information in commodity options volume and open … · information in commodity options volume and...

Information in Commodity Options Volume and Open Interest

Semyon Malamud∗, Michael C. Tseng, and Yuan Zhang

May 12, 2017

Abstract

Commodity options serve as an important instrument for both hedging and specula-tion. While commodity futures have been a subject of extensive research, very little isknown about commodity options, their liquidity, their role in price discovery and hedg-ing, and their link to spot and futures prices dynamics. In this paper, we provide amodel that captures the economic relationship between informed trading, option prices,and option open interest. Within the context of our model, informed order flow haszero total price impact of across strikes. Rather, it is options open interest that reflectsinformed trading. We verify our model prediction empirically by showing that optionopen interest is a significant predictor of future returns.

JEL classification: G00.

∗SFI EPFL, Quartier UNIL Dorigny, 1015 Lausanne. e-mail: [email protected]. Tel: +4179 599 10 28

1 Introduction

Commodities are growing in popularity as a separate asset class. Many institutionalinvestors are including commodities in their asset allocation mix, and hedge funds are alsoincreasingly active players in commodities. As a result, trading in commodity options isbecoming more and more active. While trading commodity futures still largely dominatesthe market activity in commodity derivatives, commodity options are steadily growing intheir importance as a tool for speculating and hedging non-linear exposures. For example,the respective average daily volumes for commodity futures and options thereon are givenapproximately by 2 million versus 200 thousand for energy futures; 800 thousand versus150 thousand for agricultural futures; and 300 thousand versus 30 thousand for metalfutures.

Despite these large volumes, we still know very little about the structure of this mar-ket. Some questions that remain unanswered are, for example, how liquid and how deepit is, how much asymmetric information and informed trading is present in this market,and the extent to which option prices respond to hedging pressure and demand/supplyshocks in the underlying commodities. In this paper, we perform the first detailed anal-ysis of the whole universe of commodity options traded on exchanges from the CMEGroup and on ICE Europe Commodities exchange.2 We find evidence that informedtrading occurs in the options market and that informed trading is localized to certainstrike prices; options open interest predicts future prices.

The rest of this paper is organized as follows. Section 2 reviews relevant literature.Section 3 offers a theoretical model where we derive equilibrium properties regardinghow an informed trader might allocate his trades in the options market. Section 4 givesan first order approximation around the limit case where the amount of noise trades islarge. Section 5 contains empirical results. Section 6 concludes.

2 Literature Review

A number of recent papers have examined the risk and return characteristics of invest-ments in individual commodity futures or commodity indices composed of baskets ofcommodity futures. See, e.g., Erb and Harvey (2006), Gorton and Rouwenhorst (2006),and Kat and Oomen (2006) and Kat and Oomen (2007). However, with few exceptions,3

very little is known about commodity futures options, their value for portfolio diversifi-cation and insurance, and their role in hedging, liquidity, and price discovery. Naturally,commodity futures serve as a major instrument for hedging commodity price or quantityrisk, and hence their prices respond to hedging pressure. See, for example, Hirshleifer

2These exchanges cover a major fraction of exchange-traded commodity derivatives.

3For example, Trolle and Schwartz (2009) study pricing and risk premia of energy volatility usingnatural gas and crude oil options.

1

(1990) for the basic model, and De Roon et al. (2000) for empirical evidence.4 5 In partic-ular, De Roon et al. (2000) show that hedging pressure (as measured by the CommodityFutures Trading Commission (CFTC) reports about hedgers’ positions) predicts futuresreturns. As CFTC reports do not distinguish between futures and options on futures,the relative roles of futures and options open interest remain unexamined. In this paper,using detailed commodity options data, we distangle6 hedging and speculative pressurescoming from the options market and that from the futures market.

Moskowitz et al. (2012) show that the profitability of time series momentum strategies(which are commonly used by the so-called Commodity Trading Advisors (CTA), a classof hedge funds that trade futures) arises because speculators profit from time seriesmomentum at the expense of hedgers, in agreement with Keynes (1923) theory. Optionopen interest and volume can therefore be used to forecast normal backwardation andcontango regimes, and for timing momentum strategies.

Hong and Yogo (2012) shows that open interest growth rate is informative aboutfutures returns in the presence of hedging demand and limited risk absorption capacityin futures markets. In particular, they find that changes in open interest forecast futurereturns, while sufficiently high heding demand may lead to negative serial correlationin returns. In this paper, we develop a model that incorporates options in a similarsetup. To reflect the use of options in hedging nonlinear risk, the market in our modelis complete.

Roll et al. (2009) develops a new empirical construct, the options/stock trading vol-ume ratio (O/S), and show it is linked to stock returns. Johnson and So (2012) findthat O/S is strongly negatively related to future returns. In this paper, we extend theirresults to commodity futures, and study the link between relative volumes and futuresreturns.

Ready et al. (2013) shows that “commodity currencies” tend to have high interestrates while low interest rate currencies belong to exporters of finished goods, and acommodity-based strategy explains a substantial portion of the carry-trade risk premia,and all of their pro-cyclical predictability with commodity prices. Using options openinterest, we can use the hedging pressure coming from the option market and link it tocarry trade returns.

4In the multi-good setting of Hirshleifer (1990), a risk-sharing arrangement between the commodityproducer and consumer leas to contango (resp. backwardation) if the commodity and the consumptiongood are complementary (resp. substitutes).

5See also Baker (2014).

6CFTC reports directional information, classifying positions across different traders’ classes. Usingoptions data, one can only derive bounds on futures and options positions. Here, intra-day data TAQis particularly helpful because it allows me to infer (with some noise) from quotes whether the tradesare coming from dealers or from customers.

2

3 Model

We model the information asymmetry between options traders by combining the Kyle(1985) and Arrow-Debreu frameworks, where the Arrow-Debreu states having empiricalinterpretation as option strike prices.7 Keyne’s backwardation theory envisions a scenariowhere a risk averse commodity producer enters a short futures position at a futures pricelower than expected future spot price, thereby conceding a risk premium—the differencebetween the current futures price and expected future price —to its counterparty. Ourmodel retains this risk-sharing feature between a producer and counterparty and alsointroduces information asymmetry between the two. In practice, the producer may havedifferent hedging strategies based on his private information regarding, for example, out-look of future production. The counterparty, who may not be privy to this information,can infer from the producers order flow. The uninformed trader in our model, who isrisk neutral, bears all the risk conditional on information contained in order flow.8

There are two types of traders who trade Arrow-Debreu securities. The informedtrader receives a signal regarding the likelihood of each state. The uninformed traderdoes not observe the signal and therefore must infer the likelihood of each state fromaggregate order flow. The informed trader is risk-averse while the uninformed traderis risk neutral. The uninformed trader also acts as the market maker. In this strategicsetting, the Arrow-Debreu prices is therefore endogenously set by the uninformed trader.The informed trader trades-off between having the uninformed trader bear more risk(which smooths his own consumption claims across states) and incurring more priceimpact (which increases the variability of his consumption claims).

