Price Pressure in Commodity Futures or Informed Trading in Commodity Futures Options. Abstract

Transcription

1 Price Pressure in Commodity Futures or Informed Trading in Commodity Futures Options Alexander Kurov, Bingxin Li and Raluca Stan Abstract This paper studies the informational content of the implied volatility spread computed from options on commodity futures. We show that the implied volatility spread is mainly triggered by price pressure in the underlying commodity futures market: buying (selling) pressure in the futures market causes the futures price to deviate from its option-implied fundamental value, and consequently increases (decreases) the implied volatility spread, as calls become more (less) expensive relative to puts. We find that the spread negatively predicts the subsequent commodity futures returns, indicating a return reversal or correction of the temporary mispricing caused by price pressure in the commodity futures market. * Corresponding author. Department of Finance, College of Business and Economics, West Virginia University, P.O. Box 6025, Morgantown, WV 26506, bgli@mail.wvu.edu Alexander Kurov is a professor of finance in the Department of Finance, West Virginia University, Morgantown, West Virginia. Bingxin Li is an assistant professor of finance in the Department of Finance, West Virginia University, Morgantown, West Virginia. Raluca Stan is a doctoral student in finance in the Department of Finance, West Virginia University, Morgantown, West Virginia. 1

2 1. Introduction Put-call parity is a no arbitrage relation, which relates the value of a call option with a certain strike price and expiration to the value of a put option with the same strike price and expiration. Violations of put-call parity for European options reveal arbitrage opportunities (in the absence of transaction costs). However, in the case of American options, put-call parity is an inequality that provides no-arbitrage borders within which the bid and ask prices of the underlying asset can fluctuate. When accounting for transaction costs, margin requirements, taxes, lending rates not equal to borrowing rates, etc., deviations from put-call parity do not necessarily represent tradable arbitrage opportunities. Such deviations can be driven by market imperfections (particularly noise), short-sale constrains, or even trading activity of informed investors (Cremers and Weinbaum, 2010). This paper investigates whether the deviations from put-call parity for the market of options on commodity futures are informative about the subsequent price movements in the commodity futures market. We measure the deviations from put-call parity by the implied volatility spread of options on commodity futures. This spread is computed as the weighted average difference between Black (1976) implied volatility (adjusted for early exercise) of call and put options (with the same strike price and maturity), across option pairs. Similar to Cremers and Weinbaum (2010), we use as weights the average open interest in calls and puts. This paper aims to understand whether the implied volatility spread is caused by movements in the underlying commodity futures market (the market momentum hypothesis), and more precisely whether the spread is mainly driven by price pressure in the underlying futures market or by informed trading. We also investigate whether movements in the implied volatility spread can predict subsequent commodity futures returns. We focus on three different commodities: crude oil, natural gas, and gasoline. Our results are consistent across commodities and support the market momentum hypothesis, namely that movements in the underlying commodity futures market have a positive impact on the implied volatility spread of commodity futures options. Buying pressure in the commodity futures market might lead to an increase in the futures price above its option-implied fundamental value. These deviations from fundamental value are captured by greater implied volatility spreads because 2

3 calls become more expensive relative to puts. Similarly, selling pressure in the commodity futures market might lead to a decrease in the futures price below its option-implied fundamental value, resulting in a lower implied volatility spread because puts become more expensive relative to calls. We find that the deviations of futures prices from their fundamental values caused by price pressure tend to be reversed in subsequent periods. That is, the implied volatility spread can predict subsequent commodity futures returns and is strongly related to return reversals or corrections of the temporary mispricing caused by buying/selling pressure. Deviations from put-call parity have only been studied in the market of stock options. For example, Pinto et al. (2016) attribute deviations from put-call parity in stock options to price pressure in the underlying stock market. Similarly, Amin, Coval, and Seyhun (2004) find that systematic price pressure in the S&P 100 index affects the implied volatility spread of options written on this index (OEX). They show that strong positive (negative) past market returns lead to violations of the American put-call boundary conditions by increasing the OEX call (put) option prices relative to OEX put (call) option prices (and hence increase (decrease) the volatility spread). Deviations from put-call parity have also been associated to the informational efficiency of option markets relative to the market of the underlying asset. For example, Cremers and Weinbaum (2010) measure the deviations from put-call parity by the implied volatility spread between pairs of call and put options on stocks, and show that such spread can positively predict future stock return. They also show that the degree of predictability is larger (low) when liquidity is high (low) in the options market and low (high) in the stock market. Similarly, Atilgan, Bali, and Demirtas (2015) find that the implied volatility spread computed from options on the S&P 500 index can predict the future spot returns at the daily and weekly frequencies. We study the deviations from put-call parity in the market of options on commodity futures, and measure such deviations similar to Amin, Coval, and Seyhun (2004). That is, we measure deviations from put-call parity by the implied volatility spread computed from options on commodity futures. We find that volatility spread is mainly triggered by the price pressure in the underlying futures market, as the volatility spread negatively predicts the subsequent commodity futures returns. If the price pressure in the futures market gets reflected in the implied volatility spread of futures options, we would expect to see a correction of the futures mispricing in the 3

