market microstructure and algorithmic tradingcfrei/pims/almgren4.pdfpims summer school 2016...
TRANSCRIPT
Robert Almgren
Market Microstructureand
Algorithmic Trading
PIMS Summer School 2016University of Alberta, Edmonton
Lecture 4: July 6, 2016
Edmonton mini-course, July 2016
Trade trajectory determination
Overall schedule of tradeActual order placement by "micro" algo
Schedule to receive "best" pricerelative to benchmarkminimize variance
Real implementation different than theorybut theory is useful for ideas
2
Edmonton mini-course, July 2016
Real examples
3
Buy 2932 FGBMU6
Produced by Quantitative Brokers from internal and Eurex Market Data
Edmonton mini-course, July 2016 4
2.801
2.802
2.803
2.804
2.805
2.806
2.807
2.808
2.809
2.810
09:03:10 09:03:20 09:03:30 09:03:40 09:03:50 09:04:00 09:04:10 09:04:20 09:04:30
CDT on Tue 05 Jul 2016
BUY 17 NGQ6 BOLT
09:03:19
Done at 09:04:23
Exec 2.806VWAP 2.806
Strike 2.8065
NG
Q6
Passive fillsCumulative execMarket tradesLimit ordersCumulative VWAPMicropriceBid-ask
Exec = 2.806 Cost to strike = -0.38 tick = -$3.82 per lot
09:03:10 09:03:20 09:03:30 09:03:40 09:03:50 09:04:00 09:04:10 09:04:20 09:04:30
0
5
10
15
Exe
cute
d an
d w
orki
ng q
uant
ity
100
200
300
400
500
581
Cum
ulat
ive
mar
ket v
olum
e
09:03:19
Done at 09:04:23
2 @ 2.808
1 @ 2.808
1 @ 2.808
1 @ 2.808
2 @ 2.807
1 @ 2.807
2 @ 2.806
4 @ 2.805
2 @ 2.804
1 @ 2.803
2.9% mkt / Limit = 8%
17 passv 0 aggrPassive fillsWorking quantityCumulative Market VolumeFilled quantityAggressive quantity
2.801
2.802
2.803
2.804
2.805
2.806
2.807
2.808
2.809
2.810
09:03:10 09:03:20 09:03:30 09:03:40 09:03:50 09:04:00 09:04:10 09:04:20 09:04:30
CDT on Tue 05 Jul 2016
BUY 17 NGQ6 BOLT
09:03:19
Done at 09:04:23
Exec 2.806VWAP 2.806
Strike 2.8065
NG
Q6
Passive fillsCumulative execMarket tradesLimit ordersCumulative VWAPMicropriceBid-ask
Exec = 2.806 Cost to strike = -0.38 tick = -$3.82 per lot
09:03:10 09:03:20 09:03:30 09:03:40 09:03:50 09:04:00 09:04:10 09:04:20 09:04:30
0
5
10
15
Exe
cute
d an
d w
orki
ng q
uant
ity
100
200
300
400
500
581
Cum
ulat
ive
mar
ket v
olum
e
09:03:19
Done at 09:04:23
2 @ 2.808
1 @ 2.808
1 @ 2.808
1 @ 2.808
2 @ 2.807
1 @ 2.807
2 @ 2.806
4 @ 2.805
2 @ 2.804
1 @ 2.803
2.9% mkt / Limit = 8%
17 passv 0 aggrPassive fillsWorking quantityCumulative Market VolumeFilled quantityAggressive quantity Slow because
no passive fills
Sudden fillsat end
Produced by Quantitative Brokers from internal and CME Market Data
Edmonton mini-course, July 2016
Outline
1. Benchmarks
2. Market impact models
3. Mean-variance trajectory optimization
4. Option hedging
5
Edmonton mini-course, July 2016
1. Benchmark
“Contract” with clientWhat would constitute an ideal tradeChoice of benchmark determines algoMain benchmarks:
Arrival PriceVWAPTWAP
6
Edmonton mini-course, July 2016 7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The Implementation Shortfall: Paper Versus RealityPerold, Andre F.Journal of Portfolio Management; Spring 1988; 14, 3; ABI/INFORM Globalpg. 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The Implementation Shortfall: Paper Versus RealityPerold, Andre F.Journal of Portfolio Management; Spring 1988; 14, 3; ABI/INFORM Globalpg. 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The Implementation Shortfall: Paper Versus RealityPerold, Andre F.Journal of Portfolio Management; Spring 1988; 14, 3; ABI/INFORM Globalpg. 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IS ≡ "Arrival Price"
Edmonton mini-course, July 2016
Arrival price positives:corresponds to real trade decisioncannot be gamed by executing broker
Arrival price negatives:subject to price motion
impossible to separate alpha from impactstatistically very noisy
8
123−00
123−00+
123−01
123−01+
123−02
123−02+
123−03
08:19:20 08:21:20 08:23:20
CDT time on Wed 06 Jul 2011
2000 lots08:20:34
Strike 123−01¾