Informed trader’s problem State space is discrete, indexed by j = 1, · · · , N . Con-ditional on a binary signal s ∈ {l, h}, the state j has probability ηj(s). After observinga binary signal s ∈ {l, h}, the informed trader maximizes ex ante CARA utility

maxW ∗s (·)

U(W, s) = maxW ∗s (·)

−E

[∑j

ηj(s) e−α(Wj−

∑k η

Uk (W,ε)Wk)

].

The price of informed trader’s portfolio W set by the competitive risk neutral unin-formed trader is

∑k η

Uk (W, ε)Wk), where ηUk (W, ε) is the uninformed trader’s posterior,

is determined as follows. The uninformed trader conjectures the informed trader’s strat-egy to be s 7→ (W ∗

j (s))j for each s. The uninformed trader observes Yj = Wj + εj

7In the classical Arrow-Debreu endowment economy setting, risk sharing is a consequence fromthe market clearing condition. In our model, the informed trader places market orders and theircounterparties—uninformed traders—are competitive and have infinitely elastic demand after settingthe price, as in Kyle (1985). Risk sharing in the sense of comonotonicity of consumption across statestherefore does not exist in our model. Nevertheless, equality of marginal utility between agents stillholds, modulo a price impact term which is ex ante zero. See Proposition 3.2.

8In comparison, in the model of Hong and Yogo (2012), the counterparty has limited risk absorbtioncapacity and futures open interest drives return on futures through a underreaction-to news-channel.

3

where εj ∼ N(0, σ2j ) is order flow from noise traders. Upon observing aggregate or-

der flow across states (Yj)j, the uninformed trader’s updated belief ηUk (W, ε) regardingprobability of state k is

ηUk (W, ε) =

∫ηk(s)dπ(s,W, ε)

where dπ(s,W, ε) is uninformed trader’s posterior on the signal space {s}:

dπ(s,W, ε) =e− 1

2

∑i

(W∗i )2(s)

σ2i

+∑i

W∗i (s)Wi

σ2i

+∑i

W∗i (s)εi

σ2i dπ0(s)∫

e− 1

2

∑i

(W∗i

)2(s′)σ2i

+∑i

W∗i

(s′)Wiσ2i

+∑i

W∗i

(s′)εiσ2i dπ0(s′)

=eδ(s)+

∑i λi(s)Wi+Z(s,ε)∫

eδ(s′)+∑i λi(s

′)Wi+Z(s′,ε)dπ0(s′)dπ0(s)

with

λi(s) ≡W ∗i (s)

σ2i

, Z ≡∑i

λi(s) εi, δ(s) ≡ −1

2

∑i

(W ∗i )2(s)

σ2i

.

Proposition 3.1 The first order condition for Wj for an informed trader who observess is

ηj(s)e−αWjE[eα

∑k η

Uk (W,ε)Wk)] −

∑i

ηi(s) e−αWiE

[e∑k αη

Uk (W,ε)Wk

(ηUj (W, ε) +

∑k

Wk∂

∂Wj

ηUk (W, ε)

)](1)

= 0.

The FOC of Equation 1 contains both an Arrow-Debreu term and a Kyle term. Wecan rewrite Equation 1 as

ηj(s)E[e−(αWj−α∑k η

Uk (W,ε)Wk))] = E

[(∑i

ηi(s)e−(αWi−

∑k αη

Uk (W,ε)Wk)) · ηUj (W, ε)

]︸︷︷︸

Arrow-Debreu term M1

(2)

+ E

[(∑i

ηi(s)e−(αWi−

∑k αη

Uk (W,ε)Wk)) · (

∑k

Wk∂

∂Wj

ηUk (W, ε))

]︸︷︷︸

Kyle term M2

,

or

4

E[ηj(s)e

−(αWj−α∑k η

Uk (W,ε)Wk))∑

i ηi(s)e−(αWi−

∑k αη

Uk (W,ε)Wk)︸︷︷︸

martingale measure

] = E

[ηUj (W, ε) +

∑k

Wk∂

∂Wj

ηUk (W, ε)

]. (3)

The left hand side of Equation 2 is the informed trader’s expected marginal utility. Onthe right hand side, the first term M1 is an Arrow-Debreu term prescribing the risk-sharing arrangement between the informed trader and the market maker. In the stan-dard Arrow-Debreu setting, the normalized marginal utilities form the density of themartingale/risk-neutral measure. The normalization constant is the expected marginalutility—the quantity

∑i ηi(s)e

−(αWi−∑k αη

Uk (W,ε)Wk) of Equation 2, which is also the marginal

rate of substitution between agents. In our setting, this quantity is a function of noiseorder flow, therefore random. The risk-neutral measure coincide with state prices in thestandard Arrow-Debreu setting. In our setting, the risk-neutral measure is equal to thestate probability ηUj (W, ε) assigned by the risk neutral uninformed trader plus a secondterm M2 on the right hand side which reflects the total price impact,∑

k

Wk∂

∂Wj

ηUk (W, ε),

across states. In other words, the marginal utility of the risk neutral uninformed traderbreaks down to two parts—from the profit due to one more order at current price (M1)and from the price adjustment made upon receiving one more order (M2).

Proposition 3.2 (Zero Ex Ante Price Total Impact)

E

[∑j

∑k

Wk∂

∂Wj

ηUk (W, ε)

]= 0.

In other words, conditional on market maker’s conjecture, the informed trader arrangeshis trade so that the ex ante total price impact across all states is zero. In particular,the disutility from the cost of portfolio and total price impact are uncorrelated for theoptimizing informed trader:

E

[e∑k αη

Uk (W,ε)Wk

(∑j

∑k

Wk∂

∂Wj

ηUk (W, ε)

)]= 0.

The marginal effect of order flow for state j AD security on the uninformed trader’sposterior probability of state k (conditional on noise order flow ε) is

5

∂

∂Wj

ηUk (W, ε)

=∂

∂Wj

∫ηk(s)

eδ(s)+∑l λl(s)Wl+Z(s)∫

eδ(θ)+∑l λl(θ)Wl+Z(θ)dπ0(θ)

dπ0(s)

=

(∫eδ(θ)+

∑l λl(θ)Wl+Z(θ)dπ0(θ)

)−2

×∫ηk(s)e

δ(s)+∑l λl(s)Wl+Z(s)

∫(λj(s)− λj(θ))eδ(θ)+

∑l λl(θ)Wl+Z(θ)dπ0(θ)dπ0(s)

=

∫ηk(s)

∫(λj(s)− λj(θ))dπ(θ)dπ(s).