4 subsequent period. The fact that the volatility spread predicts a return reversal in the futures market does not necessarily exclude the presence of private information in the option market. But, if private information was the main trigger of the implied volatility spread (and not the temporary price pressure in the futures market) we should observe a positive relation between the volatility spread and the subsequent futures returns. Our results suggest that such relation is negative. The remainder of the paper is organized as follows. Section 2 provides an overview of the literature on information discovery in the options market, and on how deviations from put-call parity are related to price pressure and informed trading. Section 3 describes the data and the method used to compute the implied volatility spread. Section 4 provides evidence that deviations from put-call parity are related to momentum in the underlying futures market. Section 4 also contains a plan of future work, which should help us test for informed trading in the futures options market. Conclusions are summarized in section Background and Hypotheses 2.1. Information Discovery in Options Market Prior literature finds mixed results about the price discovery process in the options market. One strand of the literature argues that the options market leads the stock market in price discovery. For example, Manaster and Rendleman (1982) find that the implied stock price computed from the Black-Scholes option pricing model contains information about the equilibrium prices that is not fully reflected in the observed stock prices, and Kumar, Sarin and Shastri (1992) find abnormal option returns in the 30 minutes before block trades in the underlying stock. Another representative paper is Chakravarty, Gulen, and S. Mayhew (2004), who analyze stock and option data for 60 firms, and indicate that on average, the contribution of the option market to price discovery is around 17%. They use a modification of Hasbrouck s (1995) information share, and find that price discovery in the option market is closely related to stock volatility, trading volume, and spreads in both markets. However, compared to Chakravarty, Gulen, and S. Mayhew (2004), who include only call options in their analysis, Cremers and Weinbaum (2010) look at the information contained in both call and put prices, and report evidence that option prices can lead stock prices by days, not minutes. Similarly, Atilgan, 4

5 Bali, and Demirtas (2015) study the relation between options on a stock market index (S&P 500) and the underlying index, and find an information flow from the option market to the stock market. They claim that the implied volatility spread computed from puts and calls can predict the expected returns on the stock market index. Also, they show that the predictability/information flow is stronger when S&P 500 constituent firms announce their earnings, when the cash flow and the discount rate news are large in magnitude, or when the consumer sentiment index reaches extreme values. A second strand of the literature finds no evidence that option prices can lead stock prices (Chan, Chung, and Johnson, 1993; Stephan and Whaley, 1990). For example, Muravyev, Pearson, and Broussard (2013) argue that option market quotes do not contain significant information about future stock prices beyond what is already reflected in the current stock price. They use tick-by-tick data for 39 liquid US stocks and options on them, and focus on the events when the two markets disagree about the stock price, i.e. when the actual stock price is inconsistent with the option-implied stock price from put-call parity. Their findings show that option market quotes adjust to eliminate the disagreement, while the stock market behaves as if there were no disagreement. Such discrepancies can be caused by stock price movements, although the signed option volume in the option market can help eliminate the discrepancies. We contribute to this literature by studying the price discovery process, and particularly the informed trading issue, in two markets that are relatively new for this research area: the commodity futures market and the market of options on commodity futures. Boyd and Locke (2014) use a transactional based approach to study the price discovery in natural gas futures and futures options markets, and find little price discovery in both these markets. The approach used in the current paper is different, however. We compute the implied volatility spread from pairs of options on commodity futures with the same strike price and maturity. The implied volatility spread measures deviations from put-call parity and might contain information from the options market that is not already incorporated in the underlying futures market. That is, we plan to test whether such spread contains information that has not been fully reflected in the underlying futures market, and whether it has predictive power on the subsequent returns of the underlying commodity futures. 5

6 2.2. Deviations from Put-Call Parity The difference between the traded price of the underlying asset and its put-call parity implied value has been attributed in literature to either informational efficiency of option markets relative to the market of the underlying asset, or to price pressure in the market of the underlying asset. In the absence of transaction costs, put-call parity for European options links the value of the European puts and calls with the same strike price and expiration date, to the value of their underlying asset. A violation of the parity relation brings an arbitrage opportunity. However, in the case of American options, put-call parity is an inequality, and provides borders for the bid and ask prices of the underlying asset (given the bid and ask prices of the corresponding options). Consequently, this no-arbitrage range for the price of the underlying asset can be wide Price Pressure Pinto et al. (2016) study the stock and the stock options markets, and explain the deviation of the traded stock price from its fundamental option implied value as a consequence of price pressure in the stock market. Put-call parity for American options indicate a wide no-arbitrage range for the stock price to fluctuate. The midpoint of this range can be a noisy proxy for the fundamental value of the stock. In the presence of upward (downward) pressure on the stock, the traded stock price can be moved above (below) its fundamental value (proxied by the optionimplied midpoint), and so the price is expected to decrease (increase) in the short term. One of their main results is that the distance between the option-implied midpoint price and the actual traded stock price is a strong predictor of future stock returns. Amin, Coval, and Seyhun (2004) study the relation between S&P 100 and the options written on this index (OEX). They find that strong positive (negative) past market returns lead to violations of American put-call boundary conditions by increasing the call (put) option prices. That is, after large stock price increases (decreases), OEX calls are significantly overvalued (undervalued) relative to OEX puts. They claim that if systematic violations of the arbitrage bounds are a function of past stock returns, this provides strong evidence of systematic price pressure. While Pinto et al. (2016) predict future stock returns by using the difference between the traded stock price and the midpoint of the put-call parity relation implied range (i.e DOTS), Amin et al. (2004) predicts the subsequent stock returns by using the implied volatility spread 6

