations in Section 4).

Table 1 summarizes information about the series.

Olsen and Associates provide the exchange rate and XAU series. The USD/EUR, USD/GBP

and JPY/USD are sampled using last mid-quotes (average of log bid and log ask) of each 5-

minute interval. The CHF/USD and XAU series are sampled through a linear interpolation of

mid-quotes around 5-minute interval points. The exchange rates series cover about 18 years of

data (1986-2003), while 15 years are available for XAU (1986-2001).

The Dow Jones and 30-year U.S. T-bonds futures contracts series are traded on the Chicago

Board of Trade (CBOT), while the Nasdaq and S&P 500 futures trade on the Chicago Mercantile

Exchange (CME). The futures’ sample ranges vary across series: bond futures data cover about 12

years, the S&P series about 19 years, and 6 years are available for Nasdaq and Dow Jones futures.

8

We construct continuous series by splicing contracts with liquid trading. That is, we roll-over to

another contract 6 business days before maturity (15 business days in the case of U.S. T-bonds).

The currency and XAU markets are decentralized, traded around the clock, and around the

world. A 24 hour trading day is thus divided into 288 5-minute or 96 15-minute intervals. As

standard in the literature, we define trading day t to start at 21.15 GMT on day t − 1 and end

at 21.00 GMT on day t.9 So the first price of trading day t is the last price of the 21.00-21.15

interval (of calendar day t− 1), when prices are sampled at 15-minute. The first return of the day

is a change over the 21.00-21.15 interval.

However, CBOT and CME have limited pit trading hours. We cannot assess whether there

is a jump in the much longer overnight return, because it cannot be directly compared to a local

volatility estimate. Thus, our calculations will omit this return. For the Nasdaq and S&P 500

traded at the CME, we retain the following hours for 15-minute sampled prices: 9.45 - 16.15 EST

for both future contracts, the market opening at 9.30 EST. On these CME markets, the first return

of the day is thus a change over the 9.45-10.00 interval. For the Dow Jones and U.S. T-bonds

futures traded at the CBOT, the market opens at 8.20 EST, and, for 15-minute sampled prices,

we retain 8.25 - 14.55 and 8.25 - 16.10 EST, respectively. So for the CBOT markets, the first

return of the day covers the 8.25-8.40 interval.

We remove week-ends and a set of fixed and irregular holidays, from the intradaily return

series, as well as days where there are too many missing values, constant prices, and/or days with

the longest constant runs activity. The regular holidays removed are December 24 through the

26, December 31 through January 2 and July 4. Irregular holidays include Good Friday, Easter

Monday, Memorial Day, Labor Day, Thanksgiving and the day after. The first two lines of Table

2 report the number of observations and sample days for each asset.

3.2 Jumps and cojumps

In this subsection, we characterize the (co)jumping behavior of financial assets with a sampling

frequency of 15 minutes. Simulation results in Lee and Mykland (2006) show that the test statis-

tic provides excellent results at that frequency. Moreover, though not reported here, volatility

signature plots show that realized volatility starts to stabilize at about 15 minutes. So we expect

our estimates to be free of the noise present in higher frequency returns. We describe jumps

conservatively, analyzing jumps with a very low significance level (α) of 0.0001. We first describe

9This is motivated by the ebb and flow in the daily FX activity patterns. See Bollerslev and Domowitz (1993).

9

individual jumps before focusing on simultaneous jump occurrences.

3.2.1 Jumps

Figure 1 provides a bird’s eye view on the time series of jumps (Jt+j∆, as defined in Section 2),

illustrating that jumping behavior varies by asset class.10 For example, Nasdaq futures, a highly

volatile market11, seem to exhibit fewer but much larger jumps than exchange rates (though one

should not be misled by the different sample length on the X-axis). Moreover, there are big

jumps during major crises as, for example, in October 1987 on the S&P 500 futures.12 When

comparing jumps across series, one should remember that the exchange rate and XAU series have

more trading hours than do the stock index and bonds futures markets. The remainder of this

section contrasts jumps statistics across series.

Table 2 reveals different jump frequencies across series. This table reports the probability that

a day contains at least one jump and the probability that an intra-day return is a jump. For

the latter approach, we also provide information for positive and negative jumps separately. For

example, the first column—labeled “DJ”—shows that the Dow Jones futures series jumped on 25

days, which was 1.43 % of the sample and the expected number of jumps on jump days was 1.04.

Jump days are much less frequent on stock index futures than on U.S. bonds futures (Table

2, second horizontal panel). 5.32% of days have jumps in the US sample, while the DJ, ND

and SP exhibit jumps on only 1.43, 0.70, and 1.70% of days, respectively. Bond futures exhibit

fewer jumps than dollar exchange rates, but about the same proportions as non-dollar exchange

rates. Jumps seem to be very frequent on the XAU series, occurring on 22% of all days. And

the average number of jumps—on jump days—reaches a maximum of 1.36 for the XAU series

(Table 2, second horizontal panel, last line). This heterogeneity in jump frequency is unsurprising

across such different markets. The decentralized 24 hour exchange rate markets, with overlapping

international trading segments, are more likely to produce jumps than a market with limited hours,

such as the futures markets.

When comparing jump probabilities, one should recall that there are more observations per10For clarity, we ignore here the cross exchange rate series recovered under a no-triangular-arbitrage assumption.11Though not reported here, statistics for the daily continuous component of realized volatility show that the

Nasdaq futures market ranks among the most volatile markets.12It is not obvious that “market crashes” create jumps estimated as such. Indeed, the two greatest jumps observed

on the S&P 500 in October 1987 have opposite signs. That means that the S&P 500 lost a great deal of its value

without the negative discontinuities significantly outweighing the positive discontinuities. The jumps identified

during this crisis do not account for a large part of the S&P variation during that period.

10

day on decentralized 24 hours markets. This can be illustrated by comparing jumps per ob-

servation (Table 2, third panel, second line): For example, the bonds future market (column

4, US) exhibits more jumps per observation (P (jump) = 0.2109%) than the USD/EUR market

(column 5) (P (jump) = 0.1630%) but the USD/EUR market exhibits jumps on 13 percent of

days (P (jumpday) = 13.05%) while the bond futures market only jumps on 5 percent of days

(P (jumpday) = 5.32%). The USD/EUR exhibits more jumps per day because it has many more

observations per day but the USD/EUR is less likely to jump on any given observation.

Is there asymmetry in positive and negative jumps? While we analyze jumps rather than re-

turns, previous theoretical and empirical results on returns suggest that markets respond more to

negative surprises in good times. The literature has suggested both behavioral and rational expec-

tations explanations for such asymmetric responses. Barberis, Shleifer, and Vishny (1998) offer

a behavioral approach, while Veronesi (1999) provides a rational expectations model. Moreover,

practitioners commonly accept that markets will strongly respond to bad news in good times,

as explained in Conrad, Bradford, and Landsman (2002) and Andersen, Bollerslev, Diebold, and

Vega (2003). Because surprises are mean zero and most of our sample covers expansions, we might

expect more significant negative jumps, at least for equities.13 The sign of responses to negative

news is less clear in other markets. The number of positive and negative detected jumps (first lines

of fourth and fifth panels of Table 2) bears out that negative jumps are much more frequent than

positive ones on S&P futures. We also observe asymmetry on dollar exchange rates: U.S. dollar

jump depreciations are more common than jump appreciations.14 For example, comparing panels

4 and 5 of Table 2, there were 378 jump depreciations of the USD versus 304 jump appreciations of

the USD. Other markets, i.e. DJ, ND, and US, display no apparent asymmetry between positive

and negative jumps. The SP, however, displays many more negative jumps than positive jumps,

as one might expect from an equity market.

When do jumps usually occur? Figure 2 shows the estimated number of jumps, by time of

day, for each series. Exchange rates, XAU, and the S&P 500 futures have common seasonality,

with lots of jumps between 1200 and 1800. That is, most of the jumps on the 24 hours markets13According to NBER business cycle expansions and contractions dates, only two periods covering about one year

and half of our sample (from July 1990 to March 1991 and from March until November 2001) can be considered as

contractions. These recession periods represent a small fraction of our longest samples that cover about 18 years

of data.14The four dollar exchange rates are USD/EUR, USD/GBP, JPY/USD, and CHF/USD. So a positive jump

means a dollar depreciation for the first two markets and a dollar appreciation for the last two.

11

(exchange rates and XAU) occur after the North-American segment opening at about 1300. Sim-

ilarly, most of the jumps on the U.S. T-bonds futures market occur at the beginning of the U.S.

trading day (returns from 8.25 to 8.40 EST). This is consistent with the idea that macroeconomic

announcements, which are mostly released at 8:30 EST, cause many jumps.

Table 2 and Figure 3 provide further information concerning jump moments and frequencies.

Table 2 (panel 3, 4 and 5, last two lines) provides sample moments for jumps, while Figure 3 is a

scatter plot of mean jump size versus jump frequency. Stock index futures exhibit extremely large

(above 1% in absolute value) but relatively infrequent jumps. Exchange rates (dollar and non-

dollar) and XAU exhibit smaller jumps (between 0.4 and 0.6% in absolute value) than do equities.

Compared with cross rates, dollar exchange rates exhibit more frequent jumps of comparable size.

The bond market stands in the middle in terms of jump size (with an average of about 0.8%

in absolute value) with frequency comparable to those of cross exchange rates, i.e. bond prices

jump less often than do exchange rates and XAU prices. Table 2 shows that jump sizes are highly

variable; the standard deviations for positive and negative jumps often exceed 1% for stock index

futures, lie roughly between 0.2% and 0.35% for bonds and exchange rates, and are about 0.5%

for XAU.