(4)

For each signal s, the market maker adjusts his belief regarding state k probability by theaverage deviation

∫(λj(s)− λj(θ))dπ(θ) according to his own conjecture (W ∗

j ) and thenaverages over his posterior. Proposition 3.2 then follows by summing over states j inEquation 3. This is in contrast with the Kyle-only framework, where the informed traderdoes not have the ability to trade off price impact across states. In terms of empiricalprediction, our model predicts that options order at some strikes to have negative priceimpact.

Denote

Γj(W (s)) ≡E[e∑k αη

Uk (W,ε)Wk

(ηUj (W, ε) +

∑kWk

∂∂Wj

ηUk (W, ε))]

E[eα∑i ηUi (W,ε)Wi ]

. (5)

Then we can rewrite the first order condition of Equation 1, for signal s and state j as

ηj(s)e−αWj = Γj(W (s))

∑i

ηi(s) e−αWi .

As a consequence of Proposition 3.2, we get that∑

j Γj(W (s)) = 1.

Reparametrization In preparation of characterization of equilibrium, we reparametrizethe informed trader’s FOC via appropriate constants.

Define ∑i

ηi(s) e−αWi = Ψ0(s).

By choice of exponential utility, the function Ψ0(s) is endogenously determined up to amultiplicative constant, i.e. we can distinguish s 7→ (Wi(s))i up to s 7→ (Wi(s) + const)i.In the binary signal case, this means that Ψ0(s) is determined up to an endogenousconstant

Ψ0(h)

Ψ0(l)=

∑i ηi(h) e−αWi(h)∑i ηi(l) e

−αWi(l)

6

orψ ≡ log Ψ0(h)− log Ψ0(l) = log

∑i

ηi(h) e−αWi(h) − log∑i

ηi(l) e−αWi(l),

which is a function of (∆Wj) = (Wj(h) − Wj(l)). The optimal order flow Wj of theinformed trader for state j then satisfies

Wj(s) =1

α(log ηj(s)− Γj(W (s))− log Ψ0(s)) . (6)

To obtain an expression for the uninformed trader’s updated belief on state k probability

ηUk (W, ε) =

∫ηk(s)dπ(s,W, ε),

the general posterior

dπ(s,W, ε) =eδ(s)+

∑i λi(s)Wi+Z(s,ε)∫

eδ(s′)+∑i λi(s

′)Wi+Z(s′,ε)dπ0(s′)dπ0(s).

in the binary signal case becomes

π(h,W, ε) =e

∑k

W∗k (h)−W∗k (l)

σ2k

(Wk+εk)− 12

((W∗k (h))2−(W∗k (l))2)

σ2k ph

e

∑k

W∗k

(h)−W∗k

(l)

σ2k

(Wk+εk)− 12

((W∗k

(h))2−(W∗k

(l))2)

σ2k ph + (1− ph)

,

and

π(l,W, ε) = 1− π(h,W, ε) .

So

ηUk (W, ε) = π(h,W, ε)ηk(h) + (1− π(h,W, ε))ηk(l).

Similarly, the quantity from Equation 4

∂

∂Wj

ηUk (W, ε) =

∫ηk(s)

∫(λj(s)− λj(θ))dπ(θ)dπ(s)

in the binary case simplifies to

∂

∂Wj

ηUk (W, ε) =

∫ηk(s)

∫(λj(s)− λj(θ))dπ(θ)dπ(s)

= ηk(h)(λj(h)− λj(l))π(l)π(h) + ηk(l)(λj(l)− λj(h))π(h)π(l)

= (ηk(h)− ηk(l))(λj(h)− λj(l))π(l)π(h)

= (ηk(h)− ηk(l))(W ∗

j (h)−W ∗j (l))

σ2j

Θ(W, ε)

7

with

Θ(W, ε) =ph(1− ph)(

e

∑k

W∗k

(h)−W∗k

(l)

σ2k

(Wk+εk)− 12

((W∗k

(h))2−(W∗k

(l))2)

σ2k ph + (1− ph)

)2 .

The price impact of state j order flow on state k price depends on uninformed trader’sconjectured difference W ∗

j (h) −W ∗j (l) of state j order flow across signals, his signal-to-

noise ratio ph(1−ph)σj

for state j, and the difference ηk(h) − ηk(l) of state k probability

across signals.Define

A(s,W ) ≡E[e∑k αη

Uk (W,ε)Wkπ(h,W, ε)

]E[eα

∑k η

Uk (W,ε)Wk ]

∈ R

B(s,W ) ≡E[e∑k αη

Uk (W,ε)WkΘ(W, ε)

]E[eα

∑k η

Uk (W,ε)Wk ]

∈ R

C(s,W ) ≡∑k

Wk(ηk(h)− ηk(l)) ∈ R .

(7)

Using vector notation σ = (σj)Nj=1, W

∗ = (W ∗j )Nj=1, and Γ(W (s)) = (Γj(W (s)))Nj=1, 9

Γ(W (s)) = η(l) + A(W (s))(η(h)− η(l)) + B(W (s))C(W (s))W ∗(h)−W ∗(l)

σ2. (8)

Substituting the equilibrium condition W (s) = W ∗(s) for s ∈ {l, h} into the expres-sion forA(s,W ), B(s,W ), and C(s,W ) gives endogenous constants a(s) ≡ A(s,W ) , b(s) ≡B(s,W ), c(s) ≡ C(s,W ), s = h, l , and corresponding equilibrium quantities Γ(h,W (h),W (l)),and Γ(l,W (h),W (l)). For example,

Γ(h,W (h),W (l)) = η(l) + a(h)(η(h)− η(l)) + b(h)c(h)W (h)−W (l)

σ2.

Equilibrium in our model is therefore characterized jointly by the following two setsequations, one for each signal:{

e−αW (h)η(h) = Γ(h,W (h),W (l))∑

k ηk(h)e−αW (h)k

e−αW (l)η(l) = Γ(l,W (h),W (l))∑

k ηk(l)e−αW (l)k

.

This is a system of 2N nonlinear equations with 2N unknowns W = (W (h),W (l)).

9As a slight abuse of notation, we let W∗(h)−W∗(l)σ2 denote component-wise division of the vector

W ∗(h)−W ∗(l) by the vector σ.

8

Equilibrium As remarked above, the informed trader’s optimal strategy is identifiedonly up to ∆W = W (h) − W (l). Consequently the equilibrium is pinned down onlyup to ∆W . Let the parameter set P consist of 6 endogenous constants a(s), b(s), c(s)(s = h, l) together with ψ:

P ≡ (a(l), a(h), b(l), b(h), c(l), c(h), ψ).

Taking the ratio of the the two sets of equations state-by-state gives N equations

eα(W (h)−W (l)) =η(h)

η(l)

Γ(l,W (h),W (l))

Γ(h,W (h),W (l))e−ψ =

η(h)

η(l)

η(l) + a(l)(η(h)− η(l)) + b(l)c(l)W (h)−W (l)σ2

η(h) + a(h)(η(h)− η(l)) + b(h)c(h)W (h)−W (l)σ2

e−ψ .