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Arrival Price
Minimize slippage to arrival price benchmarkby completing trade as rapidly as possible
Produced by Quantitative Brokers from internal and CME Market Data
Edmonton mini-course, July 2016 9
14:00 14:01 14:02 14:03 14:04 14:05 14:06 14:07 14:08 14:09 14:10 14:11
0
20
40
60
80
2k
4k
6k
8k
9k
SELL 80 ZBU1 BOLT
CDT time on Thu 30 Jun 2011
Exec
uted
and
wor
king
qua
ntity
14:01:10
14:10:001 @ 123−00 1 @ 123−00
4 @ 123−00
4 @ 123−00 2 @ 123−01
4 @ 123−01 2 @ 123−01
1 @ 123−01
3 @ 123−01
3 @ 123−01
4 @ 123−01
2 @ 123−01 2 @ 123−01
20 @ 123−02
8 @ 123−03 2 @ 123−03
1 @ 123−03
4 @ 123−03 2 @ 123−03 2 @ 123−03 1 @ 123−03
0.87% mkt
56 passv 24 aggr
Aggressive FillsPassive FillsFilled quantityWorking quantity
Market volume
Working quantity
Filled quantity
Front-loaded (approximately)
Produced by Quantitative Brokers from internal and CME Market Data
Arrival Price Example
Edmonton mini-course, July 2016
VWAP benchmark
Volume-Weighted Average Pricebetween given start time and end time“what the market did”
Positives:easy to evaluate ex post: select siz wavg prc slippage is very consistent
Negatives:Does not correspond to any investment goalCan be gamed by brokerDifficult to forecast volume profile during trading
10
Minimize slippage to VWAP benchmarkby trading exactly along market profile
Edmonton mini-course, July 2016 11
12:00 12:20 12:40 13:00 13:20 13:40 14:00 14:20 14:40 15:00 15:20
0
500
1000
1500
20k
40k
60k
80k
100k
120k
140k
148k
BUY 1830 ZNU1 STROBE
CDT time on Wed 06 Jul 2011
Exec
uted
and
wor
king
qua
ntity
12:19:07
15:00:00
1 @ 122−28+6 @ 122−30+
11 @ 122−30+
30 @ 123−01 14 @ 123−00+
29 @ 123−00+11 @ 123−00+
5 @ 123−00 6 @ 122−31+
14 @ 122−31+22 @ 123−00+
4 @ 123−00+17 @ 123−00
3 @ 123−00 14 @ 123−00
11 @ 123−00+4 @ 123−00+13 @ 123−01+
17 @ 123−00+1 @ 123−01+
3 @ 123−01 6 @ 123−01
26 @ 123−02 4 @ 123−02
31 @ 123−02 31 @ 123−02
2 @ 123−01+13 @ 123−00+
8 @ 122−31 4 @ 123−00
32 @ 122−31+13 @ 122−30+
1 @ 123−00 20 @ 123−01
8 @ 122−31+8 @ 122−31+
10 @ 123−00+2 @ 123−00
6 @ 122−31+11 @ 122−30+
13 @ 122−31 5 @ 122−31
5 @ 122−30+1 @ 122−30+
1.2% mkt
1611 passv 219 aggr
Aggressive FillsPassive FillsAhead/behind boundariesBase profileFilled quantityWorking quantity
Market volume
Cumulative actual market volume
Executions trackforecast market volume
burst at 14:00
Produced by Quantitative Brokers from internal and CME Market Data
VWAP Example (1)
Edmonton mini-course, July 2016
VWAP Example (2)
12
Blue Line: where we predictedVWAP trajectory, relative to actual
Triangles: where we executed, close to predicted curve
but far from actual
Market printing more than forecast:we fall behind VWAP
Market printing less than forecast:we get ahead of VWAP
122−26
122−27
122−28
122−29
122−30
122−31
123−00
123−01
123−02
123−03
12:00 12:20 12:40 13:00 13:20 13:40 14:00 14:20 14:40 15:00 15:20
CDT time on Wed 06 Jul 2011
BUY 1830 ZNU1 STROBE
12:19:07
15:00:00
Exec 123−00.12VWAP 123−00.05
Strike 122−28¾
Aggressive FillsPassive FillsCumulative execLimit ordersMarket priceCumulative VWAP
Exec = 123−00.12 Cost to VWAP = 0.14 tick = $2.24 per lot
12:00 12:20 12:40 13:00 13:20 13:40 14:00 14:20 14:40 15:00 15:20
−200
−150
−100
−50
0
50
100
−10%
−5%
5%
−0.8
−0.6
−0.4
−0.2
0.2
0.4
Ahea
dBe
hind
Lead
/lag
rela
tive
to re
alis
ed V
WAP
Slip
page
to V
WAP
(tic
ks)
12:19:07
15:00:00
1.2% mkt1611 passv 219 aggr
Take
Post
Aggressive FillsPassive FillsAhead/behind boundariesFilled quantityWorking quantity
Slippage
Produced by Quantitative Brokers from internal and CME Market Data
Edmonton mini-course, July 2016
TWAP benchmark
Time-Weighted Average Priceignoring trade volume
Positives (relative to VWAP):easy to achieveeasy to measure where volume info is unreliable
Negatives (relative to VWAP):not related to market activity
13
Minimize slippage to TWAP benchmarkby trading exactly along straight-line profile