The next section characterizes how markets jump together, or cojump.

3.2.2 Markets interdependence: an analysis of cojumps

This section shows that jumps can occur simultaneously on different markets and characterizes

those cojumps. We denote a cojump on a set of markets M at time t+ j∆ as COJMt+j∆ and define

it as:

COJMt+j∆ =

∏

M

I(Jmi

t+j∆), (11)

where I is the indicator function, Jmi

t+j∆ refers to jumps on market mi in the set M at time t+ j∆.

For clarity in the notations, the superscript referring to markets is omitted. Moreover, we denote

the probability of a cojump P (COJt+j∆ = 1) by P (coj).

Table 3 provides a detailed view on how markets jump together. Table 3 denotes the number

of observations as #obs, the number of cojumps as #coj, the probability of a cojump as P (coj),

and the probability of cojumping under the null that jump processes are independent as P (coj)

if indep. The first (top) horizontal panel of Table 3 shows the likelihood of cojumps on all

combinations between stock index futures and 30-year U.S. T-bonds. For example, the first row

shows that the ND-DJ pair exhibited 4 cojumps over 46548 observations, which produced a jump

12

propensity of 0.0086 percent per observation. The second horizontal panel shows statistics for

cojumps on dollar exchange rates. The third horizontal panel reports results for simultaneous

jumps on pairs of markets with the most liquid exchange rate, the USD/EUR market. The last

horizontal panel shows results for cojumps occurring on all dollar exchange rates plus another

market.

The table allows us to compare the actual probability of cojumping (P (coj)) with the proba-

bility of cojumping under the null of independence P (coj) if indep to assess whether jumps are

independent events. The latter probability is the product of the jump proportions in the respec-

tive markets. The actual proportions of cojumps are overwhelmingly greater than the probability

under the null of independence, indicating that cojumps do not occur by chance. For example, the

observed proportion of cojumps on the ND-DJ markets was 0.0086%, but the expected probability

under the null that the jumps are independent is essentially zero. Formal tests of this hypothesis,

using the properties of the binomial distribution reject the null of independent jumps for all cases

in which there are cojumps.

The data show that cojumps occur frequently on certain markets. But the probability of a

cojump is bounded by the minimum probability of a jump across all the markets considered. For

example, there are only 12 jumps on the ND market; cojumps involving the ND are necessarily

unfrequent. But cojumps might compose a very large proportion of all jumps on some markets.

Therefore we examine the probability of cojumps conditional on jumps in individual markets

(P (coj|jump)). This gives a clearer picture of the dependence of a given market with other

markets. In the third vertical panel of Table 3, the five columns, numbered from 1 to 5, correspond

to individual markets in the order in which they appear on the first column of Table 3. Thus, a

conditional probability on line x and column y gives the probability of a cojump on the markets

considered in line x given that a jump occurred on the market that has the yth position in the

markets of line x. For example, the first conditional probability on the first line of the Table

(33.33%) means that 1/3 of all jumps on the ND market are also cojumps with the DJ prices

(the corresponding line is ND-DJ). Likewise, conditional on a jump in the DJ, the probability of

a cojump on the ND-DJ pair is 15.83%. Column 1 refers to ND; column 2 refers to DJ.

The column labeled “1” under P (coj|jump) in Table 3 shows that when a jump occurs on

the ND market, the probability that it jumps with another market in the group considered here

(stock index and bond futures) is at least 16.67% (ND - US) and can be as high as 41.67% (ND -

SP). That is, many of the infrequent Nasdaq jumps occurred at the same time as jumps on other

13

markets, mainly other stock index futures. For the DJ market, the probability of a cojump, given

a jump on SP, is somewhat smaller than the ND’s. It reaches a maximum of 30.77 % for DJ - US

cojumps. It is even smaller for the SP where the maximum P (coj|jump) is 7.69% for ND-DJ-US

cojumps.

On markets with infrequent jumps, these rare jumps are highly dependent. In particular,

stock index futures and bonds are highly dependent. This is particularly true for the ND market;

when the ND jumps, the SP is also very likely to jump. The probability of a cojump on ND-SP,

conditional on a jump in ND, is 41.67%. Table 3, second panel shows that cojumps are not rare

on dollar exchange rates. There are 391 cojumps on the USD/EUR - CHF/USD market pair,

implying a probability of cojump of about 0.093% (per observation). Because we work with 15-

minute returns, this means that a cojump is expected to occur every 11 days. Cojumps are an

important feature of this market.

Naturally, the number of cojumps declines as the number of markets considered increases.

Nevertheless, the probability of cojump remains substantial even for the four dollar exchange

rates, with P (coj) = 0.0199 %; one expects a cojump in all four USD rates every 52 days. Figure

4 displays the full time series of cojumps for the different dollar exchange rate combinations.

This figure illustrates the frequent cojumps on these markets. Moreover, P (coj|jump) estimates

are also very high. The conditional probabilities show that when a jump occurs on any dollar

exchange rates, the chance of a cojump on all four USD exchange rates exceeds 10% (see the last

row of the second horizontal panel of Table 3). The maximum P (coj|jump) estimates are found

for USD/EUR - CHF/USD cojumps. When a jump occurs on one of these markets, a cojump

occurs on both with probability above 50%. We can conclude that cojumps are common on dollar

exchange rates, and that jumps on these markets are strongly dependent.

The third horizontal panel shows strong linkages between USD/EUR and several assets: Trea-

sury bonds (US), stock index futures (DJ) and EUR/JPY. The probability of cojumps on these

market pairs can be very high (see Table 3, third horizontal panel). For example, it reaches 0.045%

for USD/EUR - US cojumps. This implies an expected cojump every 23 days. Conditional cojump

probabilities can also be very high. For example, more than one in five (21.08%) Treasury bond

futures (US) jumps are also USD/EUR cojumps. And almost one in two (42.95%) EUR/JPY

jumps are USD/EUR - EUR/JPY cojumps.

The fourth horizontal panel of Table 3 shows statistics on cojumps on the four USD markets

plus another. Jumps across these five markets are much less likely; both P (coj) and P (coj|jump)

14

are relatively low, compared to other market combinations. The largest such P (coj) is 0.0091,

with the US.

At what time do cojumps usually occur? This question is of primary interest as one of our

goals is to understand whether macroeconomic releases cause cojumps. The arrival time for

macroeconomic news is almost always known in advance and is most often at 8:30 U.S. Eastern

Time (12.30 or 13.30 GMT), for the news considered in our study. Figure 5 shows histograms for

cojumps arrival, where we focus our attention on dollar exchange rates combinations. It displays

the count of cojumps per intra-day period, as in Figure 2 for jumps. The cojumps clearly occur

near the opening of the North American markets and the release of macro announcements. This

period also coincides with the overlap of the London - New York markets.

The next subsection describes our macroeconomic announcement data, before we go on to

analyze how (co)jumps relate to macro news.

3.3 Macroeconomic announcements

As is standard in the literature, we use the International Money Market Service data on surveyed

and realized macroeconomic fundamentals. Table 4 provides summary information on these data.

As in Balduzzi, Elton, and Green (2001) or Andersen, Bollerslev, Diebold, and Vega (2003), we

standardize surprises to easily compare coefficients across surprises and series. The standardized

surprise for announcement i at time t is defined by Nit = Rit−Eit

σi, where Rit is the realization

of announcement i at time t, Eit is its survey expectation and σi its standard deviation. These

macro news are scheduled at a monthly frequency. Balduzzi, Elton, and Green (2001) have shown

that the expected value of macro news predicts the announcement in an approximately unbiased

manner.

4 Macroeconomic announcements, jumps and cojumps: em-

pirical analysis

In this section, we analyze the impact of U.S. macroeconomic announcements on (co)jumps.

We first describe the data before moving on to estimate limited dependent variable models for

(co)jumps. We drop from the analysis markets that open after news arrival, i.e. SP and ND

futures. Indeed, these markets open at 9.30 EST (see Table 1) while most announcements are

15

scheduled at 8.30 EST.

4.1 Descriptive analysis

4.1.1 The distribution of jumps conditional on macroeconomic announcement

Table 5 presents conditional jump moments for days without any news and days with at least one

announcement. We provide statistics for all jumps in absolute value, as well as for positive and

negative jumps (with significance level α = 0.0001). The provided descriptive statistics are the

number of observations, jump probabilities, and the first two moments.

Every one of the assets displays a higher proportion of jumps on U.S. announcement days. This

suggests that announcements indeed create jumps. Under the null that jump probabilities are equal

in the announcement sample and in the non-announcement sample, the difference between the

probabilities in the two samples follows a normal distribution with mean zero and variance equal

to Pnews(1−Pnews)Nnews

+ Pnonews(1−Pnonews)Nnonews

, where Pnews (Pnonews) denotes the jump probability in the

announcement (non-announcement) sample, and Nnews (Nnonews) the number of observations in

the announcement (non-announcement) sample. This simple test of proportions equality rejects

the null of equal means, for most markets. The mean absolute value of jumps on announcement

days is significantly larger than jumps on non-announcement days for all the USD exchange rates,

all the futures markets, the JPY/EUR, the CHF/JPY and (at the 10 percent level) the XAU. Both

positive and negative jumps are often significantly more frequent in the announcement sample,

although the tests sometimes fail to reject because of lower power with fewer observations (Table

5). To sum up, jumps are more frequent on announcement days.