(9)Taking the log gives

∆W =1

α(log

η(h)

η(h) + a(h)(η(h)− η(l)) + b(h)c(h)∆Wσ2

− logη(l)

η(l) + a(l)(η(h)− η(l)) + b(l)c(l)∆Wσ2

− ψ).

This implicitly defines ∆Wk = ∆Wk(a(l), a(h), b(l), b(h), c(l), c(h), ψ), for k = 1, · · · , N .The other equilibrium quantities can be computed as follows:

π(h,W, ε) =e

12

∑k

(Wk(h)−Wk(l))2

σ2k

+∑kWk(h)−Wk(l)

σ2k

εkph

e12

∑k

(Wk(h)−Wk(l))2

σ2k

+∑kWk(h)−Wk(l)

σ2k

εkph + (1− ph)

=e

12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph

e12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

= Πh(∆W (a(l), a(h), b(l), b(h), c(l), c(h), ψ), ε)

≡ Π∗h(a(l), a(h), b(l), b(h), c(l), c(h), ψ, ε)

= Π∗h(P , ε),

9

π(l,W, ε) =e− 1

2

∑k

(Wk(h)−Wk(l))2

σ2k

+∑kWk(h)−Wk(l)

σ2k

εkph

e− 1

2

∑k

(Wk(h)−Wk(l))2

σ2k

+∑kWk(h)−Wk(l)

σ2k

εkph + (1− ph)

=e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph

e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

= Πl(∆W (a(l), a(h), b(l), b(h), c(l), c(h), ψ), ε)

≡ Π∗l (a(l), a(h), b(l), b(h), c(l), c(h), ψ, ε)

= Π∗l (P , ε),

Θ(h,W, ε) =ph(1− ph)(

e

∑kWk(h)−Wk(l)

σ2k

(Wk(h)+εk)− 12

((Wk(h))2−(Wk(l))2)

σ2k ph + (1− ph)

)2

=ph(1− ph)(

e12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

)2

≡ θ∗h(∆W (P), ε) = θ∗h(P , ε),

Θ(l,W, ε) =ph(1− ph)(

e

∑kWk(h)−Wk(l)

σ2k

(Wk(l)+εk)− 12

((Wk(h))2−(Wk(l))2)

σ2k ph + (1− ph)

)2

=ph(1− ph)(

e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

)2

≡ θ∗l (∆W (P), ε) = θ∗l (P , ε),

a(s) =E[e∑k αη

Uk (W (s),ε)W (s)kπ(h,W (s), ε)

]E[eα

∑k η

Uk (W (s),ε)W (s)k ]

=E[eαΠ∗s(P,ε)c(s)Π∗s(P , ε)

]E[eαΠ∗s(P,ε)c(s)]

, s = h, l

b(s) =E[eαΠ∗s(P,ε)c(s)θ∗s(P , ε)


, s = h, l .

10

As c(s) only appears in the exponents, we can take

c(s) =∑k

Wk(ηk(h)− ηk(l))

=∑k

α−1(ηk(h)− ηk(l)) logηk(s)

ηk(l) + a(s)(ηk(h)− ηk(l)) + b(s)c(s)σ−2k ∆Wk(P)

(10)Note that, remarkably, the condition

∑i Γi(s) = 1 for equilibrium (W = W ∗)is

equivalent to10

∑k

Wk(ηk(h)−ηk(l))·∑k

W ∗k (h)−W ∗

k (l)

σ2k

=∑k

Wk(ηk(h)−ηk(l))·∑k

Wk(h)−Wk(l)

σ2k

= 0 .

Thus, we arrive at the following system for seven equilibrium parameters P :

a(s) =E[eαΠ∗s(P,ε)c(s)Π∗s(P , ε)


, s = h, l

b(s) =E[eαΠ∗s(P,ε)c(s)θ∗s(P , ε)


, s = h, l

c(s) =∑k

α−1(ηk(h)− ηl(h)) logηk(s)

ηk(s) + a(s)(ηk(h)− ηk(l)) + b(s)c(s)σ−2k ∆Wk(P)∑

k

∆Wk(P)

σ2k

= 0 .

(11)

4 Large Noise

In general, the equilibrium system needs to be solved numerically. But one can find afirst order approximate solution around the limiting case where noise order flow is large.

10We should have ∑j

W ∗j (h)−W ∗j (l)

σ2j

= 0

because for generic parameters this is the only way to kill two conditions with one.

11

Specifically, assume σ2k ≈

σ2∗(k)κ

for κ small. Substituting, we get

α∆Wk = logηk(h)

ηk(h) + a(h)(ηk(h)− ηk(l)) + bk(h)ck(h)∆Wk

σ2k

− logηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l)) + b(l)c(l)∆kWσ2k

− ψ

≈ logηk(h)

ηk(h) + a(h)(ηk(h)− ηk(l))−

bk(h)ck(h) ∆Wk

σ2∗(k)

ηk(h) + a(h)(ηk(h)− ηk(l))κ

−

(log

ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))−

bk(l)ck(l)∆Wk

σ2∗(k)

ηk(l) + a(l)(ηk(h)− ηk(l))κ

)− ψ.

So11

∆Wk ≈Hk

α +Gkκ

≈ Hk

α− HkGk

α2κ,

∆W 2k ≈

H2k

α2− 2

H2kGk

α3κ,

Hk = logηk(h)

ηk(h) + a(h)(ηk(h)− ηk(l))− log

ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))− ψ,

Gk =bk(h)ck(h) 1

σ2∗(k)

ηk(h) + a(h)(ηk(h)− ηk(l))−

bk(l)ck(l)1

σ2∗(k)

ηk(l) + a(l)(ηk(h)− ηk(l)),

π(h,W, ε) =e

12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph

e12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

≈ ph + ph(1− ph)(1

2

∑k

H2k

α2σ2∗(k)

+∑k

Hk

ασ2∗(k)

εk)κ,

11The term Hk is what one would obtain for ∆Wk if σ2k is formally set to ∞.