Edmonton mini-course, July 2016
TWAP Example (1)
14
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
0
200
400
600
800
1000
1200
20k
40k
60k
80k
100k
120k
140k
150k
SELL 1233 ZTU1 STROBE
CDT time on Wed 06 Jul 2011
Exec
uted
and
wor
king
qua
ntity
07:00:00
15:00:00
1 @ 109−24¾1 @ 109−25 1 @ 109−25
1 @ 109−24¾4 @ 109−24¾
6 @ 109−24¾1 @ 109−24¼17 @ 109−24+
1 @ 109−24¼3 @ 109−24+
1 @ 109−24 1 @ 109−24¼
1 @ 109−24+1 @ 109−24¾
2 @ 109−25 6 @ 109−24¾
1 @ 109−24+6 @ 109−24+
2 @ 109−24+3 @ 109−24¾
1 @ 109−24¾1 @ 109−24+8 @ 109−24¼
1 @ 109−24¼1 @ 109−24¼
6 @ 109−24¼3 @ 109−24¼
1 @ 109−24 17 @ 109−24¼
2 @ 109−24+13 @ 109−24¼
1 @ 109−24+22 @ 109−24+
2 @ 109−24+10 @ 109−24+
17 @ 109−24+1 @ 109−24+
1 @ 109−24¾1 @ 109−24¾
1 @ 109−24¾1 @ 109−24¼
5 @ 109−24¼1 @ 109−24+
8 @ 109−24+1 @ 109−24+
1 @ 109−24¼1 @ 109−24¼
0.82% mkt
849 passv 384 aggr
Aggressive FillsPassive FillsAhead/behind boundariesBase profileFilled quantityWorking quantity
Market volume
Executed quantitytracks straight line
Ignore actual market volume
Produced by Quantitative Brokers from internal and CME Market Data
Edmonton mini-course, July 2016
TWAP example (2)
15
Cumulative fill quantity consistently within ±1% of true TWAP
109−24
109−24¼
109−24+
109−24¾
109−25
109−25¼
109−25+
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
CDT time on Wed 06 Jul 2011
16:01
SELL 1233 TUU1 STROBE
07:00:00
15:00:00
Exec 109−24.49TWAP 109−24.51
Strike 109−24.62
Aggressive FillsPassive FillsCumulative execLimit ordersMarket priceCumulative TWAP
Exec = 109−24.49 Cost to TWAP = 0.07 tick = $1.08 per lot
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
−30
−20
−10
0
10
20
−2%
−1%
1%
2%
−0.6
−0.4
−0.2
0.2
0.4
Ahea
dBe
hind
Lead
/lag
rela
tive
to T
WAP
Slip
page
to T
WAP
(tic
ks)
07:00:00
15:00:00
16:01
0.82% mkt849 passv 384 aggr
Take
Post
Aggressive FillsPassive FillsAhead/behind boundariesFilled quantityWorking quantity
Slippage
Price slippage within0.1 bid-ask spread
Produced by Quantitative Brokers from internal and CME Market Data
Edmonton mini-course, July 2016
Other benchmarks
Daily close price, or settlementwithout impacting it too much
Option hedgingachieve delta-neutral position, depending on price(work with Tianhui Li, Princeton)
Etc.
16
Benchmark must be agreed in advanceExecution is tailored to benchmarkResults must be evaluated against same benchmark
Edmonton mini-course, July 2016
Execution is uncertain
Market price moves during executionLimit orders may or may not get filledLiquidity appears and disappearsVolume profiles are unpredictable
Result of execution is a “random variable”Execution strategy tailors its properties
e.g. mean and variance
17
Perold's "cost of not trading"
Edmonton mini-course, July 2016
Fundamental Balance of Execution
18
Cost Risk(mean of executed price relative to benchmark)
(variance of executed price relative to benchmark)
Alpha (forecastable price change)Passive fill probabilityMarket impact
Price volatility (most important)
vs
Edmonton mini-course, July 2016
Example #1: Arrival Price
Minimize risk: execute as quickly as possibleButToo fast = lower chance of passive fills when to cross spread to reduce risk?Too fast = market impact pushes price how much is it worth it to push price?Alpha signal says price will get worse how much should you accelerate? increase impactAlpha signal says price will improve how much slower should you trade? increase risk
19
Edmonton mini-course, July 2016
Example #2: TWAP
Ideal profile: evenly spaced in time
Should you cross spread whenever neededor wait for passive fills even if behind?
Alpha signal: how much should you deviate from schedule to exploit signal? (Signal may be very uncertain)
20
Edmonton mini-course, July 2016
Example #3: VWAP
Track volume forecast, fixed or dynamic
Should you worry less about deviating from schedule, since schedule itself is uncertain?