Are jump means different on announcement days? A simple test of the null of no difference

between jump means in the news and the no-news samples reveals different mean jump sizes in

four cases: US, JPY/USD, CHF/USD and CHF/JPY (see means in Table 5). The signs of the

differences are inconsistent, however. In two cases, absolute jumps are larger on announcement

days and in two cases they are smaller (Table 5). There is no evidence that jumps are larger on

announcement days.

We observed in Table 2 that jump USD depreciations were more frequent than jump USD

appreciations. Table 5 confirms this phenomenon: jump USD depreciations are more numerous

than jump USD appreciations on announcement days. Moreover, there are more positive jumps

in U.S. bond futures prices than negative ones (63 positive against 43 negative jumps), suggesting

16

some asymmetry in reactions to news. As positive jumps indicate rises in bond prices—a large

fall in yields—it appears that bond prices could be more sensitive to negative news about long

run economic activity or inflation.

In the next section, we investigate how macro news releases match jumps, and what types of

releases are most influential.

4.1.2 Matching jumps and macroeconomic announcement

Do jumps on financial markets closely match announcements? What sorts of news are most likely

to produce discontinuities? This subsection answers these questions.

Figures 6 and 7 present time histograms of jump occurrences on days without and with an-

nouncements, respectively. Jumps tend to cluster around announcement times on announcement

days, on most markets. Moreover, these figures show that, though jumps are more concentrated

around announcement time on news days, many jumps occur before 12.30 GMT or 13.30 GMT on

these days. This illustrates the necessity to study intraday data to understand what causes jumps

and avoid spuriously associating jumps with surprises.

Let us analyze the jump-announcement relationship in greater detail. The upper panel of Table

6 shows how announcements match jumps, while the lower panel details results across announce-

ments. We report in the upper panel the number of sample days (# days) and observations (#

obs.), the number of jumps and announcement days (# jumps and # news days), the count of

jumps matching announcements (# Jump-news match, where we count a match if a jump occurs

within one hour after the announcement), the probability of a news (P (news)), the probability of a

jump given a news (P (jump|news)), the probability of a news given a jump (P (news|jump)), and

finally the probability of observing a day where news and jumps match exactly (P (jump, news)).

When a generic announcement occurs, there is a 10.85% chance of a USD/EUR jump (see Table

6, upper panel, P (jump|news)). In general, the propensity of news to cause jumps is highest for

bond futures, USD exchange rates and XAU series where between 6% and 11% of announcements

generate a jump in prices. This ratio is much lower on non-dollar exchange rates (between 1.04%

and 3.28%) and DJ futures (0.75 %). The higher probability of jumps, conditional on news, for

the USD exchange rates, U.S. bonds and XAU seems sensible. Non-dollar exchange rates surely

respond less to U.S. announcements than dollar exchange rates. And the stock index futures

markets are not open during times of announcements. The high probability that news will induce

jumps in the bond market is also unsurprising given that researchers have long found Treasury

17

markets to be sensitive to macro news announcements (Ederington and Lee, 1993; Fleming and

Remolona, 1997; 1999).

How many jumps are caused by news? If a high proportion of jumps are caused by news, then

P (news|jump) will be high compared to P (news). In fact, it appears that news causes many

jumps, at least on some markets. The probability of an announcement, conditional on a jump,

can reach 48.19%, for bond futures (see Table 6, upper panel, P (news|jump)). This is relatively

high compared to the unconditional news probability on the bond market, which is equal to 1.15%

(Table 6, upper panel, P (news)). The row labeled P (news|jump), in the upper panel of Table

6, suggests that announcements create about 15 % to 20% of USD jumps, roughly 4% to 13% of

non-dollar exchange rate jumps and 9.91% of XAU jumps. The unconditional probability of a

news is about 0.3% for most markets.

What news announcements are the most likely to create surprises that lead to jumps? The

second horizontal panel of Table 6 decomposes results per news. It shows that the employment

report (nonfarm payroll employment and unemployment) and trade balance news are outstanding

in terms of jump association. The employment report is particulary important for DJ, US and

USD exchange rates. The trade balance report is important for exchange rates. For example, as

much as one payroll news in four (27.67%) and one trade balance news in five (20.28%) cause

jumps on the USD/EUR market (see P (jump|news)). The proportion of jumps associated with

these news is also relatively high. For example, we see in Table 6 (lower panel, P (news|jump))

that 33.57% of U.S. bond jumps are associated with payroll news. Price level (PPI, CPI) surprises

are important for bonds and USD exchange rates. The probability of a jump in the bond market

(US) conditional on a CPI news release, is 10.64% and the probability of news release, conditional

on a jump in bond futures is 8.82 %. The probability of a jump on the CHF/USD market, given

a durable goods announcement, is 6.82%.

The relative response of foreign exchange and bond markets to PPI and CPI shocks is consistent

with standard intuition about how (non)tradeables inflation should influence those markets. Jumps

in foreign exchange markets appear to respond better to PPI announcements, while jumps in

bond prices appear to respond more strongly to CPI news. This is sensible because exchange

rates should be more sensitive to tradeable goods prices—which the PPI better reflects—while the

bond market should respond to a broader price index, such as the CPI. The fact that cross-rates

are more sensitive to PPI shocks (reflecting international tradeables prices) also supports this

explanation.

18

The next subsection describes how cojumps match announcements.

4.1.3 Cojumps and macroeconomic announcements

The last column of Table 3 provides insights into cojump dynamics with respect to news arrival.

Our cojump indicator equals one when jumps occur simultaneously on different markets. So

working at a 15-minute frequency, we very precisely estimate cojump timing. Many cojumps

occur right after news arrival. For example, 67 of the 243 cojumps found on the USD/EUR -

USD/GBP markets match exactly news arrival (Table 3, # coj. matching news).

Moreover, the greater the number of market considered, the greater the proportion of cojumps

associated with news. Indeed, about half of the cojumps detected on the four dollar exchange

rates markets match perfectly news arrival. Besides cojumps on dollar exchange rates markets,

the combinations of markets where the probability of a cojump is relatively high are USD/EUR

- US, USD/EUR - XAU, and USD/EUR - EUR/JPY, where we detect 35, 34, and 134 cojumps,

respectively (see Table 3, # coj.). Again, many of these cojumps exactly match news arrival.

The proportion of cojumps matching exactly news is about 2/3, 1/3 and 1/5 of all cojumps on

USD/EUR - US, USD/EUR - XAU, and USD/EUR - EUR/JPY, respectively. For example,

USD/EUR - US had 35 cojumps (# coj.), of which 23 (# coj. matching news) exactly matched

news releases.

This descriptive subsection has characterized how (co)jumps relate to a set of macroeconomic

announcements. There are more jumps on days of macro announcements. Moreover, on some

markets, we detect asymmetry between positive and negative jumps on announcement days, sug-

gesting that news might have asymmetric effects. Matching news and jumps closely, we find

that between 0.75% and 10.85% of announcements create jumps (P (jump|news)), while between

5.79% (CHF/EUR) and 48.19% (US) of jumps match perfectly announcements (P (news|jump)).

Employment reports, trade balance releases and price level news are most likely to create jumps.

Finally, macro announcements appear to produce many of the cojumps.

It is necessary, however, to model (co)jumps formally so that proper inference can be made

about the link between (co)jumps and macro surprises. The next and final subsection models the

effects of surprises on the absolute value of jumps and on the probability of cojumps.

19

4.2 Modeling jumps and cojumps in Tobit-probit framework

In this subsection, we use Tobit and probit models to formally study the link between (co)jumps

and macro news. We focus on the series where (co)jumps are the most frequent, and where the

link with macro news is likely to be strongest. For jumps, the regression analysis includes dollar

exchange rates, XAU, U.S. T-bonds and Dow Jones futures. For cojumps, we focus on dollar

exchange rates.

4.2.1 Modeling jumps to assess the impact of macro announcements

We estimate the impact of macroeconomic announcements on jumps with a Tobit model (Table

7) to estimate the determinants of absolute jumps, which have a limited distribution.

|J∗t+j∆| = xt+j∆ + εt+j∆, (12)

xt+j∆ = µ + αt+j∆ + µt+j∆ + ξt+j∆,

|Jt+j∆| =

|J∗t+j∆| if |J∗t+j∆| > 0,

c if |J∗t+j∆| ≤ 0

where εt+j∆|xt+j∆ is N(0, σ20). The time index is denoted as before and refers to high frequency

points in time: t + j∆, where ∆ is the sampling interval, t refers to days, while j is an integer.

|Jt+j∆| represents significant jumps in absolute value, as defined by the Lee and Mykland (2006)

technique (see Section 2), while |J∗t+j∆| is its latent counterpart. αt+j∆ and µt+j∆ are defined as

linear combinations of day-of-the-week dummies and U.S. announcements, respectively:

αt+j∆ = α1TUESDAYt+j∆ +α2WEDNESDAYt+j∆ +α3THURSDAYt+j∆ +α4FRIDAYt+j∆,

(13)

where TUESDAYt+j∆, WEDNESDAYt+j∆, THURSDAYt+j∆ and FRIDAYt+j∆, are day-of-

the-week dummies, α1 to α4 are parameters to estimate and µt+j∆ describes the impact of U.S.