12

π(l,W, ε) =e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph

e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

≈ ph + ph(1− ph)(−1

2

∑k

H2k

α2σ2∗(k)

+∑k

Hk

ασ2∗(k)

εk)κ

θ∗h(∆W (P), ε) =ph(1− ph)(

e12

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

)2

≈ ph(1− ph)(1− 2ph(1

2

∑k

H2k

α2σ2∗(k)

+∑k

Hk

ασ2∗(k)

εk)κ) ,

θ∗l (∆W (P), ε) =ph(1− ph)(

e− 1

2

∑k

∆W2k

σ2k

+∑k

∆Wkσ2k

εkph + (1− ph)

)2

≈ ph(1− ph)(1− 2ph(−1

2

∑k

H2k

α2σ2∗(k)

+∑k

Hk

ασ2∗(k)

εk)κ) ,

E[eαΠ∗h(P,ε)c(h)Π∗h(P , ε)

]E[eαΠ∗h(P,ε)c(h)]

≈E

[eαph

(ph+ph(1−ph)( 1

2

∑k

∆W2k

σ2∗(k)+∑k

∆Wkσ2∗(k)

εk)κc(h)

)·(ph + ph(1− ph)(1

2

∑k

∆W 2k

σ2∗(k)

+∑

k∆Wk

σ2∗(k)

εk)κ)]

E[eαph

(ph+ph(1−ph)( 1

2

∑k

∆W2k

σ2∗(k)+∑k

∆Wkσ2∗(k)

εk)κ

)c(h)

]

≈ ph − (ph(1− ph)(1

2

∑k

H2k

α2σ2∗(k)

)(1− c(h)αph(1− ph))κ,

E[eαΠ∗l (P,ε)c(l)Π∗l (P , ε)

]E[eαΠ∗l (P,ε)c(l)]

≈ ph + (ph(1− ph)(1

2

∑k

H2k

α2σ2∗(k)

)(1− c(h)αph(1− ph))κ,

E[eαΠ∗h(P,ε)c(h)θ∗h(P , ε)

]E[eαΠ∗h(P,ε)c(h)]

≈ ph(1− ph)

(1− ph

∑k

H2k

α2σ2∗(k)

κ

),

13

E[eαΠ∗l (P,ε)c(l)θ∗l (P , ε)

]E[eαΠ∗l (P,ε)c(l)]

≈ ph(1− ph)

(1 + ph

∑k

∆H2k

α2σ2∗(k)

κ

),

Thus, we arrive at the approximate system for seven equilibrium parameters in P :

a(h) = ph − (ph(1− ph)(1

2

∑k

H2k

α2σ2∗(k)

)(1− c(h)αph(1− ph))κ

a(l) = ph + (ph(1− ph)(1

2

∑k

H2k

α2σ2∗(k)

)(1− c(l)αph(1− ph))κ

b(h) = ph(1− ph)

(1− ph

∑k

H2k

α2σ2∗(k)

κ

)

b(l) = ph(1− ph)

(1 + ph

∑k

H2k

α2σ2∗(k)

κ

)

c(h) =1

α

∑k

(ηk(h)− ηk(l)) logηk(h)

ηk(h) + a(h)(ηk(h)− ηk(l)) + b(h)c(h) Hkασ2∗(k)

κ

c(l) =1

α

∑k

(ηk(h)− ηk(l)) logηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l)) + b(l)c(l) Hkασ2∗(k)

κ∑k

∆Wk

σ2∗(k)

κ =κ

α

∑k

1

σ2∗(k)

(logηk(h)


ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))− ψ) = 0.

(12)The last equation becomes

ψ =1∑

k1

σ2∗(k)

∑k

1

σ2∗(k)

(logηk(h)

ηk(h) + a(h)(ηk(h)− ηk(l))−log

ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))).

So

Hk = logηk(h)


ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))− ψ

= logηk(h)


ηk(l)

ηk(l) + a(l)(ηk(h)− ηk(l))

− 1∑i

1σ2∗(i)

∑i

1

σ2∗(i)

(logηi(h)

ηi(h) + a(h)(ηi(h)− ηi(l))− log

ηi(l)

ηi(l) + a(l)(ηi(h)− ηi(l))).

Informed trader strategy In the large noise limit, i.e. κ = 0, a(h) = a(l) = p. So

14

α∆Wk = logηk(h)

ηk(h) + p(ηk(h)− ηk(l))− log

ηk(l)

ηk(l) + (ηk(h)− ηk(l))− ψ

= logηk(h)


ηk(l)

ηk(l) + p(ηk(h)− ηk(l))

− 1∑i

1σ2∗(i)

∑i

1

σ2∗(i)

(logηi(h)

ηi(h) + p(ηi(h)− ηi(l))− log

ηi(l)

ηi(l) + p(ηi(h)− ηi(l))).

Two factors determine whether ∆Wk > 0—the (log-)likelihood ratio of state k and theamount of noise trading at state k. Suppose ηk(h) > ηk(l), then the the difference oflog-likelihood ratios between the informed and uninformed traders is

Lk = logηk(h)


ηk(l)

ηk(l) + p(ηk(h)− ηk(l))

= logηk(h)

ηk(l)− log

ηk(h) + p(ηk(h)− ηk(l))ηk(l) + p(ηk(h)− ηk(l))

> 0.

∆Wk > 0 if Lk is greater than the “average” log-likelihood ratio

1∑i

1σ2∗(i)

∑i

1

σ2∗(i)Li.

The average log-likelihood ratio assigns weight 1σ2∗(k)

to state k—a high level of noise

trading σ2∗(k) at a state therefore induces the informed trader to place larger orders.

Informed trader options position Empirically, the states in our model are futurespot prices. Assuming the prices are sufficiently “dense” on the real line, the distributionsof states η can be approximated by continuous distributions. For a portfolio W (x) ofArrow-Debreu securities, the corresponding futures and options positions can be backedout from the formula

W (x) = W (K0) +W ′(K0)(x−K0) +

∫ K0

−∞W ′′(K)(x−K)−dK +

∫ ∞K0

W ′′(K)(x−K)+dK

for a fixed strike price K0. The difference of informed trader’s options positions acrossstates is then1213

12We assume α = 1 for the discussion on informed trader’s option position and on examples ofparametric families.

13The second equality holds because 1∫1

σ∗(x′)dx′

∫L(x′) 1

σ∗(x′)dx′ is an endogenous constant.

15

(∆W )′′ =d2

dx2(log

ηh(x)

ηl(x)− log

ηh(x) + p(ηh(x)− ηl(x))

ηl(x) + p(ηh(x)− ηl(x))︸︷︷︸L(x)

− 1∫1

σ∗(x′)dx′

∫L(x′)

1

σ∗(x′)dx′)

= (logηh(x)

ηl(x))′′ − (log

ηh(x) + p(ηh(x)− ηl(x))

ηl(x) + p(ηh(x)− ηl(x)))′′ (= L′′(x)).

Options are only necessary in achieving nonlinear positions. A linear position W (x)would have W ′′ ≡ 0. The trader only needs to have futures contracts in his portfolio totake a linear position. If the informed trader knows realized states are restricted to asmall region of a state space, it is not desirable for him to place large bets away from theregion. Options allow the trader to take a localized position. The term (log ηh(x)

ηl(x))′′ is the

difference in marginal change of (semi-)elasticity of likelihood across informed trader’s

signals. The term (log ηh(x) + p(ηh(x)−ηl(x))ηl(x) + p(ηh(x)−ηl(x))

)′′ has a similar interpretation with respect tothe uninformed trader’s posterior. In other words, the informed trader’s incorporatesoptions in his portfolio when the variability of elasticity of likehood across states is high.Interpreted state-by-state, (∆W )′′ is also the difference in information sets of informedand uninformed traders. For a given x, normalizing the likelihoods by ηh(x) + ηl(x),(∆W )′′ is the log-odds ratio between signals h and l,

logηh(x)

ηl(x)= log

ηh(x)ηh(x)+ηl(x)

ηl(x)ηh(x)+ηl(x)

.