21
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2. Price dynamics and market impact
1. Mathematical model for trading and impact
2. Definition of objective function
3. Mathematical optimization
22
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Trading trajectory
X = target number of shares to buyT = time limitx(t) = shares remaining at time t x(0) = X, x(T) = 0v(t) = -dx/dt = rate of buyingx(t), v(t) can depend on all information to time t or be fixed in advance (adaptive / non-adaptive)Detailed orders are placed by micro-algorithm
23
t
x(t)
X
00 T
Edmonton mini-course, July 2016
Market model (Almgren/Chriss ‘00)
= stock price
= volatility
24
�(t)
S(t)dS(t) = �(t)dB(t) + g
�v(t)
�dt
g(v) = permanent market impact
Arbitrage exists unless g(v) is linearg(v) = �v
Integrates out so neglect permanent impact
Edmonton mini-course, July 2016
S(t) = S(t) + h�v(t)
�
Temporary market impact
25
Market parameters σ(t) and η(t)- constant, predictable, or random processes- observable in real time
S(t) = realized trade price
Linear case: h(v) = �(t)v
Edmonton mini-course, July 2016
Temporary market impact
26
Time t
Price S(t)
Realised price S(t)
Market price S(t)Pre-tradeprice S(0)
0 T
Other effects:- permanent impact- nonlinear impact- time decay- short-term drift- etc
Edmonton mini-course, July 2016
Cost of trading
27
=� T
0S(t)v(t)dt
= X S0 +� T
0⇥(s)x(s)dB(s) +
� T
0�(t)v(t)2 dt
“Capture”= Dollars
realized onselling X shares
C =� T
0⇥(s)x(s)dB(s) +
� T
0�(t)v(t)2 dt
Random because of price changeand trade trajectory decisions
Cost = capture - initial value X S0
Edmonton mini-course, July 2016
3. Mean variance optimization
Minimize both E = expectation of C V = variance of C
28
minx(s):t�s�T
E(C) + � Var(C)At each time t
E
V
VWAP
Fast
Variance of cost
Expectedcost
Efficient frontier
Risk parameter λ set by client
Edmonton mini-course, July 2016
Solution
29
C = ⇥� T
0x(t)dB(t) + �
� T
0v(t)2 dt
V = ⇥ 2� T
0x(t)2 dt, E = �
� T
0v(t)2 dt
(for a precomputed fixed trajectory, which is optimal solution)
Calculus of variations with quadratic objective: Exponential solution
x(s) = x(t) sinh��(T � s)
⇥
sinh��(T � t)
⇥
v(s) = � x(t) cosh��(T � s)
⇥
sinh��(T � t)
⇥⇥2 = ⇤⌅ 2
�
Time scale
Edmonton mini-course, July 2016
Arrival price solution
30
Time
Shares remaining to execute
x(t)
Orderentry time
Imposedend time
High urgency(immediate)
E large, V small
Low urgency (TWAP)
E small, V large
E
V
VWAP
Fast
Variance of cost
Expectedcost
Efficient frontier
⇥2 = ⇤⌅ 2
�
Time constant
Solution trajectorydoes not change as
price motions are observedduring execution
Edmonton mini-course, July 2016
Extensions
Portfolios (Almgren/Chriss 2000)
Nonlinear market impact (Almgren 2003)
Adaptive trajectories (Lorenz/Almgren 2011)
Stochastic liquidity and volatility (Almgren 2012)
Bayesian update price drift (Almgren/Lorenz 2006)
Option hedging (Almgren/Li 2016)
Many others ...
31
Edmonton mini-course, July 2016
Critique of arrival price solutions
Well calibrated market impact modelKnown & constant risk aversion parameter λReasons to trade slowly: reduce market impact
slow steady trading leaks informationprice drift can lead to trade fasteropportunistic trading
Reasons to trade fast: reduce volatility riskevent riskreduce number of open orders
Market impact is more complicated than thispersistence in time (integral kernels)bursty trading can be cheaper than steady
32
Edmonton mini-course, July 2016
4. Option hedging
33
Black-Scholes with market impactEffect on public markets
Option Hedging with Smooth Market Impact
Robert Almgren*
Quantitative Brokers, New York, NY, [email protected]
Tianhui Michael Li
The Data Incubator, New York, NY, USA
Accepted 15 April 2016Published
We consider intraday hedging of an option position, for a large trader who experi-ences temporary and permanent market impact. We formulate the general modelincluding overnight risk, and solve explicitly in two cases which we believe are rep-resentative. The ¯rst case is an option with approximately constant gamma: theoptimal hedge trades smoothly towards the classical Black–Scholes delta, withtrading intensity proportional to instantaneous mishedge and inversely proportionalto illiquidity. The second case is an arbitrary non-linear option structure but with nopermanent impact: the optimal hedge trades toward a value o®set from the Black–Scholes delta. We estimate the e®ects produced on the public markets if a largecollection of traders all hedge similar positions. We construct a stable hedge strategywith discrete time steps.
Keywords: Option hedging; market impact; optimal trading.
1. Introduction
Dynamic hedging of an option position is one of the most studied problems inquantitative ¯nance. But when the position size is large, the optimal hedgestrategy must take account of the transaction costs that will be incurred byfollowing the Black–Scholes solution. This large position may be the positionof a single large trader, or may be the aggregate position of a collection oftraders, for example the entire sell-side community, who all hold similarpositions, and all of whom hedge while their counterparties do not. In
*Corresponding author.