7 computed from pairs of calls and puts with the same strike price and expiration. However, the DOTS and the implied volatility spread measures are closely related. Low values of DOTS (traded stock price is below the option-implied price) most likely indicate temporary selling pressure, that is also reflected in greater put option prices relative to the call option prices (greater implied volatility for puts relative to the implied volatility of calls). Consequently, low DOTS is also associated with lower implied volatility spread (call minus put). Under perfect market conditions and for a given maturity, the implied volatility of calls should equal the implied volatility of puts on each date. When the implied volatility spread (call minus put) is positive, calls are overpriced relative to puts, and vice versa. Amin et al. (2004) show that the volatility spread increases after stock market increases and decreases after stock market decreases Informed Trading There are quite several papers in the literature discussing the informational role of options, including Grossman (1988) and John, Koticha, Narayann, and Subrahmanyam (2003). A representative theoretical paper is Easley, O Hara, and Srinivas (1998), who present a sequential trade model with both uninformed and informed traders. The uninformed investors trade for exogenous reasons in both the stock and the stock option markets, while the informed traders have to decide whether to trade in the stock market, the options market, or both. When the informed investors have positive (negative) signals, they can either buy (sell) the stock, buy (sell) a call, or sell (buy) the put. Due to private information, put-call parity does not need to be satisfied at each point in time, and the prices are not full information efficient. Also, the options price or the underlying price can carry information about subsequent prices. This is because by buying calls/selling puts (selling calls/buying puts), call prices increase (decrease) relative to put prices, and the trade itself carries positive (negative) information about future stock prices. The idea that deviations from put-call parity can predict subsequent returns on the underlying stock (as long as informed traders trade both in the stock and option markets) is also discussed by Cremers and Weinbaum (2010). They proxy such deviations from put-call parity by the implied volatility spread between pairs of call and put options (on stocks) with the same strike price and expiration, and show that such spread can predict future stock return. Also, they show that in the presence of more information risk, option prices are more likely to deviate from the 7

8 strict put-call parity. The degree of predictability is larger (low) when liquidity is high (low) in the options market and low (high) in the stock market. Similarly, Atilgan, Bali, and Demirtas (2015) find that the implied volatility spread computed from options on a stock market index (S&P 500) can predict the future spot returns at the daily and weekly frequencies. The informational content of the implied volatility spread is also studied by Chan, Ge, and Lin (2015), who focus their analysis around acquisitions. They find the volatility spread predicts positively the cumulative abnormal return of the acquirer, and such predictability is indeed stronger around actual merger and acquisition days, as compared to pseudo-event days. We hope to add to this literature by investigating the deviations from put-call parity for the market of options on commodity futures: options on crude oil futures, natural gas futures, and gasoline futures. We examine whether the deviations from put-call parity, as captured by the implied volatility spread of options on commodity futures, contain information that can predict the subsequent commodity futures returns. We also investigate whether such deviations can be mainly attributed to price pressure in the commodity futures market, or to informed trading in the futures options market. In other words, we want to mainly test the following two hypotheses. Hypothesis 1: Past commodity futures return exert important influence on the implied volatility spread of commodity futures options. More precisely, the volatility spread increases (decreases) after increases (decreases) in the commodity futures market (the market momentum hypothesis). Hypothesis 2: The implied volatility spread (as a measure of deviations from put-call parity) can predict subsequent commodity futures returns, being strongly related to return reversals. If the implied volatility spread is not mainly due to temporary buying/selling pressure, but is mainly due to news reflected in the futures option prices (before it is fully incorporated in the underlying futures prices), then we would not necessarily expect unusual past futures returns to predict the spread. Also, if the implied volatility spread predicts a return reversal in the futures market, this would not necessarily exclude the presence of private information in the option market. On the other hand, when private information is the main trigger of the implied volatility spread, and not the temporary buying/selling pressure in the futures market, then we should observe a positive relation between the volatility spread and the subsequent futures returns. 8

9 3. Data 3.1. Commodity Futures We use daily datasets of Chicago Mercantile Exchange (CME group, formerly NYMEX) crude oil futures and options data 1, Henry Hub natural gas futures and options data 2, and gasoline futures and options data 3. The dataset of crude oil options on futures starts from January 2, 1990, the dataset of natural gas options on futures starts from October 5 th, 1992, while the dataset of gasoline options on futures starts from May 16, Our analysis uses data available until May 30, We screen futures contracts based on patterns in trading activity. Open interest for futures contracts tends to peak approximately two weeks before expiration. Among futures and options with more than two weeks to expiration, the first six monthly contracts tend to be very liquid. For contracts with maturities over six months, trading activity is concentrated in the contracts expiring in March, June, September, and December. Following Trolle and Schwartz (2009), we therefore screen the available futures and options data according to the following procedure: we discard all futures contracts with 10 or fewer business days to expiration. Among the remaining, we retain the six shortest maturities. Furthermore, we choose the two shortest maturity contracts from those with expiration either in March, June, September or December. This procedure leaves us with eight futures contract series for each commodity which we label as M1, M2, M3, M4, M5, M6, Q1, Q2. Figure 1 (Panels A, B and C) plots the continuously compounded returns of commodity futures contracts with maturity one month (M1). It seems that the pattern followed by the returns of the one-month crude oil futures (Panel A), the natural gas futures (Panel B), and the gasoline 1 Crude oil futures contracts expire on the third business day prior to the 25 th calendar day (or the business day right before it if the 25 th is not a business day) of the month that precedes the delivery month. Crude oil options written on futures expire three business days prior to the expiration date of the futures. 2 Natural gas futures contracts expire three business days prior to the first day of the delivery month. Natural gas options written on futures expire on the business day immediately preceding the expiration of the underlying futures contract. 3 Gasoline futures expire on the last business day of the month preceding the delivery month. Gasoline options written on futures expire three business days before the expiration of the underlying futures contract. 9