Then (log ηh(x)ηl(x)

)′′ is the (Fisher) information of the informed trader at x in s = h relative

to s = l.14 In summary, the size of the informed trader’s bet is monotonically ordered inlikelihood of state across signals and the size of his options position and the size of hisoptions position is monotonically ordered in the information contained in likelihood ofstate across signals.

Intuitively, high (log-)concavity of the probability density ηs(x)—for example, a bumpat x—induces the trader to take a position local around x and therefore larger optionspositions. In the presence of information asymmetry, informed trader’s options positionsconditional on h is larger than that conditional on s when his local information (con-ditional on h relative to l) is better than that of the market maker. The structure ofinformed trader’s information in our model therefore links empirically to options open

14In a statistics context, for a parametric family of probability densities η(ω, θ) parametrized by θ,

Fisher information at θ is the expected value of the statistic d2

dθ2 η(ω, θ). In our setting, the relevantquantity is the difference between the realizations s ∈ {h, l} rather than the mean, as the informedtrader knows the realization of s.

16

interest. Options allow the informed trader to taylor his state-contingent bets to hisinformation, as well as hiding his order flow among noise trades, achieving zero priceimpact (Proposition 3.2).15 Next we consider some parametric examples.

Example (exponential distribution) Consider the case of exponential distributionsηh(x) = λhe

−λhx and ηl(x) = λle−λlx on [0,∞). Then

(∆Wk)′′ =

λhλl(λh − λl)2eλh+λlp(−λ2l e

2λhx(p− 1) + λ2he

2λlx(p+ 1))

(λleλhx(p− 1)− λheλlxp)2(λleλhxp− λheλlx(1 + p))2≥ 0.

In other words, the sign of options positions does not change with respect to the distri-bution of states in this case.

Example (Pareto distribution) Consider the case where ηh(x) = λhxλh+1 and ηl(x) =

λlxλl+1 are densities of Pareto distributions on [1,∞) with parameters λh and λl respec-tively. Then

L′′(x) = (λh − λl)ph×(λ4

l (ph − 1)2phx4λh + λ4

hph(ph + 1)2x4λl + 2λ2hλ

2l ph(−2 + 3p2

h)x2(a+b)

+ ab3(ph − 1)(1− λh + λl − 4p2h)x

3(λh+λl) + λ3λl(ph + 1)(1 + λh − λl − 4p2h)x

λh+3λl)

divided by a positive term.16

Proposition 4.1 Let p 6= 12.

(i) If 0 < λl, λh ≤ 1, then for any λl, there exists a λh ∈ (λl, 1) such that (∆Wk)′′(x)

is a positive function for all λh ∈ (λh, 1]. For λh /∈ (λh, 1], (∆Wk)′′(x) may be negative

or take both positive and negative values function.(ii) If 1 < λl, λh < ∞, then for any λl, there exists a neighborhood (a, b) of λl

(∆Wk)′′(x) is a positive function for all λh /∈ (a, b). For λh ∈ (a, b), (∆Wk)

′′(x) may benegative or take both positive and negative values function.

5 Empirical Results

Data description In the empirical investigation, trades and quotes (TAQ) data forfutures and options on futures contracts traded on CME exchanges (CME, CBOT,

15In practice, options market are noiser than futures markets.

16The expression of the numerator is

x2(λl(ph − 1)xλh − λhphxλl)2(λlphxλh − λh(1 + ph)xλl)2.

17

Table 1: Summary of Open Interest RegressorsName Definition 5%/Sign 1%/Sign 0.1%/SignOptOI Raw open interest (OI) NoneCminusP Call OI − Put OI NoneITMcall plus OTMput ITM call OI + OTM put OI NoneITMput plus OTMcall ITM put OI + OTM call OI Precious metal/− Energy/−ITM call ITM call OI Precious metal/+ITM put ITM put OI Energy/−OTM call OTM call OI Grains/− Energy/−OTM put OTM put OI Energy/+ Grains/+

All open interests are weighted by moneyness except for OptOI.

COMEX, NYMEX) is used. The time span of our sample is from January 2006 toNovember 2015. The data is acquired from Nanex, which provides historical exchangetape messages in 25 milliseconds resolution for each trading day. We extract the mes-sage sent at around 6AM each trading day on the end-of-day settlement report for theprevious trading day. In particular, we extract the category 68 report (open interest andvolume),17 the category 84 report (settlement price) for each contract. Then we matcheach option with its underlying futures using a modified version of Nanex JTools anddoublecheck the result with a contract-maturity dictionary built using CME rule books.

We select the following commodities that have the most liquid option markets andwhose trading volume constitutes a large share of total volume:

• grains and seeds (corn, soybean, soybean meal, soybean oil, wheat),

• energy (crude oil, natural gas),

• precious metal (gold, silver).

We use only the regular expiration (third Friday of the maturity month) option series.

Variable definitions We construct the futures return from our sample as follows. Foreach commodity i, we take the front month futures price of each day to obtain a dailytime series of size 1180. From the daily time series, we take monthly averages to obtaina time series F i

t . The futures return monthly series is then defined by

FMreturnt =F it

F it−1

− 1.

Futures position typically involves leverage and this definition corresponds to the returnof a fully collaterized commodity futures position in excess of risk free rate. An investor

17The end-of-day report seperates trading volume for pit and globex. We do not distringuish betweenthe two, hence we aggregate them into one volume measure.

18

who enters into a long futures position at Ft−1 while posing collateral Ct−1 = Ft−1 andcloses his posiion at Ft obtains return

(1 + rt)Ct−1 + Ft − Ft−1

Ct−1

= FMreturnt + rt,

where rt is the risk free rate. For each sector—energy, precious metal, and grains—wecompute the return of a equally weighted portfolio of commodities in that sector.

In terms of trading strategy, our definition of return is that obtained by first takinga position built up in equal daily increments (longing or shorting an equal numberof contracts each days) over a given month then closing the position in equal dailyincrements over the next month.

A monthly futures open interest variable is constructed similarly. For each commod-ity, a monthly time series of front month futures contract open interest is obtained bytaking monthly average of the daily time series of front month open interests. For eachsector, we then average over commodities in that sector. This variable is denoted byFuturesOIt.

The main predictor variables in our regression are constructed using options openinterest. It is natural to first separate options in to calls and puts. We take the differencebetween the call and put open interests daily time series and average monthly. Thisvariable is denoted by CminusPt.