June 13, 2016 5:43:10pm WSPC/298-MML 1650002 ISSN: 2382-62662nd Reading
Market Microstructure and LiquidityVol. 2, No. 1 (2016) 1650002 (26 pages)°c World Scienti¯c Publishing CompanyDOI: 10.1142/S2382626616500027
1650002-1
Edmonton mini-course, July 2016
Equity price swings on July 19 2012 (one day prior to options expiration)
34
...
http://www.bloomberg.com/news/2012-07-20/hourly-price-swings-whipsaw-investors-in-ibm-coke-mcdonald-s.html
Marko Kolanovic, global head of derivatives and quantitative strategy at JPMorgan & Chase Co
Edmonton mini-course, July 2016 35
CA CHEUVREUX QUANTITATIVE RESEARCH
QUANT NOTE
28th of August, 2012
www.cheuvreux.com
What does the saw-tooth pattern on US markets on 19 July 2012 tell us about the price formation process The saw-tooth patterns observed on four US securities on 19 July provide us with an opportunity to comment on common beliefs regarding the market impact of large trades; its usual smoothness and amplitude, the subsequent “reversal” phase, and the generic nature of market impact models. This underscores the importance of taking into account the motivation behind a large trade in order to optimise it properly, as we already emphasised in Navigating Liquidity 6. We used different intraday analytics to work out what happened: pattern-matching techniques, market impact models, order flow imbalances and PnL computations of potential stat. arb intraday strategies. After looking at open interests of derivatives on these stocks, we conclude that repetitive automated hedging of large-exposure derivatives lay behind this behaviour. This is an opportunity to understand how a very crude trading algorithm can impact the price formation process ten times more than is usually the case.
FIGURE 1: SAWTOOTH PATTERNS ON COCA-COLA, MCDONALD'S, IBM AND APPLE ON 19 JULY 2012
92
92.5
93
93.5
09:3110:35
11:4012:45
13:5014:55
16:00
McDonald's
194
194.5
195
195.5
196
196.5
197
09:3110:35
11:4012:45
13:5014:55
16:00
IBM
608
610
612
614
616
09:3110:35
11:4012:45
13:5014:55
16:00
Apple
76.4
76.6
76.8
77
77.2
77.4
77.6
77.8
09:3110:35
11:4012:45
13:5014:55
16:00
Coca Cola
The market impact is one of the main factors of the price formation process
Strange patterns were observed on four large cap US stocks (Coca-Cola, McDonald's, IBM and Apple) on 19 July 2012. A few days later the “Knight Algorithm Went Crazy” issue eclipsed this strange phenomenon, by raising the usual concerns about the current market microstructure, the integrity of the price formation process, etc.
We have been hearing such complaints for years now (during the public hearing in MiFID Review in September 2010, after the SEC issued a concept release seeking comment on the structure of equity markets in January 2010). What has changed? Not much: we continue to observe glitches on US markets, and the MiFID review in Europe has been under discussion for months, with no clear agenda about elements as crucial as the tick size.
We look at the events of 19 July to learn more about the price formation process. Our intention here is not to merely say that the way a (reputed) fair price is formed, thanks to matching of supply and demand, is simple. The roots of its mechanism are not very difficult to understand. Its complexity stems from the way they combine.
Charles-Albert LEHALLE Matthieu LASNIER Global Head of Quantitative Research [email protected] (33) 1 41 89 80 16
Market microstructure specialist, Quantitative Research, Paris
Paul BESSON Hamza HARTI Weibing HUANG Nicolas JOSEPH Lionel MASSOULARD Index and Portfolio Research Specialist, Quantitative Research, Paris
Trading specialist, Quantitative Research, Paris
PhD student, Quantitative Research, Paris
Performance analysis specialist, Quantitative Research, London
Trading specialist, Quantitative Research, New-York
CA CHEUVREUX QUANTITATIVE RESEARCH
QUANT NOTE
28th of August, 2012
www.cheuvreux.com
What does the saw-tooth pattern on US markets on 19 July 2012 tell us about the price formation process The saw-tooth patterns observed on four US securities on 19 July provide us with an opportunity to comment on common beliefs regarding the market impact of large trades; its usual smoothness and amplitude, the subsequent “reversal” phase, and the generic nature of market impact models. This underscores the importance of taking into account the motivation behind a large trade in order to optimise it properly, as we already emphasised in Navigating Liquidity 6. We used different intraday analytics to work out what happened: pattern-matching techniques, market impact models, order flow imbalances and PnL computations of potential stat. arb intraday strategies. After looking at open interests of derivatives on these stocks, we conclude that repetitive automated hedging of large-exposure derivatives lay behind this behaviour. This is an opportunity to understand how a very crude trading algorithm can impact the price formation process ten times more than is usually the case.
FIGURE 1: SAWTOOTH PATTERNS ON COCA-COLA, MCDONALD'S, IBM AND APPLE ON 19 JULY 2012
92
92.5
93
93.5
09:3110:35
11:4012:45
13:5014:55
16:00
McDonald's
194
194.5
195
195.5
196
196.5
197
09:3110:35
11:4012:45
13:5014:55
16:00
IBM
608
610
612
614
616
09:3110:35
11:4012:45
13:5014:55
16:00
Apple
76.4
76.6
76.8
77
77.2
77.4
77.6
77.8
09:3110:35
11:4012:45
13:5014:55
16:00
Coca Cola
The market impact is one of the main factors of the price formation process
Strange patterns were observed on four large cap US stocks (Coca-Cola, McDonald's, IBM and Apple) on 19 July 2012. A few days later the “Knight Algorithm Went Crazy” issue eclipsed this strange phenomenon, by raising the usual concerns about the current market microstructure, the integrity of the price formation process, etc.