10 futures (Panel C) indicate stationary series, which do experience some extreme positive and negative values during the recent financial crisis of The returns of the futures contracts with longer maturity follow a similar pattern as the returns reported in Figure 1, but have lower volatility than the returns of the futures with shortest maturity. [Insert Figure 1 about here] Descriptive statistics for the returns of the crude oil, the natural gas, and the gasoline futures of different maturities are summarized in Table 1. The crude oil futures with different maturities provide a similar average daily return across our sample period of about 0.03%. Likewise, natural gas futures and gasoline futures of various maturities have an average daily return of about 0.01%- 0.02%. A general pattern observed is that the futures returns of contracts with shorter maturity tend to be more volatile. Also, the futures contracts with shorter maturities tend to provide both the minimum and the maximum returns per day across our sample period. [Insert Table 1 about here] 3.2. Options on Commodity Futures We include options on the eight futures contracts mentioned above. Similar to Trolle and Schwartz (2009), for each option maturity, we consider eleven moneyness intervals ( , , , , , , , , , , and ), where the moneyness is defined as the option strike price divided by the price of the underlying futures contract. Among the options within a given moneyness interval, we select the one that is closest to the mean of the interval. We exclude options with prices lower than 5 cents. The crude oil options, the natural gas options and the gasoline options consist of American options on the corresponding futures contracts. The CME has also introduced European-style options, however the trading history is much shorter than for the American options. Since option pricing formula is designed for European option, we have to either convert American option prices to European option prices or use Binomial model to calculate implied volatility. The literature in the commodity market such as Trolle and Schwartz (2009), 10

11 Christoffersen, Jacobs, and Li (2016) apply the Barone-Adesi and Whaley (1987) formula to get implied volatility and they use only out of the money (OTM) and at the money (ATM) options to minimize the effect of errors in the early exercise approximation. For the purpose of our research, we need in the money (ITM) options as well. Thus, the Barone-Adesi and Whaley (1987) method might not be accurate enough for our setup. Other popular closed-form approximations include Ju and Zhong (1999) and Bjerksund and Stensland (2002). We apply the method of Bjerksund and Stensland (2002), and exclude those observations with implied volatility less than 1% or greater than 200%. We thus convert the American option prices to European option prices and get implied volatility. According to the put-call parity relation for European options on futures contracts (Hull, 2004), the following equality must hold: (1) where is the futures price at date 0, r denotes the risk-free rate, while c and p represent the European call and put prices on options with the same strike K and identical expiration date, T. The Black (1976) formula satisfies put-call parity for any assumed value of the volatility parameter σ, so that: (2) where and are the Black call and put prices as functions of the volatility parameter σ. From (1) and (2), we have that: (3) By definition, implied volatility is the specific number for which the following relations are satisfied: and, which implies that (4) Therefore, for European options, put-call parity is equivalent to the statement that Black (1976) implied volatilities of pairs call and put options on futures contracts must be equal. In our case, we consider American exchange-traded options, and the put-call parity relation takes the form of inequality. 11

12 No Arbitrage Bounds Implied by Put-Call Parity Put-call parity for American options on crude oil futures provides boundaries for the bid and ask price of the futures prices. The put-call parity relation for American options on futures contract is summarized below: (5) where is the futures price, C and P are the call and the put prices of the American style futures options, while r denotes the continuously compounded risk-free rate. Rearranging the relation we can get an expression for the lower and upper no-arbitrage borders of the futures price. ( ) (6) (7) Temporary price pressure can move a traded futures price away from its fundamental value (which can be proxied by the midpoint of these lower and upper no-arbitrage boundaries). However, as argued before, the implied volatility spread (computed from options with the same strike price and expiration) can capture this temporary mispricing in the futures prices, and can consequently predict return reversals/subsequent correction of the initial mispricing Implied Volatility Spread Following Amin, Coval, and Seyhun (2004) and Cremers and Weinbaum (2010), we refer to the difference between call and put implied volatilities as the volatility spread. Because we work with American options, relation (5) is no longer a no arbitrage relation, since the value of early exercise premium is incorporated explicitly, assuming lognormal distributions of futures prices. This is a similar procedure to Cremers and Weinbaum (2010). Differences between call and put implied volatilities do not represent pure arbitrage opportunities (unless the futures prices are outside the boundaries from (6) and (7)), but rather contain significant information about subsequent futures returns. 12