The more liquid trading conditions of at-the-money options makes their open interestsmore noisy. Therefore, in addition to separating into calls and puts, we weigh the eachoption open interest by moneyness, a measure of distance between strike price of theoption and the futures price. The moneyness of a call option is defined to be

1− Strike price

Futures price,

normalized to be zero at-the-money, > 0 in-the-money, and < 0 out-of-the-money. Sim-ilarly, the moneyness of a put option is

Strike price

Futures price− 1.

We construct several variables that takes into account moneyness of the underlyingoption. The variables defined by

ITM call = (1− Strike Price

Futures Price)+ ×Option open interest,

ITM put = (Strike price

Futures price− 1)+ ×Option open interest

for calls and puts respectively are in-the-money options open interest weighted by mon-eyness. Similarly, out-of-money options open interest weighted by moneyness are definedas

19

OTM call = (1− Strike Price

Futures Price)+ ×Option open interest,

and

OTM put = (Strike price

Futures price− 1)− ×Option open interest

for calls and puts respectively. The specifications we consider are of the form

FMreturnt = α + βOptions OI variablet− 1 + (control) + εt

For the energy sector (crude oil and natural gas), the inventory levels are obtained fromthe U.S. Department of Energy monthly review.18

Definitions of variables and regression results are summarized in Table 1. Detailedregression results are shown in Table 5, Table 5, Table 5, and Table 5. We find that rawoptions open interest in general not significant but some options open interest weightedby moneyness significant as predictors of futures returns.19 To stablize the variance, wetake log of level quantities then, to detrend the time series, take first difference, therebyconverting the variables into growth rates.

Table 2: Commodity Sectors and AbbreviationsSector Commodity AbbreviationEnergy Crude Oil CLEnergy Natural Gas NGPrecious Metal Gold GCPrecious Metal Silver SIGrains Corn ZCGrains Soybean Oil ZLGrains Soybean Meal ZMGrains Soybean ZS

Summary statistics The summary statistics of the variables defined above are shownin Table 3, Table 4, and Tabel 5, for the energy, precious metal, and grains sectorsrespectively. The liquidity of the options market compared to the futures market—as measured by open interest—differs from sector to sector. For energy and precious

18For crude oil, we use U.S. stocks excluding SPR of crude oil, , in thousands of barrels, obtained fromhttp://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=MCESTUS1&f=M. For natural gas,we use U.S. total natural gas in underground storage (working gas), in millions of cubic feet, obtainedfrom http://www.eia.gov/dnav/ng/hist/n5020us2m.htm.

19In results not reported here, we also divide options option interests into separate bins according tomoneyness, and found that the results align with what we report here. In particular, open interest ofat- or near-the-money options are not significant as predictors.

20

commodities, the option open interest is an order of magnitude higher than futures openinterest. For agricultural grains, the futures open interest is an order of magnitudehigher than options open interest. A more liquid market better allows the informedtrader minimize his price impact. One would expect an informed trader be active inmore liquid markets. This is in line with our empirical results below, where we findstrongest footprint of informed trading—in the form of a synthetic futures position thatpredicts price change—in the energy sector.

Table 3: Summary Statistics: Energy

Num. Obs. Mean Std. Dev. Min 25% 50% 75% Max

CminusP 119 6.262 5.813 -4.669 1.719 6.707 10.77 16.05ITM call 119 2.749 2.181 0.031 0.510 3.261 4.250 8.027OTM call 119 17.96 9.197 2.465 10.94 18.57 23.33 44.49ITM put 119 3.113 2.524 0.031 1.173 2.771 4.507 10.44OTM put 119 4.613 2.241 1.284 3.182 3.990 5.472 11.10ITMcall plus OTMput 119 7.363 4.102 1.315 3.990 6.776 9.609 19.13ITMput plus OTMcall 119 21.07 11.31 2.496 12.13 21.67 27.24 54.68FuturesOI 119 1.742 0.331 1.123 1.562 1.742 1.913 2.817FMreturn 119 -0.365 7.790 -20.06 -5.159 -0.6552 5.391 25.12

Open interest variables are reported in units of 100000 numbers of contracts. Front month futures

returns are reported in percentage points. 25%, 50%, and 75% denote corresponding quantiles.

Table 4: Summary Statistics: Precious Metal


CminusP 119 1.636 1.183 0.263 0.726 1.062 2.554 4.187ITM call 119 0.040 0.034 0.003 0.017 0.029 0.051 0.183OTM call 119 1.216 1.092 0.061 0.380 0.697 2.299 4.056ITM put 119 0.035 0.042 0.001 0.007 0.017 0.043 0.192OTM put 119 0.262 0.135 0.067 0.165 0.244 0.334 0.686ITMcall plus OTMput 119 0.302 0.160 0.073 0.183 0.266 0.368 0.869ITMput plus OTMcall 119 1.251 1.119 0.062 0.405 0.724 2.406 4.179FuturesOI 119 0.565 0.458 0.015 0.173 0.367 0.926 1.811FMreturn 119 0.7387 5.919 -15.80 -3.533 -0.091 4.758 15.00



Informed options trading For the energy sector, in-the-money put and out-of-moneycall options open interests are significant at the 99% level, with the regression coefficienthaving negative sign. According to our model, informed traders trade options in order to

21

Table 5: Summary Statistics: Grains


CminusP 119 0.293 0.528 -1.010 0.080 0.386 0.663 1.317ITM call 119 0.088 0.094 0.003 0.020 0.055 0.111 0.424OTM call 119 0.477 0.315 0.084 0.294 0.418 0.572 2.176ITM put 119 0.071 0.099 0.000 0.010 0.039 0.079 0.640OTM put 119 0.315 0.190 0.031 0.174 0.265 0.415 0.953ITMcall plus OTMput 119 0.403 0.279 0.037 0.201 0.324 0.523 1.334ITMput plus OTMcall 119 0.548 0.407 0.084 0.315 0.465 0.647 2.815FuturesOI 119 1.389 0.520 0.482 1.084 1.338 1.709 2.949FMreturn 119 0.597 6.065 -20.25 -2.531 0.485 4.127 17.85



place bets localized to his information. Within the context of the model, the regressionresults for the energy sector therefore indicates that informed trading occurs on optionswith strike prices larger than current futures price. The negative sign of the regressioncoefficient implies that it is the short position on out-of-money calls and long positionon in-the-money puts which are informed. At the same strike, short position on a calland long position on a put is equivalent to a short synthetic futures position. While aproducer of commodities such as crude oil or natural gas would also take a short futuresposition in hedging price risk, the counterparty typically require a risk premium so thatthe futures price is less than current price. In our results, the synthetic futures positionwould be at a price higher than current price. Such activity is more likely to result frominformed trading rather than hedging pressure.

For the precious metal sector, the sum of in-the-money put and out-of-money calloptions open interests is significant at the 95% level, but with the regression coefficienthaving positive sign. Therefore it would be the long position of the synthetic futurescontract who is informed. This again suggests informed trading rather than hedgingpressure.