20

news.15

µt+j∆ =β1CPIt+j∆ + β2PPIt+j∆ + β3TRADEBALt+j∆ + β4DURABLEt+j∆ (14)

β5LEADINGIt+j∆ + β6HOUSINGt+j∆ + β7NFPAY ROLt+j∆,

where β’s are parameters to be estimated and the explanatory variables are the standardized

surprises magnitudes.16

We have tested a specification for µt+j∆ that permits surprises to influence jumps asymmetri-

cally. That is, where positive and negative surprises enter the equation with separate coefficients.

To evaluate whether surprises did influence jumps asymmetrically, we performed simple Wald tests

for the equality of the parameters of positive and negative surprises and were usually unable to

reject symmetry. For this reason, we only report results for µt+j∆ containing surprises in absolute

value, which enforces a symmetric response to positive and negative shocks. Because a coefficient

is unidentified unless there is a non-zero value for the regressor that is coincident with a jump,

only regressors that have at least one contemporaneous match with the dependent variable are

included in the estimations.

All models are estimated at an intra-day level. This raises some issues due to the nature of the

data in question. First of all, the huge number of observations and the high level of censoring of

the jump series imposes substantial computational demands in maximum likelihood estimation.

To conserve memory to permit maximization of the likelihood function, we reduce the sampling

frequency (∆) to 30 minutes. The second issue is that, as shown in Figure 2, intraday jumps

may have a seasonal component, separate from effects caused by announcements. To control for

potential impact of volatility seasonal components on jumps, we include regressors based on a

flexible fourier form that captures seasonality. That is, we include

ξt+j∆ = γ1trendt+j∆ + γ2trend2t+j∆ +

p∑

i=1

(γ2+i cos κi(t+j∆) + γ2+p+i sin κi(t+j∆)), (15)

where trend is a trend component across intra-day periods, κi(t+j∆) = 2π∆× i× trendt+j∆, and

15In a previous version of the paper, we have tested the effect of some European announcements on RV and its

continuous and jump components, using BNS statistics. Some news were found to affect the continuous component

of realized volatility but not jumps. Moreover, we have also tested a specification accounting for business cycles,

allowing for different impact of news on recession times compared to expansions. Probably given the small recession

period of the sample, we could not find any model improvement by including interaction terms between macro news

and a dummy indicating recession.16Export-import and unemployment news are not included in the regressors set because they are highly correlated

with trade balance and non-farm payroll news, respectively.

21

p is fixed at a conservative level of 4 or 5 terms (depending on the series), such that the fitted

seasonal component follows closely the intra-day seasonality pattern. Except for the DJ series,

this seasonal component significantly improves the likelihood of the models.

Table 7 (upper panel) presents estimation results for the impact of U.S. macro news on the

retained series. We find that, as reported by other studies in the context of news impact on returns

or volatility, payroll and trade balance announcements strongly predict jumps in financial markets,

particularly on foreign exchange markets. The remainder of this Section details the results by asset

type.

Exchange Rates Table 7 shows that some announcements affect jumps in all dollar ex-

change rate series. Indeed, absolute PPI (but not CPI) surprises have a significant positive effects

on foreign exchange jumps. Payroll and trade balance announcements both produce consistent

and important effects. The estimated coefficients for these surprises are highly significant every-

where. Durable good orders are significant on two exchange rate markets markets (USD/EUR

and CHF/USD).

XAU The determinants of XAU jumps are similar to those of exchange rates. Unlike for

some exchange rate markets, durables surprises are insignificant in the model for XAU, while

housing news have a significant—but perverse—effect. That is, large shocks to housing starts

actually reduce the predicted jumps in the gold market. But similarly to exchange rate markets,

PPI (and not CPI), payroll and trade balance news are significant predictors in the tobit model

for XAU jumps.

U.S. T-bonds futures The U.S. bonds market is usually thought as being very sensitive to

public news due to the nature of bond pricing. Announcements do cause jumps, to a statistically

significant degree. CPI and payroll surprises are significant. The coeffcient on PPI is much smaller

than that on CPI shocks and only marginally significant. Trade balance news are also significant,

but are wrongly signed, however. That is, a surprise announcement of a larger trade deficit in

absolute value significantly reduces jumps in the bond market.

Dow Jones futures The only announcement that is identified in the Dow-Jones futures

data is the payroll announcement. These payroll surprise shocks significantly explain size and

occurrence jumps in 30-minute data.

22

We note that the index of leading indicators is the only variable that never produces statistically

significant effects. This is not surprising as market participants can predict this index very well

from public information, prior to its release.

Finally, we report the McKelvey-Zavoina R2, that provides an estimate of the fitted latent

variable variance over the total variance. We obtain values between 6% and 17%, while the U.S.

bond futures model estimation yields a surprising 99%. This is consistent with the fact that most

of the jumps occur at the same time on this market. Jumps are indeed concentrated at 8.30

EST (see Figure 2). The strong ability of macro announcements to predict jumps in bond prices

is consistent with Fleming and Remolona (1997, 1999). Thus, it appears that macro surprises

together with regressors capturing seasonality allow to explain a great deal of variation in the

latent variable.

4.2.2 Modeling cojumps

Table 7 (lower panel) presents evidence on the link between macro news and cojumps with a

probit model. We use probit estimation with a qualitative indicator for cojumps because there is

no unambiguous way to attach a single magnitude to cojumps.

COJ∗t+j∆ = xt+j∆ + εt+j∆, (16)

xt+j∆ = µ + αt+j∆ + µt+j∆ + ξt+j∆,

COJt+j∆ =

1 if COJ∗t+j∆ > 0

0 if COJ∗t+j∆ ≤ 0,

where εt+j∆ is NID(0, 1). COJt+j∆ is the cojump indicator (see Equation 11), while COJ∗t+j∆ is

the associated latent variable. The remaining variables are defined as above, in the Tobit model:

αt+j∆ controls weekly seasonality; µt+j∆ includes macro surprises in absolute value; ξt+j∆ controls

for intradaily seasonality.

The seasonal component significantly improves the models’ likelihood, as it does for the Tobit

models. Moreover, we also tested for the presence of asymmetric response of markets in terms of

cojumps, specifying µt+j∆ such that surprises influence jumps asymmetrically (as explained for

the Tobit models). We could not find evidence of asymmetry, as in Tobit models. Consequently,

only results for surprises in absolute value are presented in Table 7.

23

Payroll and trade balance news produce the most significant effects. Across all combinations of

two dollar exchange rates, these news announcements always have significant impacts on cojumps.

While PPI news are significant at the two-sided 5% level in all exchange rates’ Tobit models, they

seem to have slightly less significant effects in probit models for pairs of exchange rate cojumps

(significance is found at the two-sided 10% level, on most market combinations). On the other

hand, they are much more important and consistent determinants of exchange rate cojumps than

shocks to CPI.

We obtain McFadden R2s of 14% to 27 % for the exchange rate cojumping variables. U.S.

announcements explain a substantial portion of exchange rate cojumps.

5 Conclusion

This paper has extended the previous literature studying jumps and the reactions of financial

markets to macroeconomic announcements in several ways. We apply the Lee and Mykland (2006)

statistic to characterize the timing and size of intraday jumps in a variety of markets, USD and

cross exchange rates, U.S. Treasury bond futures, U.S. equity futures and gold futures. Because

we can (almost) exactly determine jump times, we can more precisely associate them with macro

announcements. Precise timing also permits us to characterize the propensity of “cojumps”—

simultaneous jumps on multiple markets—and their association with macro announcements.

We first informally describe the data, finding that jumps are more frequent on announcement

days but that there is no evidence that jumps are consistently larger on announcement days.

Some markets (e.g. the bond market) display evidence of asymmetry in jump frequency. There

are more negative bond jumps than positive bond jumps. A precisely comparison of the timing of

announcements and jumps indicates that announcements create about 15% to 20% of USD jumps,

roughly 4% to 13% of non-dollar exchange rate jumps and 9.91% of XAU jumps.

When we compare the probabilities of jumps, conditional on macro surprises, we find that

jumps and cojumps in foreign exchange markets appear to respond better to PPI announcements,

while jumps in bond prices appear to respond more strongly to CPI news. This is consistent

with foreign exchange markets responding more strongly to tradeables inflation (better proxied

by PPI) and bond markets should react more strongly to overall inflation (better proxied by the

CPI). Consistent with this, cross-exchange rates react to PPI, which better reflects international

commodity prices, but not CPI.

24

We follow our data description by estimating Tobit models of jumps and probit models of

cojumps. Because the data generally rejected formal tests of asymmetry in either Tobit or probit

models of jump reaction to news (that is, negative suprises are usually no more or less likely to

produce cojumps than are positive surprises), we report the impact of absolute value surprises on

(co)jumps. Of all the surprises that we investigate, payroll and trade balance news consistently

significantly create jumps and cojumps. Price level shocks and surprises to durable goods orders

also often produce jumps. The index of leading indicators and housing starts do not significantly

explain jumps.