13 High call implied volatilities relative to put volatilities suggest that calls are expensive relative to puts, and high put implied volatility relative to call implied volatilities suggest the opposite. We compute the average difference in implied volatilities, or the volatility spread, between call options and put options (with the same strike and maturity) across option pairs. That is, for every day t, we compute the volatility spread (VS) as: ( ) (8) Where j refers to pairs of put and call options and thus indexes both strike prices and maturities, are weights, there are valid pairs of options on commodity futures on day t, and represents the Black (1976) implied volatility. Similar to Cremers and Weinbaum (2010), we eliminate option pairs for which either the call or put has zero open interest or bid price of 0. Also, the option quotes should allow the computation of implied volatilities (the call option bid-ask midpoint should not exceed the stock price less the present value of the strike price). The reported results use average open interest in the call and put as weights. Table 2 reports the descriptive statistics for the implied volatility spread (VS), computed as a weighted average across option pairs on futures contracts with all the aforementioned different maturities. The implied volatility spread tends to be greater on average for options on crude oil futures, reaching an average value of 0.12%, while the average VS for the natural gas and gasoline futures options is only 0.02% and 0.01%, respectively. Across our sample, the highest and the lowest values in the spread were reached in the natural gas futures options market, which is by far the most volatile out of the three different commodity markets. The weighted average volatility spread is positive for all markets, suggesting that call options were generally overvalued relative to their corresponding puts. In addition, unreported results indicate that the volatility spread computed from options with shorter maturity are greater on average, indicating that calls on the futures contracts with shorter maturity were usually overpriced relative to their corresponding puts. [Insert Table 2 about here] We provide a plot of the implied volatility spreads corresponding to each particular commodity in Panels A, B, and C, of Figure 2. There is some variability in the VS-s of all these commodity markets across time. Although the magnitude of the VS might look relatively small, 13

14 especially towards the second part of our sample (see for example the natural gas implied VS), even a small value of the spread captures important information about the buying/selling pressure in the underlying commodity futures market. It can also contain information relevant for the prediction of the subsequent commodity futures return. [Insert Figure 2 about here] 4. Methodology and Selected Empirical Results 4.1. Price Pressure The main focus of our study is to understand how deviations from put-call parity in the market of options on commodity futures (as captured by the implied volatility spread) are related to the momentum in the commodity futures market. That is, whether increases in the commodity futures market are followed by increases in the implied volatility spread, and vice versa. In addition, we also want to understand whether such movements in the implied volatility spread can predict subsequent returns in the commodity futures market, and whether such predictions are mainly due to price pressure in the futures market, or to informed trading in the futures option market. Whether the implied volatility spread is a consequence of price pressure or informed trading, and whether such spread can predict subsequent futures returns could depend on the level of liquidity from the futures and futures option markets. As such, if the volatility spread is a consequence of price pressure and captures temporary mispricing, such mispricing is unlikely to be quickly corrected in the presence of illiquid markets. Cremers and Weinbaum (2010) find evidence consistent with our argument. When studying the stock and the stock option markets, they show that the volatility spread has a stronger (weaker) predictability of the underlying stock return when liquidity is high (low) in the options market. In our analysis, we account for the liquidity of the commodity futures and the liquidity of their corresponding futures options. [Insert Table 3 about here] Table 2 also reports the descriptive statistics of the implied volatility spread per quintiles of option liquidity, where option liquidity is proxied by the daily options trading volume. As 14

15 noticed, greater liquidity in the option market is associated with greater values for the mean and the median of the implied volatility spread. Table 3 provides more details about the overall daily trading activity (i.e. volume) in the market of options on crude oil futures (Panel A), the market of options on natural gas futures (Panel B), and the market of options on gasoline futures (Panel C). For testing our hypotheses, we first investigate the overall relation between the implied volatility spread and the commodity futures returns over time, and then examine how sensitive such relation is to liquidity. All commodity futures returns and their corresponding volatility spreads are stationary (in the sense of not having a unit root), as indicated by the Augmented Dickey-Fuller Unit Root Tests reported in Table 4. [Insert Table 4 about here] We start our analysis by performing Granger causality tests between the commodity futures return and its corresponding weighted average implied volatility spread, for each of the commodities analyzed. The results are reported in Panel A of Table 5. As noticed, the crude oil futures returns do Granger cause the implied volatility spread, suggesting that movements in the crude oil futures market, including buying/selling pressure can indeed affect the implied volatility spread computed from options on the crude oil futures. In addition, there seems to be a feedback effect as well, since the implied volatility spread Granger causes the crude oil futures returns. In other words, information impounded into the spread can have a significant impact on the futures crude oil returns. The results are similar for the natural gas and gasoline futures and their corresponding volatility spreads. [Insert Table 5 about here] The Granger causality test provides evidence that both variables, the commodity futures return and the volatility spread, can affect each other. In order to capture this bi-directional effect, we estimate the vector autoregressive (VAR) model summarized in (9), where both the commodity futures return and the implied volatility spread enter as endogenous variables. The model is given by: 15