For the grain commodities (corn and soybean), we find out-of-money put open interestsignificant at the 99% level, with the regression coefficient having positive sign, and out-of-money call open interest significant at the 95% level, with the regression coefficienthaving negative sign. This suggests that informed trading occurs on both sides of thecurrent futures price. In the both out-of-money put and out-of-money call cases, itis the short position correct anticipate price change on average. When prices are inbackwardation, informed traders write put options and when prices are in contango,they write call options.

22

Model 1 Model 2 Model 3 Model 4 Model 5(Intercept) 0.00546 0.00489 0.00541 0.00439 0.00437

(0.00447)(0.00449)(0.00450)(0.00445) (0.00448)FuturesOI 0.02710 0.03768 0.02657 0.04478 0.00859

(0.05721)(0.05307)(0.05754)(0.05297) (0.05139)CminusP −0.01163

(0.02163)OptOI 0.00266

(0.01147)ITMcall plus OTMput −0.01146

(0.02174)ITMput plus OTMcall 0.00002

(0.00014)ITM call 0.00025

(0.00022)ITM put 0.00038

(0.00113)OTM call −0.01652∗

(0.00798)OTM put 0.02082∗∗

(0.00761)R2 0.00733 0.00528 0.00758 0.01719 0.09300Adj. R2 -0.01009 -0.01217 -0.01877 -0.00890 0.06892Num. Obs. 117 117 117 117 117RMSE 0.04752 0.04757 0.04772 0.04749 0.04562∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05

Table 6: ZC, ZL, ZM, ZS aggregated, monthly frequency

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Model 1 Model 2 Model 3 Model 4 Model 5 Model 6(Intercept) −0.00144−0.00220−0.00169 0.00099 0.00133 −0.00082

(0.00404)(0.00404)(0.00409) (0.00384) (0.00399) (0.00382)FuturesOI −0.07782−0.09369−0.09153 −0.09104 −0.09360 −0.11627

(0.07584)(0.07600)(0.07539) (0.07081) (0.07079) (0.07089)Inventory −0.06770

(0.05067)AvgCminusP 0.00122

(0.02688)AvgOptOI −0.01096


(0.02515)ITMput plus OTMcall −0.05730∗∗∗

(0.01343)ITM call 0.00236

(0.00336)ITM put −0.01231∗∗∗

(0.00298)OTM call −0.05665∗∗∗

(0.01446)OTM put 0.03393∗

(0.01478)R2 0.02892 0.01360 0.01753 0.15147 0.15839 0.17235Adj. R2 0.01174 -0.00386 0.00014 0.12874 0.13584 0.15018Num. Obs. 117 117 117 117 117 117RMSE 0.04308 0.04341 0.04333 0.04045 0.04028 0.03994∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05

Table 7: CL, NG aggregated, monthly frequency, not controlling for inventory

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Model 1 Model 2 Model 3 Model 4 Model 5 Model 6(Intercept) −0.00144−0.00143−0.00094 0.00151 0.00178 −0.00035

(0.00404)(0.00407)(0.00412) (0.00387) (0.00403) (0.00386)FuturesOI −0.07782−0.07805−0.07522 −0.07925 −0.08319 −0.10515

(0.07584)(0.07665)(0.07612) (0.07160) (0.07205) (0.07202)Inventory −0.06770−0.06777−0.06777 −0.05133 −0.03921 −0.04257

(0.05067)(0.05097)(0.05079) (0.04777) (0.04827) (0.04738)CminusP −0.00073

(0.02683)OptOI −0.01100


(0.02516)ITMput plus OTMcall −0.05611∗∗∗

(0.01347)ITM call 0.00198

(0.00340)ITM put −0.01207∗∗∗

(0.00299)OTM call −0.05554∗∗∗

(0.01452)OTM put 0.03280∗

(0.01485)R2 0.02892 0.02893 0.03291 0.16020 0.16336 0.17833Adj. R2 0.01174 0.00292 0.00700 0.12994 0.13321 0.14872Num. Obs. 117 117 117 117 117 117RMSE 0.04308 0.04327 0.04318 0.04042 0.04034 0.03998∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05

Table 8: CL, NG aggregated, monthly frequency, controlling for inventory

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Model 1 Model 2 Model 3 Model 4 Model 5(Intercept) −0.00673−0.00513−0.00367−0.00725−0.00459

(0.00580)(0.00554) (0.00585) (0.00579)(0.00568)FuturesOI 0.07536 0.12396 −0.00408−0.00287−0.04321

(0.08920)(0.08873) (0.09422) (0.08559)(0.09082)CminusP 0.01048

(0.02445)OptOI −0.02708

(0.01477)ITMcall plus OTMput 0.00534

(0.02411)ITMput plus OTMcall −0.03527∗

(0.01542)ITM call 0.01144∗

(0.00560)ITM put −0.00183

(0.00154)OTM call −0.02898

(0.01809)OTM put 0.03052

(0.02546)R2 0.00637 0.03325 0.05035 0.05652 0.06132Adj. R2 -0.01107 0.01629 0.02514 0.03147 0.03639Num. Obs. 117 117 117 117 117RMSE 0.06029 0.05947 0.05920 0.05901 0.05886∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05

Table 9: GC, SI aggregated, monthly frequency

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Energy Metal Grains(Intercept) −0.01589∗ −0.01462 −0.01443 0.00874

(0.00764) (0.00773) (0.00937) (0.00464)FuturesOI −0.11832 −0.10358 0.02011 0.04148

(0.07404) (0.07524) (0.08231) (0.05163)SignedOI call −0.00007 −0.00007 −0.00032 −0.00037∗

(0.00005) (0.00005) (0.00020) (0.00019)SignedOI put −0.00009∗ −0.00009∗ −0.00074∗∗ 0.00048∗

(0.00004) (0.00004) (0.00027) (0.00022)Inv −0.05395

(0.04994)R2 0.05728 0.06691 0.06877 0.04977

Adj. R2 0.03247 0.03388 0.04426 0.02476Num. Obs. 118 118 118 118∗∗∗p < 0.001, ∗∗p < 0.01, ∗p < 0.05

Table 10: OI signed by direction of price change, monthly frequency

6 Conclusion

In this paper we showed that commodity options open interest predicts future pricesand provided theoretical underpinning for how this may be an indication of informedtrading. Topics for future research include how movements in open interest correlateswith macroeconomic activity—for example, if limited risk absorption capacity of thefutures markets causes hedging presure to spill into options markets, open interestsin calls (respectively, puts) might be pro-cyclical (respectively, counter-cyclical) withrespect to macroeconomic activity and futures prices. Analyzing the dynamics of volumeand open interest at different frequencies, from intraday to longer-term), to may allowone to see how options inventories build up over time, and how information contained ininventory positions gets incorporated into commodity options and futures prices.

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information in commodity options volume and open … · information in commodity options volume and...

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