We have been hearing such complaints for years now (during the public hearing in MiFID Review in September 2010, after the SEC issued a concept release seeking comment on the structure of equity markets in January 2010). What has changed? Not much: we continue to observe glitches on US markets, and the MiFID review in Europe has been under discussion for months, with no clear agenda about elements as crucial as the tick size.
We look at the events of 19 July to learn more about the price formation process. Our intention here is not to merely say that the way a (reputed) fair price is formed, thanks to matching of supply and demand, is simple. The roots of its mechanism are not very difficult to understand. Its complexity stems from the way they combine.
Charles-Albert LEHALLE Matthieu LASNIER Global Head of Quantitative Research [email protected] (33) 1 41 89 80 16
Market microstructure specialist, Quantitative Research, Paris
Paul BESSON Hamza HARTI Weibing HUANG Nicolas JOSEPH Lionel MASSOULARD Index and Portfolio Research Specialist, Quantitative Research, Paris
Trading specialist, Quantitative Research, Paris
PhD student, Quantitative Research, Paris
Performance analysis specialist, Quantitative Research, London
Trading specialist, Quantitative Research, New-York
Edmonton mini-course, July 2016 36
28 August 2012
CA CHEUVREUX QUANTITATIVE
RESEARCH Saw-tooth effect on the Us market
18 www.cheuvreux.com
Q Repetitive delta hedging seems to be the most plausible explanation
Options stucturers and market-makers need to delta hedge their positions in order to offset their market exposure. So-called "dynamic hedging" flows can create strong selling or buying pressure, which might impact market prices. These flows can reduce or increase stock volatility depending on the hedgers' positions. If market-makers are selling vanilla options to long-only managers, then dynamic hedging will tend to increase stock volatility. This phenomenon can be particularly strong when the options get close to maturity. Intuitively, this result can be understood by considering for example that a call option seller who delta hedges his position will have to buy stocks in order to deliver them to the option buyer. He will thus positively impact the underlying stock price. This behaviour cannot logically explain a price reversal. Conversely, when market makers buy vanilla options from long only managers (through call overwriting for example), then dynamic hedging tends to reduce stock volatility. This phenomenon is called "pinning" for short-term options. Nevertheless, when open interests and the gamma are very large, hedging flow impacts can be very significant.
FIGURE 18: SAW-TOOTH ON COCA-COLA AND 77.50 CALL
76.5
76.7
76.9
77.1
77.3
77.5
09:21 10:33 11:45 12:57 14:09 15:21
High Bound (77.5 $ Strike) 50% delta
Low Bound : 14% delta
Source: Crédit Agricole Cheuvreux Quantitative Research
19 July 2012: the derivative hedging scenario
Consider Coca-Cola on 19 July (FIGURE 18 and FIGURE 19) the VWAP was 77.24. Large open interests (20 556) on the 77.5 July Call and on the 75 July Put (13 477) were observed. For a 1% price change on Coca-Cola, delta hedging of the total number of open interests would imply a trading of 1.1 million shares, 12% of the volume on 19 July. This particularly high number was due to three elements: the size of the open positions, the fact that the stock trades next to the option strike, and the 1-day remaining maturity. On that particular day the price fluctuated 10 times, nearly every thirty minutes, with a 0.8% average move. Also, the traded volume amounted to 9.0 million shares. This means that the total hedging of those options would have represented nearly 100% of the total daily volume. This shows that delta-hedging can constitute a very large share of Coca-Cola's trading volume. It is important to note that the total open interest on listed options does not necessarily imply that delta hedging will occur on this total underlying notional. The net delta hedging notional will correspond to the net volatility positions of the long only players. Usually long only funds will sell volatility through call overwriting, they could also buy volatility through calls or puts to take advantage of their directional views. In qualitative terms, these counter-cyclical hedging flows can create a strong impact on prices. This situation has also been observed for McDonald's, IBM and Apple where sizes of open interests in listed options are large.
28 August 2012
CA CHEUVREUX QUANTITATIVE
RESEARCH Saw-tooth effect on the Us market
21 www.cheuvreux.com
We present a more detailed explanation in the table below (FIGURE 21), which illustrates the delta-hedging pressure on the four stocks at each peak of the saw-tooth pattern. We assume that for the two strikes closest to the money Calls and Puts of July 2012, the share of the delta hedged options stands at 100% of the open interest. This gives us theoretical maximum delta hedging flows. Thanks to the volume analysis carried out initially that showed a 20-30% volume participation, we estimate that the real fraction of the hedged options of the four stocks ranged from 30% to 50%. For Apple, dynamic hedging seems to constitute a smaller portion of the volumes. This is consistent with the Apple's less-pronounced saw-tooth pattern.