16 ( ) ( ) ( ) ( ) ( ) (9) The regression coefficients (α-s, β-s, γ-s, δ-s) capture the time-series relation between the endogenous and exogenous variables. The estimated results are computed using Choleski decomposition. We run the model for each commodity, and report the estimates in Panels A, B, and C of Table 6. [Insert Tables 6 about here] The estimated results for crude oil, natural gas, and gasoline, all illustrate a strong positive relation between the past commodity futures return and their corresponding implied volatility spread. This provides support for the market momentum hypothesis (hypothesis 1), according to which increases (decreases) in the futures commodity market are followed by increases (decreases) in the volatility spread. For example, a buying pressure in the underlying crude oil futures market will be reflected in a greater crude oil volatility spread, suggesting that calls become relatively more expensive relative to puts. Similarly, a selling pressure in the crude oil futures will lead to a smaller crude oil volatility spread, as put options on crude oil futures become relatively more expensive compared to their corresponding call options. The interpretation is similar for the natural gas and gasoline cases. However, if the implied volatility spread captures information about movements in the underlying commodity futures market, can it in fact predict the subsequent futures returns? The estimated results from the VAR models are not very indicative, since they alternate sign and significance. We look instead at the Granger causality test based on the reduced-form VAR in (9). The results of this test are reported in Panel B of Table 5. The Wald -statistic provides evidence of whether the sum of the lag-coefficients for the causing variable is significantly different from 0. Due to the fact that the sum of the coefficients on the lags of the causing variable is proportional to the long-run impact of that variable, this test can be viewed as a long-run Granger causality test. The sum of the coefficients indicates the direction of the (long-run) relationship, so that the test is associated with a clearer direction in the causation (similar procedure as in Chaboud, Chiquoine, Hjalmarsson, and Vega (2014)). The results indicate that the crude oil futures return have a significant positive (long- 16

17 run) impact on the implied volatility spread. This is consistent with our first hypothesis that the spread captures price pressure in the underlying futures market. In addition, the implied volatility spread seems to have a significant negative (long-run) impact on the crude oil futures return. This finding is in line with our second hypothesis, which postulates that the implied volatility spread can predict the subsequent commodity futures return, indeed suggesting a return reversal. The results are similar across all three commodities. Additional evidence in favor of the price pressure explanation is provided by the impulse response functions (IRFs) of the VAR model in (9). The IRFs for the crude oil, the natural gas, and the gasoline commodities are reported in Figures 3, 4, and 5. The results are similar across commodities. For example, Panel A of Figure 3 reveals a positive and significant accumulated response of the implied volatility spread to one standard deviation shock in the crude oil futures return. This positive relation emphasizes that the implied volatility spread at any point in time is a function of the past futures returns. The volatility tends to increase after increases in the crude oil futures market, and tends to decrease after decreases in the commodity futures market. More precisely, in presence of upward pressure in the crude oil futures market, the futures price can be pushed above its fundamental value (as proxied by the option implied midpoint as in Pinto, Grundy, Hameed, Van Der Heijden, and Zhu (2016) for instance). Such deviation is captured by a greater implied volatility spread, since calls become more expensive relative to puts. Similarly, if there is downward pressure in the crude oil futures market, the futures price will be pushed below its option-implied fundamental value, and this would be reflected in a lower implied volatility spread (puts become more expensive relative to calls). This is consistent with the expectations from our first hypothesis. Panels A of Figures 4 and 5 can be interpreted similarly. [Insert Figures 3, 4, and 5 about here] Panels B of Figures 3, 4, and 5, capture the accumulated response of the commodity futures return to one standard deviation shock in the corresponding implied volatility spread. As noticed in Panel B of Figure 3, a shock in the volatility spread leads to a negative impact on the crude oil futures returns across time. The negative impact of the spread on subsequent futures returns, or the return reversal phenomenon, seems to be quicker in the gasoline (Panel B, Figure 5) and the natural gas (Panel B, Figure 4) futures markets. Overall, the results indicate that 17

18 deviations of the futures prices from their fundamental values caused by price pressure, tends to be reversed/corrected in subsequent periods Does Liquidity matter? Greater liquidity can capture various aspects, including noise trading and informed trading. A greater proportion of liquidity brought up by noise traders will be reflected in greater deviations of the price from its fundamental value, and will be reflected in the volatility spread. Since such deviations are temporary, we would expect a correction of the mispricing in the subsequent periods. Liquidity can capture informed trading as well. However, in such cases, the information is impounded into the price through trading, and the fundamental value of the security changes (leading to a change in the implied volatility spread as well). In the presence of a positive (negative) signal about commodity futures, informed traders can for instance increase (decrease) the demand for commodity futures, and/or increase the demand for call (put) options on commodity futures. The implied volatility spread will increase. Informed trading will be translated into greater subsequent returns. Hence, we would expect a positive relation between the volatility spread and subsequent commodity futures returns if informed trading is the main trigger of the volatility spread. However, our preliminary results show evidence in favor of the price pressure hypothesis. The implied volatility spread can potentially be affected by liquidity from the commodity futures market and liquidity from the market of options on commodity futures. In our Table 2, we have seen that in general the spread tends to be higher for greater liquidity in the option market. Unreported results indicate that both the liquidity in the futures market and the futures option market influence the volatility spread to some extent. We investigate whether there is a significant difference in the means of the implied volatility spread for high vs. low levels of liquidity. The results are reported in Table 7, and indicate that on average, the volatility spread is significantly higher in presence of greater liquidity in the market of options on commodity futures (consistent results across all considered commodities). Unreported results indicate that on 18