25

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28

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29

Table 1: Description of the raw original series used in the study

Asset Source Freq Trading Hours Period available

NASDAQ 100 Futures (ND) CME 5-min 9.30-16.15 EST 07/01/1998 - 01/22/2005

S&P 500 Futures (SP) CME 5-min 9.30-16.15 EST 01/02/1986 - 07/22/2005

US Treasury bonds (US) CBOT 5-min 8.20-15.00 EST 01/04/1993 - 11/29/2004

Dow Jones Futures (DJ) CBOT 5-min 8.20-16.15 EST 06/11/1998 - 07/22/2005

USD/EUR O&A 5-min 24 hours a day 01/02/1987 - 10/01/2004

USD/GBP O&A 5-min 24 hours a day 02/01/1986 - 10/01/2004

JPY/USD O&A 5-min 24 hours a day 06/26/1986 - 10/01/2004

CHF/USD O&A 5-min 24 hours a day 02/02/1986 - 09/30/2004

Gold (XAU) O&A 5-min 24 hours a day 02/03/1986 - 09/07/2001

30

Tab

le2:

Jum

pses

tim

ated

usin

gLee

-Myk

land

test

stat

isti

cD

JN

DSP

US

USD

/EU

RU

SD

/G

BP

JPY

/U

SD

CH

F/U

SD

EU

R/C

HF

EU

R/G

BP

EU

R/JPY

GBP/C

HF

GBP/JPY

JPY

/C

HF

XA

U

#obs.

56096

46602

130572

78705

418464

435648

429120

446688

420384

418080

419232

435552

426432

429120

373728

#days

1753

1726

4836

2915

4359

4538

4470

4653

4379

4355

4367

4537

4442

4470

3893

Jum

pday

(day

wit

hat

least

one

jum

p)

frequency

#ju

mp

days

25

12

82

155

569

502

467

574

188

217

282

210

260

247

858

P(j

um

pd

ay)

(%)

1.4

30.7

01.7

05.3

213.0

511.0

610.4

512.3

44.2

94.9

86.4

64.6

35.8

55.5

322.0

4

E(#

ju

mp|j

um

pd

ay)

1.0

41.0

01.1

61.0

71.2

01.2

01.1

81.2

11.2

91.1

61.1

11.1

41.1

31.1

61.3

6

All

jum

ps

(abso

lute

valu

e)

#ju

mps

26

12

95

166

682

601

551

695

242

251

312

239

294

286

1171

P(j

um

p)

(%)

0.0

463

0.0

257

0.0

728

0.2

109

0.1

630

0.1

380

0.1

284

0.1

556

0.0

576

0.0

600

0.0

744

0.0

549

0.0

689

0.0

666

0.3

133

E(|

ju

mp

siz

e||

ju

mp)

1.3

72.9

81.6

20.7

40.5

20.4

60.5

40.5

20.4

10.5

10.6

10.5

10.6

30.6

20.5

5√

Va

r(|

ju

mp

siz

e||

ju

mp)

0.8

42.2

71.7

40.3

20.2

70.2

20.3

20.2

20.2

30.2

80.3

40.2

10.3

30.2

90.5

0

Posi

tive

jum

ps

#ju

mps>

013

624

82

378

319

250

308

107

124

151

111

143

149

576

P(j

um

p>

0)

(%)

0.0

232

0.0

129

0.0

184

0.1

042

0.0

903

0.0

732

0.0

583

0.0

690

0.0

255

0.0

297

0.0

360

0.0

255

0.0

335

0.0

347

0.1

541

E(j

um

ps

iz

e|j

um

p>

0)

1.5

93.2

72.2

30.7

50.5

20.4

50.5

60.5

20.4

20.5

10.6

20.5

30.6

30.6

10.5

3√

Va

r(j

um

ps

iz

e|j

um

p>

0)

1.0

52.9

52.6

80.3

00.2

70.2

10.3

30.2

40.2

90.2

90.3

80.2

30.3

50.2

90.4

8

Negati

ve

jum

ps

#ju

mps<

013

671

84

304

282

301

387

135

127

161

128

151

137

595

P(j

um

p<

0)

(%)

0.0

232

0.0

129

0.0

544

0.1

067

0.0

726

0.0

647

0.0

701

0.0

866

0.0

321

0.0

304

0.0

384

0.0

294

0.0

354

0.0

319

0.1

592

E(j

um

ps

iz

e|j

um

p<

0)

-1.1

4-2

.68

-1.4

1-0

.72

-0.5

3-0

.47

-0.5

3-0

.52

-0.3

9-0

.51

-0.6

0-0

.50

-0.6

3-0

.64

-0.5

7√

Va

r(j

um

ps

iz

e|j

um

p<

0)

0.4

61.2

11.2

00.3

40.2

70.2

40.3

00.2

10.1

70.2

60.3

00.1

90.3

10.3

00.5

2

Note

:T

he

table

dis

pla

ys,

from

top

tobott

om

the

num

ber

of

sam

ple

poin

ts(#

obs

.)and

sam

ple

days

(#d

ay

s),

the

tota

lnum

ber

of

jum

pdays

(#ju

mp

da

ys,i.e.

days

wit

hat

least

one

jum

p),

the

pro

bability

(in

%)

of

aju

mp

day

(P(j

um

pd

ay)

=100(#

ju

mp

da

ys

/#

da

ys))

,and

the

num

ber

ofju

mps

per

jum

pday

(E(#

ju

mp|j

um

pd

ay)

=#

ju

mp

/#

ju

mp

da

ys).

We

furt

her

giv

eth

eto

talnum

ber

jum

ps

(#ju

mp

s),

their

pro

port

ion

(in

%)

over

sam

ple

obse

rvati

ons

(P(j

um

p)

=100(#

ju

mp

s/#

obs

.)),

as

well

as

their

abso

lute

mean

size

and

standard

devia

tion

(E(|

ju

mp

siz

e||

ju

mp)

and

√V

ar(|

ju

mp

siz

e||

ju

mp))

.Fin

ally,th

ela

sttw

opanels

split

the

jum

ps

intw

ose

ts:

posi

tive

and

negati

ve

jum

ps.

Pro

port

ions

(P(j

um

p>

0)

and

P(j

um

p<

0))

,m

ean

(E(j

um

ps

iz

e|j

um

p>

0)

and

E(j

um

ps

iz

e|j

um

p<

0)

)and

std.

dev.

(√V

ar(j

um

ps

iz

e|j

um

p>

0)

and

√V

ar(j

um

ps

iz

e|j

um

p<

0))

are

report

ed,

as

for

the

full

set

ofju

mps

inabso

lute

valu

e.

The

chose

nsi

gnific

ance

levelfo

rju

mps

est

imati

on

isα

=0

.0001.

The

sam

pling

frequency

is15

min

ute

.

31

Tab

le3:

Coj

umps

ondi

ffere

ntm

arke

tco

mbi

nati

ons

#obs.

#coj.

P(c

oj)

(%)

P(c

oj)

(%)

P(c

oj|j

um

p)

(%)

#coj.

ifin

dep.

12

34

5m

atc

hin

gnew

s

ND

-D

J46548

40.0

086

0.0

000

33.3

315.3

80

ND

-SP

46575

50.0

107

0.0

000

41.6

75.2

60

ND

-U

S34122

20.0

059

0.0

001

16.6

71.2

00

DJ

-SP

47142

60.0

127

0.0

000

23.0

86.3

20

DJ

-U

S42444

80.0

188

0.0

001

30.7

74.8

23

SP

-U

S64108

70.0

109

0.0

002

7.3

74.2

20

ND

-D

J-

SP

46521

40.0

086

0.0

000

33.3

315.3

84.2

10

ND

-D

J-

US

34078

20.0

059

0.0

000

16.6

77.6

91.2

00

DJ

-SP

-U

S34584

30.0

087

0.0

000

11.5

43.1

61.8

10

ND

-SP

-U

S34122

20.0

059

0.0

000

16.6

72.1

11.2

00

ND

-D

J-

SP

-U

S34078

20.0

059

0.0

000

16.6

77.6

92.1

11.2

00

USD

/EU

R-

USD

/G

BP

418080

243

0.0

581

0.0

002

35.6

340.4

367

USD

/EU

R-

JPY

/U

SD

419232

134

0.0

320

0.0

002

19.6

524.3

255

USD

/EU

R-

CH

F/U

SD

420384

391

0.0

930

0.0

003

57.3

356.2

694

USD

/G

BP

-JPY

/U

SD

426432

95

0.0

223

0.0

002

15.8

117.2

444

USD

/G

BP

-C

HF/U

SD

435552

220

0.0

505

0.0

002

36.6

131.6

568

JPY

/U

SD

-C

HF/U

SD

429120

130

0.0

303

0.0

002

23.5

918.7

155

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

417312

88

0.0

211

0.0

000

12.9

014.6

415.9

743

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

426432

85

0.0

199

0.0

000

14.1

415.4

312.2

344

USD

/EU

R-

USD

/G

BP

-C

HF/U

SD

418080

193

0.0

462

0.0

000

28.3

032.1

127.7

764

USD

/EU

R-

JPY

/U

SD

-C

HF/U

SD

419232

114

0.0

272

0.0

000

16.7

220.6

916.4

053

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

417312

83

0.0

199

0.0

000

12.1

713.8

115.0

611.9

443

USD

/EU

R-

US

77517

35

0.0

452

0.0

003

5.1

321.0

823

USD

/EU

R-

ND

41067

10.0

024

0.0

000

0.1

58.3

30

USD

/EU

R-

SP

117180

30.0

026

0.0

001

0.4

43.1

60

USD

/EU

R-

DJ

49536

80.0

161

0.0

001

1.1

730.7

73

USD

/EU

R-

XA

U347328

34

0.0

098

0.0

005

4.9

92.9

013

USD

/EU

R-

EU

R/JPY

419232

134

0.0

320

0.0

001

19.6

542.9

530

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

-X

AU

344352

90.0

026

0.0

000

1.3

21.5

01.6

31.2

90.7

76

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

-N

D40905

00.0

000

0.0

000

0.0

00.0

00.0

00.0

00.0

00

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

-SP

116370

00.0

000

0.0

000

0.0

00.0

00.0

00.0

00.0

00

USD

/EU

R-

USD

/G

BP

-JPY

/U

SD

-C

HF/U

SD

-U

S77301

70.0

091

0.0

000

1.0

31.1

61.2

71.0

14.2

26

Note

:C

oju

mps

are

defined

as

an

indic

ato

rvari

able

equal

toone

when

signific

ant

jum

ps

(at

α=

0.0

001

and

a15-m

inute

frequency)

occur

exactl

yat

the

sam

eti

me

on

diffe

rent

mark

ets

.T

he

table

dis

pla

ys,

the

num

ber

of

obse

rvati

ons,

the

num

ber

of

coju

mps,

the

coju

mp

pro

bability

(P(c

oj),

in%

),th

ecoju

mp

pro

bability

under

independence

of

the

jum

ppro

cess

es

(pro

duct

of

jum

ppro

port

ions,

in%

).C

olu

mns

6to

10

(P(c

oj|j

um

p)

in%

,num

bere

d1

to5)

report

the

pro

bability

of

acoju

mp

on

the

mark

ets

giv

en

on

aline

giv

en

aju

mp

on

am

ark

et

giv

en

by

the

num

ber

ofth

ecolu

mn

(1to

5).