FIGURE 21: PERIODIC DELTA HEDGING PROCESS ON 4 STOCKS ON JULY THE 19
100% Option hedging Coke Mac Donald's IBM AppleSawtooth Timetable Price chg Gamma Price chg Gamma Price chg Gamma Price chg Gamma
From To (%) (Shares to trade) (%) (Shares to trade) (%) (Shares to trade) (%) (Shares to trade)
9:30 AM 10:00 AM -1.2% 1 277 419 -0.4% 172 786 -0.8% 535 032 -0.7% 653 595
10:00 AM 10:30 AM 0.8% -836 500 0.8% -303 688 1.0% -718 870 0.7% -657 895
10:30 AM 11:00 AM -0.8% 853 816 -0.6% 258 342 -1.0% 711 563 -0.3% 326 797
11:00 AM 11:30 AM 0.9% -1 003 911 0.8% -303 359 0.6% -449 294 0.3% -327 869
11:30 AM 12:00 PM -0.8% 852 713 -0.5% 215 054 -0.6% 446 429 -0.2% 163 399
12:00 PM 12:30 PM 0.9% -1 002 604 0.9% -345 946 0.9% -629 012 0.5% -490 998
12:30 PM 1:00 PM -0.8% 851 613 -0.8% 300 107 -0.8% 534 351 -0.3% 285 016
1:00 PM 1:30 PM 0.7% -715 215 0.6% -259 179 0.8% -538 462 0.4% -449 163
1:30 PM 2:00 PM -0.4% 426 357 -0.8% 300 429 -0.8% 534 351 -0.4% 406 504
2:00 PM 2:30 PM 0.5% -570 687 0.5% -216 216 0.8% -538 462 0.4% -408 163
2:30 PM 3:00 PM -0.4% 425 806 -0.4% 172 043 -0.8% 534 351 -0.4% 365 854
3:00 PM 3:30 PM 0.4% -427 461 0.3% -129 590 0.5% -358 974 0.4% -367 197
3:30 PM 4:00 PM -0.1% 141 935 -0.2% 86 114 -0.5% 357 143 -0.2% 162 602
Total (Absolute nb of shares) 9 386 039 3 062 853 6 886 293 5 065 052
Hedging / dai ly volume (%) 104% 41% 66% 32%Source: Crédit Agricole Cheuvreux Quantitative Research
When the gamma is very large and the hedging process very crude, stock pinning can even forge a saw-tooth effect On a very short-term maturity, large delta hedging concentrated around specific strikes can impact prices. When some delta hedgers represent a large share of the open interest, this phenomenon can be very significant. This is what academics call "pinning", it should drive prices back to their strikes. Nevertheless, when delta hedging is combined with a simplistic execution process "pinning" can degenerate into "saw-tooth" effects. Simplistic hedging of large gamma options is a plausible explanation for the "saw-tooth" trading pattern. This explanation is consistent with the main features of this phenomenon: timing, aggressiveness, impact, predictability and information leakage which is what characterises those "saw-tooth" patterns. Fortunately, large option positions are most often managed dynamically in a continuous way, and discrete archaic hedging processes have almost disappeared in modern-day markets.
28 August 2012
CA CHEUVREUX QUANTITATIVE
RESEARCH Saw-tooth effect on the Us market
18 www.cheuvreux.com
Q Repetitive delta hedging seems to be the most plausible explanation
Options stucturers and market-makers need to delta hedge their positions in order to offset their market exposure. So-called "dynamic hedging" flows can create strong selling or buying pressure, which might impact market prices. These flows can reduce or increase stock volatility depending on the hedgers' positions. If market-makers are selling vanilla options to long-only managers, then dynamic hedging will tend to increase stock volatility. This phenomenon can be particularly strong when the options get close to maturity. Intuitively, this result can be understood by considering for example that a call option seller who delta hedges his position will have to buy stocks in order to deliver them to the option buyer. He will thus positively impact the underlying stock price. This behaviour cannot logically explain a price reversal. Conversely, when market makers buy vanilla options from long only managers (through call overwriting for example), then dynamic hedging tends to reduce stock volatility. This phenomenon is called "pinning" for short-term options. Nevertheless, when open interests and the gamma are very large, hedging flow impacts can be very significant.
FIGURE 18: SAW-TOOTH ON COCA-COLA AND 77.50 CALL
76.5
76.7
76.9
77.1
77.3
77.5
09:21 10:33 11:45 12:57 14:09 15:21
High Bound (77.5 $ Strike) 50% delta
Low Bound : 14% delta
Source: Crédit Agricole Cheuvreux Quantitative Research
19 July 2012: the derivative hedging scenario
Consider Coca-Cola on 19 July (FIGURE 18 and FIGURE 19) the VWAP was 77.24. Large open interests (20 556) on the 77.5 July Call and on the 75 July Put (13 477) were observed. For a 1% price change on Coca-Cola, delta hedging of the total number of open interests would imply a trading of 1.1 million shares, 12% of the volume on 19 July. This particularly high number was due to three elements: the size of the open positions, the fact that the stock trades next to the option strike, and the 1-day remaining maturity. On that particular day the price fluctuated 10 times, nearly every thirty minutes, with a 0.8% average move. Also, the traded volume amounted to 9.0 million shares. This means that the total hedging of those options would have represented nearly 100% of the total daily volume. This shows that delta-hedging can constitute a very large share of Coca-Cola's trading volume. It is important to note that the total open interest on listed options does not necessarily imply that delta hedging will occur on this total underlying notional. The net delta hedging notional will correspond to the net volatility positions of the long only players. Usually long only funds will sell volatility through call overwriting, they could also buy volatility through calls or puts to take advantage of their directional views. In qualitative terms, these counter-cyclical hedging flows can create a strong impact on prices. This situation has also been observed for McDonald's, IBM and Apple where sizes of open interests in listed options are large.