19 average, for crude oil and gasoline, the implied volatility spread is not significantly different in the presence of high vs. low liquidity in the commodity futures market. We investigate whether the predictability of the volatility spread on the subsequent futures return depends on the liquidity in the market of options on commodity futures. We run a similar VAR model as in relation (9), where the endogenous variables are,,. The notations were previously introduced, while is a dummy variable taking values of 1 for days when the trading volume of the commodity futures options is greater than its sample median, and 0 otherwise. We also examine whether the commodity futures return has a stronger impact on the volatility spread in the presence of high option liquidity. We run a similar VAR model as in (9), where the endogenous variables are,,. Because of limited space, we do not report the estimated VAR coefficients. We estimate both VAR models for each individual commodity, and compute the Wald -statistic (similar to our results in Table 5) to test whether the sum of the lag-coefficients for ( or is significantly different from 0. These statistics are reported in Table 8 and show that the crude oil futures return does not have a significantly stronger impact on the crude oil volatility spread in the presence of high option market liquidity. However, the crude oil volatility spread has a significantly stronger impact on the subsequent crude oil futures return in the presence of higher liquidity in the crude oil futures options. For natural gas and gasoline, we do not obtain stronger predictability in the presence of high option liquidity. In general, the results show that the option market liquidity does not affect the strength of the relation between commodity futures returns and the volatility spread computed from options on commodity futures Information efficiency in the futures option market? If the implied volatility spread were mainly triggered by informed trading, such private information would be reflected in the futures option market before being fully reflected in the underlying futures market. We would expect that such private information has a permanent 4 Unreported results show that the liquidity in the futures market has a significant impact on the relationship between commodity futures and volatility spread computed from options on commodity futures. However, such liquidity does not seem to strengthen or weaken the predictability of the volatility spread on the subsequent futures return. 19

20 rather than temporary impact on the futures market. In other words, we would expect that the implied volatility spread would positively predict subsequent future returns. If investors have positive (negative) expectations about futures market conditions, they will increase the demand for calls (puts) and/or reduce their demand for puts (calls). This would increase the call implied volatility relative to the put implied volatility, and would hence lead to a greater volatility spread, which will be followed by better prospects for the futures market. If investors private information is genuine, we would expect to see greater spread followed by greater futures returns. However, our results show the opposite pattern, i.e. greater implied volatility spread leads to subsequent return reversals. Our preliminary results indicate that the volatility spread leads to a correction in the temporary mispricing caused by price pressure in the commodity futures market Commodity Announcement and Non-Announcement Days While this predictability pattern is important for every investor trading in the commodity futures market, we would expect that it becomes particularly important around periods of public information releases. Examples of such public releases that are relevant for the commodities markets analyzed in our paper are: Total Change in Crude Oil Inventories, Total Change in Distillate Inventories, US Working Natural Gas Change in Estimated Storage, Total Change in Gasoline Inventories Data. These are examples of weekly public information releases by the Energy Information Administration (EIA). For instance, for the weekly announcement DOE Total Change in Crude Oil Inventories, the EIA Crude Oil Inventories measures the weekly change in the number of barrels of commercial crude oil held by US firms, and reports these every Wednesday, at 10:30 am for the previous week ending Friday. These inventory levels affect petroleum products and even inflation. If the implied volatility spread can help investors anticipate such price movements before the public inventory announcement is released, then investors can engage in a valuable profitable strategy. More precisely, if a greater (lower) implied volatility spread signals stronger (weaker) demand for crude oil, lower (greater) than expected inventories, and higher (smaller) expected futures crude oil prices, then one can lock in profit by taking a long (short) position in the crude oil futures market before the crude oil inventory announcement is released. 20

21 We analyze all the above mentioned commodity announcements, and test whether the predictability of the implied volatility spread on subsequent commodity futures returns is stronger during commodity announcement days relative to non-announcement days. If this is the case, this would indicate an information flow from the options market to the underlying futures market. It would show that the volatility spread can predict subsequent futures returns through private information. We performed such test for the crude oil, the natural gas and the gasoline futures, and have obtained that the predictability of the volatility spread on subsequent futures returns is not different during announcement vs. non-announcement days (unreported results). Such result does not provide evidence in favor of the informed trading being a major trigger of the implied volatility spread. Plan of future work An alternative way for testing whether the implied volatility spread is driven by informed trading would be to examine whether the implied volatility spread the day before each commodity announcement can predict movements in the commodity futures returns for the window (-90 min, -5 min) before each announcement. If such predictability exists, and the movements in the futures price before the public release follow the same pattern as the movements in the price after the release, this would be consistent with investors being able to lock in a profitable strategy by using information contained in the volatility spread. To test this, we can run the regression in (10) for both announcement and non-announcement days, where denotes the continuously compounded (i.e. log) return over the interval 9:00 am to 10:25 am of day t, while denotes the implied volatility spread on day t-1. (10) One might argue that our results can potentially be affected by announcements being released somewhat close to the beginning of the US trading hours (9:00 to 17:00 ET), period characterized by higher information asymmetry and higher adverse selection risk, relative to later hours during the trading day. We do not claim that information asymmetry will not affect the future returns at the beginning of the trading day. What we try to point out is that if the relation between volatility spread and the futures returns in the interval 9:00 am to 10:25 am were merely 21

22 a matter of market imperfections, and not necessarily an information story, we should not see any significant difference in the reaction of commodity futures returns to volatility spread between announcement and non-announcement days. In fact, we obtain no significant difference (unreported results) in the response of the commodity futures returns to volatility spread between announcement and non-announcement days The Implied Volatility Spread and the Commodity Announcement Surprises There is some evidence in literature about informed trading in the crude oil futures market, more precisely evidence of information leakage before crude oil inventory announcements. For example, Luo and Kang (2014) find that inventory shocks have explanatory power on the nearby futures returns in the pre-announcement period. We want to focus on the futures option market instead, and study whether the deviations from put-call parity, as captured by the implied volatility spread, can predict the surprises in commodity announcements. As argued before, such deviations can come mainly from price pressure in the crude oil futures market, or from informed trading in the options on futures market. If the implied volatility spread captures private information from informed trading, we would expect to find that the volatility spread has ability to predict the surprise in the commodity announcement. We want to perform such analysis for the crude oil, the natural gas, and gasoline announcements. For example, in the case of crude oil, we plan to focus on the inventory announcement days, and actually test whether the implied volatility spread from the previous day can predict the crude oil inventory surprise. We can compute the inventory announcement surprise, as the difference between the actual released value of inventory levels, and the expected value of the economic statistic. Then we standardize the announcement surprise as follows: where is the announced value of the inventory announcement, is the expected value of the inventory release based on the Bloomberg median forecast, while is the sample standard deviation of. 22