This

num

ber

refe

rsto

the

ord

er

ofth

em

ark

ets

inw

hic

hth

ey

appear

on

the

firs

tcolu

mn.

The

last

colu

mn

report

sth

enum

ber

ofcoju

mps

matc

hin

gexactl

ynew

sarr

ival.

32

Table 4: Scheduled macroeconomic announcement

Announcement Variable Name Range Unit Day of the week

Labor market

Employees on Payrolls NFPAYROL 1985-2005 change in 1000 Friday

Prices

Producer Price Index PPI 1980-2005 %change Thursday or Friday

Consumer Price Index CPI 1980-2005 %change Tuesday to Friday

Business cycle conditions

Durable Good Orders DURABLE 1980-2005 %change Tuesday to Friday

Housing Starts HOUSING 1980-2005 millions Tuesday to Friday

Leading Indicators LEADINGI 1980-2005 %change Monday to Friday

Trade Balance TRADEBAL 1980-2005 $ billion Tuesday to Friday

U.S. Exports USX 1988-2005 $ billion Tuesday to Friday

U.S. Imports USI 1988-2005 $ billion Tuesday to Friday

33

Tab

le5:

Jum

ppr

obab

iliti

esan

dm

omen

tsco

ndit

iona

lon

anno

unce

men

ts

No

announcem

ent

days

Announcem

ent

days

No

announcem

ent

days

Announcem

ent

days

Jum

ps

(abs.

val)

Jum

ps>

0Jum

ps<

0Jum

ps

(abs.

val)

Jum

ps>

0Jum

ps<

0Jum

ps

(abs.

val)

Jum

ps>

0Jum

ps<

0Jum

ps

(abs.

val)

Jum

ps>

0Jum

ps<

0

Dow

-Jones

CH

F/EU

R

P(j

um

p)

(%)

0.0

307

0.0

154

0.0

154

0.0

822**

0.0

411

0.0

411

0.0

556

0.0

254

0.0

302

0.0

621

0.0

256

0.0

365

#ju

mps

12

66

14

77

162

74

88

80

33

47

Mean

1.3

01.5

2-1

.09

1.4

21.6

6-1

.19

0.4

20.4

4-0

.40

0.3

80.4

0-0

.38

St.

Dev.

0.9

31.1

90.4

60.7

50.9

10.4

50.2

60.3

30.1

90.1

60.1

90.1

4

U.S

.T

-bonds

GBP/EU

R

P(j

um

p)

(%)

0.1

107

0.0

350

0.0

756

0.4

328

***

0.2

573***

0.1

756***

0.0

576

0.0

269

0.0

307

0.0

656

0.0

359

0.0

297

#ju

mps

60

19

41

106

63

43

167

78

89

84

46

38

Mean

0.6

50.6

6-0

.65

0.7

8***

0.7

7*

-0.7

9**

0.5

10.5

3-0

.50

0.5

00.4

8-0

.54

St.

Dev.

0.2

00.2

00.2

00.3

60.3

20.4

20.2

40.2

90.2

00.3

40.3

00.3

7

USD

/EU

RJPY

/EU

R

P(j

um

p)

(%)

0.1

240

0.0

641

0.0

600

0.2

511***

0.1

497***

0.1

014***

0.0

657

0.0

303

0.0

354

0.0

941***

0.0

490***

0.0

451

#ju

mps

360

186

174

322

192

130

191

88

103

121

63

58

Mean

0.5

10.5

1-0

.51

0.5

30.5

2-0

.56

0.6

30.6

5-0

.62

0.5

70.5

7-0

.56

St.

Dev.

0.2

70.2

90.2

50.2

60.2

40.2

90.3

80.4

50.3

20.2

60.2

50.2

6

USD

/G

BP

CH

F/G

BP

P(j

um

p)

(%)

0.1

128

0.0

605

0.0

523

0.1

950***

0.1

020

0.0

930***

0.0

526

0.0

251

0.0

275

0.0

600

0.0

262

0.0

337

#ju

mps

341

183

158

260

136

124

159

76

83

80

35

45

Mean

0.4

50.4

4-0

.45

0.4

80.4

6-0

.49

0.5

20.5

2-0

.52

0.5

00.5

4-0

.48

St.

Dev.

0.1

90.1

80.1

90.2

60.2

40.2

80.1

80.1

80.1

80.2

50.3

10.1

9

JPY

/U

SD

JPY

/G

BP

P(j

um

p)

(%)

0.1

061

0.0

480

0.0

581

0.1

789***

0.0

815***

0.0

975***

0.0

648

0.0

321

0.0

328

0.0

783

0.0

368

0.0

415

#ju

mps

316

143

173

235

107

128

192

95

97

102

48

54

Mean

0.5

70.5

9-0

.55

0.5

1**

0.5

2*

-0.5

10.6

50.6

5-0

.65

0.6

10.6

1-0

.61

St.

Dev.

0.3

50.3

70.3

30.2

70.2

80.2

60.3

40.3

50.3

30.3

10.3

50.2

8

CH

F/U

SD

CH

F/JPY

P(j

um

p)

(%)

0.1

283

0.0

585

0.0

698

0.2

182***

0.0

929***

0.1

253***

0.0

571

0.0

299

0.0

272

0.0

883***

0.0

457**

0.0

426**

#ju

mps

399

182

217

296

126

170

170

89

81

116

60

56

Mean

0.4

90.4

9-0

.49

0.5

5***

0.5

6***

-0.5

5***

0.6

60.6

4-0

.68

0.5

7***

0.5

7*

-0.5

8**

St.

Dev.

0.2

10.2

30.1

90.2

40.2

40.2

30.3

30.3

10.3

40.2

20.2

30.2

0

XA

U

P(j

um

p)

(%)

0.3

027

0.1

500

0.1

527

0.3

373*

0.1

634

0.1

739

#ju

mps

785

389

396

386

187

199

Mean

0.5

50.5

2-0

.57

0.5

60.5

6-0

.56

St.

Dev.

0.5

40.5

20.5

60.4

00.3

90.4

1

Note

:Jum

ppro

port

ions(P

(ju

mp),

in%

)and

mom

ents

(mean

and

standard

devia

tion

ofju

mpsin

abso

lute

valu

e,posi

tive

and

negati

ve)fo

rdaysw

ithoutannouncem

entand

daysw

ith

atle

ast

one

announcem

ent.

The

num

ber

ofju

mps

(com

pute

dat

a15-m

inute

frequency

wit

ha

signific

ance

level

α=

0.0

001)

isals

ore

port

ed

(#ju

mps)

.Sta

rson

the

announcem

ent

sam

ple

means

and

pro

port

ions

indic

ate

wheth

er

they

are

stati

stic

ally

diffe

rent

from

those

inth

eno-a

nnouncem

ent

sam

ple

.O

ne,tw

oand

thre

est

ars

corr

esp

ond

tosi

gnific

ance

at

1%

,5%

,and

10%

level,

resp

ecti

vely

.

34

Tab

le6:

Jum

pan

dan

noun

cem

ent

prob

abili

ties

DJ

US

USD

/EU

RU

SD

/G

BP

JPY

/U

SD

CH

F/U

SD

XA

UC

HF/EU

RG

BP/EU

RJPY

/EU

RC

HF/G

BP

JPY

/G

BP

CH

F/JPY

Overall

result

s

#days

1753

2915

4359

4538

4470

4653

3893

4379

4355

4367

4537

4442

4470

#obs.