Chevreux: sawtooths caused by options hedging28 August 2012
CA CHEUVREUX QUANTITATIVE
RESEARCH Saw-tooth effect on the Us market
19 www.cheuvreux.com
FIGURE 19: LONG VOLATILITY DELTA HEDGING
Coke: July Call 77.5 prices
0.00
0.25
0.50
76.00
76.25
76.50
76.75
77.00
77.25
77.50
77.75
78.00
Stock
Spo t price : 76.75Optio n D elta : +14%
P o sit io n hedge: -14%
Spo t price :77.5 Optio n D elta : +50%
P o sit io n hedge: -50%
F ro m 76.75 to 77.5, hedgerssell -36% fro m -14% to -50%
Lo w bo und 76.75 $
Lo w bo und 77.50 $
Source: Crédit Agricole Cheuvreux Quantitative Research
The reverting dynamic explained by a periodic operational process
While many farfetched explanations can be advanced for the "saw-tooth effect" on Coca-Cola, McDonald's, Apple and IBM. Adhering to the Occam's Razor principle, we favour this simple explanation: the sudden use of a rigid repetitive operational process for delta hedging these four stocks. Suppose a trader has to follow an existing option book without having full real-time access to his monitoring and execution tool, or that he cannot dedicate all his time to this task and therefore chooses to monitor this book every thirty minutes. Repetitive Delta hedging process
x Step 1) t0 = (initial time)
o Price the options, compute the delta on the new spot price
o Evaluate the total amount of stocks needed for the delta hedge
o Send the orders to the market.
x Step 2): TWAP execution over 30 min
x Back to Step 1) t1 = (initial time+30min) For a very large open interest position encompassing a large gamma, a significant move in the stock price will have disastrous effects for a basic rudimental hedger such as the one described above.
28 August 2012
CA CHEUVREUX QUANTITATIVE
RESEARCH Saw-tooth effect on the Us market
19 www.cheuvreux.com
FIGURE 19: LONG VOLATILITY DELTA HEDGING
Coke: July Call 77.5 prices
0.00
0.25
0.50
76.00
76.25
76.50
76.75
77.00
77.25
77.50
77.75
78.00
Stock
Spo t price : 76.75Optio n D elta : +14%
P o sit io n hedge: -14%
Spo t price :77.5 Optio n D elta : +50%
P o sit io n hedge: -50%
F ro m 76.75 to 77.5, hedgerssell -36% fro m -14% to -50%
Lo w bo und 76.75 $
Lo w bo und 77.50 $
Source: Crédit Agricole Cheuvreux Quantitative Research
The reverting dynamic explained by a periodic operational process
While many farfetched explanations can be advanced for the "saw-tooth effect" on Coca-Cola, McDonald's, Apple and IBM. Adhering to the Occam's Razor principle, we favour this simple explanation: the sudden use of a rigid repetitive operational process for delta hedging these four stocks. Suppose a trader has to follow an existing option book without having full real-time access to his monitoring and execution tool, or that he cannot dedicate all his time to this task and therefore chooses to monitor this book every thirty minutes. Repetitive Delta hedging process
x Step 1) t0 = (initial time)
o Price the options, compute the delta on the new spot price
o Evaluate the total amount of stocks needed for the delta hedge
o Send the orders to the market.
x Step 2): TWAP execution over 30 min
x Back to Step 1) t1 = (initial time+30min) For a very large open interest position encompassing a large gamma, a significant move in the stock price will have disastrous effects for a basic rudimental hedger such as the one described above.
(we show how to do this better)
Edmonton mini-course, July 2016
Our solutions with proportional cost
37
Ideal Black-Scholes hedge
Actual hedge holding
pursuit
Gârleanu & Pedersen:investment with proportional cost
✓t = � h�(T � t)
�·�Xt � target
�
Temporary impact: hedge strategyPermanent impact: effect on underlying
Edmonton mini-course, July 2016 38
stationarymodifiedvolatility
Γ<0: hedger is short the option1+νΓ<1: overreaction, increased volatilityΓ>0: hedger is long the option
1+νΓ>1: underreaction, reduced volatility
Zt = �⌫(Xt �X0) + (Pt � P0)dZt = � dWt
What happens to price process?
same as in Pt
Pt = P0 +1
1+ ⌫��⌫Yt + Zt
�
= P0 +�
1+ ⌫�
Wt + ⌫�
Z t
0e�(1+⌫�)(t�s)dWs
!
/ 1/p
Edmonton mini-course, July 2016
“Signature plot”
39
= (1+ ⌫�)
Δt
Volatility measuredon time interval
Δt�
�1+ ⌫� (� > 0)
�1+ ⌫� (� < 0)
1/
unconditional (F0)
1s � tE
�Ps � Pt
�2 =
=✓ �
1+ ⌫�
◆2
1+ (2+ ⌫�)⌫� 1� e�(s�t)(s � t)
!
Edmonton mini-course, July 2016
Nondimensional parameter
40
1 + ⌫�
⌫ = price change due to market impact
shares executed
� = shares needed to adjust hedge
market price change
Problems unless |νΓ| ≲ 1
Edmonton mini-course, July 2016
Conclusions
Many interesting math modelscalculus of variationsdynamic programming
Models are very approximatemarkets are messy
Can give insight nonethelesstrade fast vs trade slowpermanent and temporary impact
41