56096

78705

418464

435648

429120

446688

373728

420384

418080

419232

435552

426432

429120

#ju

mps

26

166

682

601

551

695

1171

242

251

312

239

294

286

#new

sdays

532

907

1336

1389

1368

1413

1192

1342

1333

1340

1389

1357

1368

#Jum

p-n

ew

sm

atc

h4

80

145

110

94

139

116

14

19

44

24

25

37

P(n

ew

s)

(%)

0.9

51.1

50.3

20.3

20.3

20.3

20.3

20.3

20.3

20.3

20.3

20.3

20.3

2

P(j

um

p|n

ew

s)

(%)

0.7

58.8

210.8

57.9

26.8

79.8

49.7

31.0

41.4

33.2

81.7

31.8

42.7

0

P(n

ew

s|j

um

p)

(%)

15.3

848.1

921.2

618.3

017.0

620.0

09.9

15.7

97.5

714.1

010.0

48.5

012.9

4

P(j

um

p,

ne

ws)

(%)

0.2

32.7

43.3

32.4

22.1

02.9

92.9

80.3

20.4

41.0

10.5

30.5

60.8

3

Result

sdetailed

per

announcem

ents

P(j

um

p|n

ew

s)

(%)

PPI

0.0

08.5

110.4

89.6

37.5

19.9

513.9

81.4

31.9

04.2

92.7

52.8

23.7

6

CPI

0.0

010.6

46.1

93.6

22.7

83.5

98.6

00.0

00.4

80.0

00.4

50.0

00.9

3

NFPAY

RO

L,U

NEM

PLO

Y3.5

733.5

727.6

720.1

814.6

223.6

413.0

41.9

24.8

38.2

13.6

72.8

47.5

5

DU

RA

BLE

0.0

02.8

87.2

51.8

54.2

56.8

25.9

51.4

40.4

91.9

30.4

60.9

51.4

2

LEA

DIN

GI

1.1

81.4

32.4

31.9

01.4

01.8

33.8

30.4

80.4

90.4

80.4

70.0

00.4

7

HO

USIN

G0.0

01.4

22.4

03.6

51.4

03.1

57.5

70.4

80.0

01.9

20.9

11.4

11.4

0

TR

AD

EBA

L,U

SI,

USX

0.0

00.7

020.2

814.2

916.8

219.8

216.2

22.3

62.3

76.6

04.1

55.1

64.2

1

P(n

ew

s|j

um

p)

(%)

PPI

0.0

07.2

33.2

33.4

92.9

03.1

72.2

21.2

41.5

92.8

82.5

12.0

42.8

0

CPI

0.0

09.0

41.9

11.3

31.0

91.1

51.3

70.0

00.4

00.0

00.4

20.0

00.7

0

NFPAY

RO

L,U

NEM

PLO

Y11.5

428.3

18.3

67.3

25.6

37.4

82.0

51.6

53.9

85.4

53.3

52.0

45.5

9

DU

RA

BLE

0.0

02.4

12.2

00.6

71.6

32.1

60.9

41.2

40.4

01.2

80.4

20.6

81.0

5

LEA

DIN

GI

3.8

51.2

00.7

30.6

70.5

40.5

80.6

00.4

10.4

00.3

20.4

20.0

00.3

5

HO

USIN

G0.0

01.2

00.7

31.3

30.5

41.0

11.2

00.4

10.0

01.2

80.8

41.0

21.0

5

TR

AD

EBA

L,U

SI,

USX

0.0

00.6

06.3

05.1

66.5

36.3

32.5

62.0

71.9

94.4

93.7

73.7

43.1

5

Note

:T

he

table

giv

es

the

overa

llm

atc

hin

gbetw

een

new

sand

jum

ps

com

pute

dat

a15-m

inute

frequency

wit

ha

signific

ance

level

α=

0.0

001

(upper

panel)

and

deta

iled

resu

lts

per

announcem

ent

(lower

panel)

.T

he

table

show

s,fr

om

top

tobott

om

,th

enum

ber

of

sam

ple

days

(#days)

,th

enum

ber

of

obse

rvati

ons

(#obs.

),th

enum

ber

of

jum

ps

and

the

num

ber

of

announcem

ent

days

(#ju

mps

and

#new

sdays)

,th

enum

ber

of

jum

ps

occurr

ing

wit

hin

one

hour

aft

er

new

sarr

ival(#

Jum

p-n

ew

sm

atc

h),

the

uncondit

ionalpro

bability

(in

%)

of

anew

s

(P(n

ew

s)

=100(#

new

sdays

/#

obs.

)),th

epro

bability

(in

%)

ofa

jum

pgiv

en

anew

s(P

(ju

mp|n

ew

s)

=100(#

Jum

p-n

ew

sm

atc

h/

#new

sdays)

),th

epro

bability

(in

%)

ofa

new

sgiv

en

a

jum

p(P

(ne

ws|j

um

p)

=100(#

Jum

p-n

ew

sm

atc

h/

#ju

mps)

),th

epro

bability

(in

%)

ofa

new

sand

aju

mp

(P(j

um

p,

ne

ws)

=100(#

Jum

p-n

ew

sm

atc

h/

#days)

).T

he

lower

paneldeta

ils

resu

lts

for

each

new

sand

dis

pla

ys

P(j

um

p|n

ew

s)

and

P(n

ew

s|j

um

p).

Note

that

labor

mark

et

new

s(N

FPAY

RO

Land

UN

EM

PLO

Y)

and

trade

rela

ted

new

s(T

RA

DEBA

L,U

SI,

USX

)are

pre

sente

dre

specti

vely

on

asi

ngle

line

because

they

are

part

ofa

single

report

.

35

Tab

le7:

Tob

itm

odel

sfo

rju

mps

and

prob

itm

odel

sfo

rco

jum

ps

Tobit

models

for

jum

ps

USD

/EU

RJPY

/U

SD

USD

/G

BP

CH

F/U

SD

XA

UU

SD

J

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

VPPI

0.5

82.2

10.7

32.3

50.5

62.4

50.6

02.3

00.9

12.2

90.5

01.8

4-

-

VC

PI

0.4

71.0

50.8

21.7

90.3

30.6

80.6

21.5

10.7

21.4

01.3

54.0

0-

-

VN

FPAY

RO

L1.9

96.7

11.6

05.3

31.5

66.1

32.0

07.0

41.0

13.2

01.7

26.5

96.6

54.5

4

VD

UR

ABLE

1.0

34.7

40.5

61.7

20.4

41.3

90.7

72.4

8-0

.18

-0.6

8-0

.92

-0.9

5-

-

VLEA

DIN

GI

--

--

-4.4

8-1

.85

0.1

10.1

5-0

.70

-0.9

0-0

.71

-0.7

5-

-

VH

OU

SIN

G-0

.68

-0.9

1-

--

--

--2

.92

-2.0

9-1

.22

-1.1

9-

-

VT

RA

DEBA

L2.1

98.0

32.5

48.2

62.1

07.6

02.2

38.2

81.3

33.6

0-8

.86

-2.0

7-

-

Const

-12.2

0-1

2.8

5-5

.42

-2.4

6-7

.07

-15.3

3-7

.43

-9.8

1-1

9.0

7-7

.20

-777.7

9-2

05.0

2-1

6.1

7-1

.56

sigm

a2.0

630.7

72.2

413.5

41.9

030.6

62.1

230.9

32.4

219.6

12.0

514.2

66.8

19.6

1

VLLF

-2669.9

0-2

532.4

8-2

216.5

9-2

611.3

8-4

335.9

2-6

34.2

4-1

70.4

3

obs

210192

214560

217824

223344

186864

40810

28048

R2 M

Z0.1

20.0

60.1

30.1

10.1

70.9

90.0

8

Probit

models

for

coju

mps

USD

/EU

R-

USD

/G

BP

USD

/EU

R-

JPY

/U

SD

USD

/EU

R-

CH

F/U

SD

USD

/G

BP

-JPY

/U

SD

USD

/G

BP

-C

HF/U

SD

JPY

/U

SD

-C

HF/U

SD

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

Est

.t-

stat.

VPPI

0.2

41.8

70.2

61.9

10.2

51.9

70.2

51.8

50.2

51.6

00.2

71.9

9

VC

PI

-0.8

0-1

.62

--

0.1

40.4

60.2

80.9

70.2

30.8

30.3

21.1

3

VN

FPAY

RO

L0.8

65.7

80.7

74.9

91.0

06.2

40.6

74.9

50.8

52.5

20.7

95.4

7

VD

UR

ABLE

0.2

91.8

10.3

32.1

70.0

90.4

20.2

21.1

00.1

40.6

20.2

61.3

7

VT

RA

DEBA

L1.2

08.0

71.2

68.6

01.1

48.1

01.2

78.6

01.1

33.7

61.2

58.6

0

Const

13.3

11.2

2-7

.90

-5.6

9-3

5.8

8-1

2.3

0-4

6.3

8-2

.98

52.0

71.1

6-1

7.6

3-3

.69

VLLF

-933.9

8-5

89.5

4-1

545.8

4-4

62.1

6-7

93.0

4-5

21.3

6

obs

208992

209568

210192

213216

217776

214560

McFadden

R2

0.2

00.2

10.1

40.2

70.2

20.2

2

Note

:The

upper

panelre

ports

Tobit

est

imate

s:|J∗ t+

j∆|=

µ+

αt+

j∆

+µ

t+

j∆

+ξ

t+

j∆

+ε

t+

j∆

,w

here|J

t+

j∆|=|J∗ t+

j∆|i

f|J∗ t+

j∆|

>0

and|J

t+

j∆|=

0if|J∗ t+

j∆|≤

0,

εt+

j∆|x

t+

j∆

isN

(0,

σ2 0),

and

the

sequence{J

t+

j∆

,x

t+

j∆}

isiid.|J

t+

j∆|re

pre

sents

signific

ant

jum

ps

as

defined

inth

eth

eore

ticalpart

.The

lower

panelre

ports

pro

bit

est

imate

s:

CO

J∗ t+

j∆

=µ

+α

t+

j∆

+µ

t+

j∆

+ξ

t+

j∆

+ε

t+

j∆

,

where

CO

Jt+

j∆

=1

ifC

OJ∗ t+

j∆

>0

and

CO

Jt+

j∆

=0

ifC

OJ∗ t+

j∆≤

0.

εt+

j∆

isN

ID

(0,1).

CO

Jt+

j∆

isth

ecoju

mp

indic

ato

r(s

ee

Equati

on

11).

Inbo

thTobit

and

pro

bit

models,

αt+

j∆

contr

ols

for

day

ofth

eweek

effects

(not

report

ed)

and

µt+

j∆

inclu

des

surp

rise

sconcern

ing

macro

announcem

ents

.For

each

seri

es,

we

regre

ssju

mps

inabso

lute

valu

e(c

oju

mp

indic

ato

rin

the

case

ofpro

bit

models

)on

surp

rise

sin

abso

lute

valu

e.

ξt+

j∆

contr

ols

for

intr

adaily

seaso

nality

(not

report

ed).

Est

imate

sand

robust

t-st

ati

stic

sare

report

ed

for

each

surp

rise

coeffic

ient,

the

const

ant

and

the

err

or

standard

devia

tion

sigm

afo

rTobit

models

.R

egre

ssors

wit

hno

conte

mpora

neous

matc

hw

ith

signific

ant

jum

ps

(coju

mp

indic

ato

rin

the

case

ofpro

bit

models

)are

exclu

ded

from

the

model.

We

furt

her

report

the

maxim

ized

log-lik

elihood

functi

on

valu

e(V

LLF),

the

num

ber

ofobse

rvati

ons

(Obs)

,as

well

as

agoodness

offit

measu

re,th

eM

cK

elv

ey-Z

avoin

aR

2(R

2 MZ

)fo

rTobit

models

,th

at

pro

vid

es

an

est

imate

ofth

efitt

ed

late

nt

vari

able

vari

ance

over

the

tota

lvari

ance,i.e.

Va

r(J∗ )

Va

r(J∗ )

+σ2

.For

pro

bit

models

,th

egoodness

offit

measu

reis

the

McFadden

R2.

36

Figure 1: Time series of significant jumps

-6

-4

-2

0

2

4

6

8

10

1998 1999 2000 2001 2002 2003 2004 2005 2006

Jum

ps

Intra-day periods

ND

-3

-2

-1

0

1

2

3

4

1998 1999 2000 2001 2002 2003 2004 2005 2006Ju

mps

Intra-day periods

DJ

-10

-5

0

5

10

15

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Jum

ps

Intra-day periods

SP

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Jum

ps

Intra-day periods

US

-3

-2

-1

0

1

2

3

4

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Jum

ps

Intra-day periods

USD/EUR

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Jum

ps

Intra-day periods

USD/GBP

-4

-3

-2

-1

0

1

2

3

4

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Jum

ps

Intra-day periods

JPY/USD

-1.5

-1

-0.5

0

0.5

1

1.5

2

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

Jum

ps

Intra-day periods

CHF/USD

-8

-6

-4

-2

0

2

4

6

8

1986 1988 1990 1992 1994 1996 1998 2000 2002

Jum

ps

Intra-day periods

XAU

Note: jumps estimated with Lee-Mykland statistic (Jt+j∆, as defined in Section 2). The chosen

significance level is α = 0.0001. The sampling frequency is 15 minute. The X-axis displays

intradaily periods over the whole sample, while the Y-axis displays returns (%) identified as

jumps, Jt+j∆.

37

Figure 2: Histograms of significant jump occurrences

0

0.5

1

1.5

2

09 10 11 12 13 14 15 16 17

Count of ju

mps

Intra-Day Periods over one day (EST)

ND

0

1

2

3

4

5

6

08 09 10 11 12 13 14 15 16 17C

ount of ju

mps


DJ

0

2

4

6

8

10

12

09 10 11 12 13 14 15 16 17

Count of ju

mps


SP

0

10

20

30

40

50

60

70

80

90

100

08 09 10 11 12 13 14 15

Count of ju

mps


US

0

20

40

60

80

100

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Count of ju

mps

Intra-Day Periods over one day (GMT)

USD/EUR

0

10

20

30

40

50

60

70

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Count of ju

mps


USD/GBP

0

10

20

30

40

50

60

70

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Count of ju

mps


JPY/USD

0

10

20

30

40

50

60

70

80

90

100

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Count of ju

mps


CHF/USD

0

10

20

30

40

50

60

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Count of ju

mps


XAU

Note: count of Lee-Mykland jumps per intradaily period, α = 0.0001, 15-min. frequency.

38

Figure 3: Scatter plot: mean jumps against jump frequency

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

0.1

0.2

0.3

Fre

quen

cy

All jumps in absolute value

XAU

U.S. Bonds Dow SP500 Nasdaq

Dollar Exchange rates

Non−dollar exchange rates

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25

0.05

0.1

0.15

Fre

quen

cy XAU

NasdaqSP500DowU.S. Bonds


Non−dollar exchange ratesPositive jumps

−2.6 −2.4 −2.2 −2.0 −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4

0.05

0.1

0.15

Jump mean

Fre

quen

cy

XAU

Nasdaq SP500 Dow U.S. Bonds


Non−dollar exchange rates

Negative jumps

39

Figure 4: Time series of cojump indicator

1990 1995 2000 2005

0.5

1 EUR − GBP

coju

mps

1990 1995 2000 2005

0.5

1 EUR − JPY

coju

mps

1990 1995 2000 2005

0.5

1 EUR − CHF

coju

mps

1990 1995 2000 2005

0.5

1 GBP − JPY

coju

mps

1990 1995 2000 2005

0.5

1 GBP − CHF

coju

mps

1990 1995 2000 2005

0.5

1 JPY − CHF

coju

mps

1990 1995 2000 2005

0.5

1 EUR − GBP − JPY

coju

mps

1990 1995 2000 2005

0.5

1 GBP − JPY − CHF

coju

mps

1990 1995 2000 2005

0.5

1 EUR − GBP − CHF

coju

mps

1990 1995 2000 2005

0.5

1 EUR − JPY − CHF

coju

mps

1990 1995 2000 2005

0.5

1 EUR − GBP − JPY − CHF

Intra−day periods

coju

mps

Note: the graphs display the time series of cojump indicator for different exchange rates

combinations. The X-axis displays intra-day periods for the sample length.

40

Figure 5: Histogram of cojump occurrences

0

10

20

30

40

50

60

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - USD/GBP

coj hist

0 5

10 15 20 25 30 35 40 45 50

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - JPY/USD

0

10

20

30

40

50

60

70

80

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - CHF/USD

0

5

10

15

20

25

30

35

40

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/GBP - JPY/USD

0

10

20

30

40

50

60

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/GBP - CHF/USD

0 5

10 15 20 25 30 35 40 45 50

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

JPY/USD - CHF/USD

0

5

10

15

20

25

30

35

40

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - USD/GBP - JPY/USD

0

5

10

15

20

25

30

35

40

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/GBP - JPY/USD - CHF/USD

0

10

20

30

40

50

60

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - USD/GBP - CHF/USD

0

5

10

15

20

25

30

35

40

45

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - JPY/USD - CHF/USD

0

5

10

15

20

25

30

35

40

20 22 00 02 04 06 08 10 12 14 16 18 20 22

coun

t of c

ojum

ps

Intra-day periods

USD/EUR - USD/GBP - JPY/USD - CHF/USD

Note: the graphs display histograms of cojump occurrences for different exchange rates

combinations. The X-axis displays intra-day periods over 24 hours in GMT time.

41

Figure 6: Histogram of jump occurrences on days without announcements

0

0.5

1

1.5

2

2.5

3

08 09 10 11 12 13 14 15 16 17

Cou

nt o

f jum

ps


DJ

0

2

4

6

8

10

12

14

16

18

20

08 09 10 11 12 13 14 15

Cou

nt o

f jum

ps


US

0

5

10

15

20

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


USD/EUR

0

2

4

6

8

10

12

14

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


USD/GBP

0

2

4

6

8

10

12

14

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/USD

0

5

10

15

20

25

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/USD

0

5

10

15

20

25

30

35

40

45

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


XAU

0

1

2

3

4

5

6

7

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/EUR

0

2

4

6

8

10

12

14

16

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


GBP/EUR

0

1

2

3

4

5

6

7

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/EUR

0

2

4

6

8

10

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/GBP

0

1

2

3

4

5

6

7

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/GBP

0

1

2

3

4

5

6

7

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/JPY

42

Figure 7: Histogram of jump occurrences on announcement days

0

0.5

1

1.5

2

2.5

3

3.5

4

08 09 10 11 12 13 14 15 16 17

Cou

nt o

f jum

ps


DJ

0

10

20

30

40

50

60

70

80

08 09 10 11 12 13 14 15

Cou

nt o

f jum

ps


US

0

10

20

30

40

50

60

70

80

90

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


USD/EUR

0

10

20

30

40

50

60

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


USD/GBP

0

5

10

15

20

25

30

35

40

45

50

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/USD

0

10

20

30

40

50

60

70

80

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/USD

0

5

10

15

20

25

30

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


XAU

0

1

2

3

4

5

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/EUR

0

2

4

6

8

10

12

14

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


GBP/EUR

0

5

10

15

20

25

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/EUR

0

2

4

6

8

10

12

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/GBP

0

1

2

3

4

5

6

7

8

9

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


JPY/GBP

0

2

4

6

8

10

12

14

16

18

20 22 00 02 04 06 08 10 12 14 16 18 20 22

Cou

nt o

f jum

ps


CHF/JPY

43

jumps, cojumps and macro announcements - duke university

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