23 If the implied volatility spread can indeed predict the crude oil inventory surprise, then the volatility spread contains information that has not been already incorporated in analysts forecasts of the crude oil inventory levels. For testing whether the volatility spread can predict crude oil inventory surprises, we plan to estimate the following model:, where is the standardized inventory surprise, and is the implied volatility spread the day before the announcement day. A significant negative estimated β would be consistent with volatility spread being able to predict the crude oil inventory surprise. If informed investors trading in the futures option market have positive information about the subsequent crude oil futures market (expect a negative inventory surprise), they would demand more calls relative to puts, and hence the implied volatility spreads would be wider. Thus, a greater implied volatility spread can be associated with negative inventory surprises. 5. Conclusion The traded price of a commodity futures contract is typically different from its put-call parity implied fundamental value. This paper investigates whether these deviations from put-call parity in the market of options on commodity futures can be mainly attributed to price pressure in the commodity futures or to the information efficiency of options on commodity futures. We study the market of options on commodity futures (crude oil, natural gas, and gasoline) and measure deviations from put-call parity by the implied volatility spread between call and put options with the same strike price and expiration. We investigate how this spread is related to the momentum in the commodity futures market and whether movements in the implied volatility spread can predict subsequent returns in the commodity futures market. We find that the commodity futures returns have a significant and positive impact on the implied volatility spread. In the presence of buying pressure in the commodity futures market, the futures price can be pushed above its fundamental value. These deviations from fundamental value are captured by greater implied volatility spreads because calls become more expensive relative to puts. Similarly, if there is selling pressure in the commodity futures market, the futures price will be pushed below its option-implied fundamental value, resulting in a lower implied volatility spread because puts become more expensive relative to calls. We find that the deviations of 23

24 futures prices from their fundamental values caused by price pressure tend to be reversed in subsequent periods. That is, the implied volatility spread can predict subsequent commodity futures returns and is strongly related to return reversals or corrections of the temporary mispricing due to buying/selling pressure. Overall, our preliminary findings indicate that movements in the implied volatility spread are mainly associated with price pressure in the commodity futures market. We do not rule out the possibility that there is some private information in the market of options on commodity futures, but we argue that it is not the main trigger of the implied volatility spread. If it were the main trigger, we should expect that the volatility spread positively predicts subsequent futures returns. However, our results indicate return reversals and a correction in the temporary mispricing due to buying/selling pressure in the underlying futures market. 24

25 References Amin, K., Coval, J., Nejat Seyhun, H., 2004, Index Options Prices and Stock Market Momentum, The Journal of Business, 77(4), Atilgan, Y., Bali, T., Demirtas, O., 2015, Implied Volatility Spreads and Expected Market Returns, Journal of Business and Economic Statistics, 33(1), Barone-Adesi, G. I, and Robert E. Whaley, 1987, Efficient analytic approximation of American option values. The Journal of Finance 42.2: Black, F., 1976, The pricing of commodity contracts, Journal of Financial Economics, 3, Boyd, N., Locke, P., 2014, Price Discovery in Futures and Options Markets, Journal of Futures Markets, 34(9), Bjerksund, Petter, and Gunnar Stensland, 2002, Closed form valuation of American options. Chaboud, A., Chiquoine, B., Hjalmarsson, E., Vega, C., 2014, Rise of the Machines: Algorithmic trading in the Foreign Exchange Market, The Journal of Finance, 69(5), Chakravarty, S., Gulen, H., and S. Mayhew, 2004, Informed trading in stock and option markets, Journal of Finance, 59, Chan, K., Ge, L., Lin, T.C., 2015, Informational Content of Options Trading on Acquirer Announcement Return, Journal of Financial and Quantitative Analysis, 50(5), Chan, K., Chung, Y.P., Johnson, H., 1993, Why Option Prices Lag Stock Prices: A Trading- Based Explanation, Journal of Finance, 48, Cremers, M., Weinbaum, D., 2010, Deviations from Put-Call Parity and Stock Return Predictability, Journal of Financial and Quantitative Analysis, 45(2), Christoffersen, P., Jacobs, K., Li, B., 2016, Dynamic jump intensities and risk premiums in crude oil futures and options markets, Journal of Derivatives, 24(2), Easley, D., O Hara, M., Srinivas, P.S., 1998, Option Volume and Stock Prices: Evidence on Where Informed Traders Trade, Journal of Finance, 53, Goncalves-Pinto, L., Grundy, B., Hameed, A., Van Der Heijden, T., Zhu, Y., 2016, Informed Trading in Options or Price Pressure in Stock? Connecting the DOTS in Option-Based Return Predictability, Working Paper. Grossman, S., 1988, An Analysis of The Implications for Stocks and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies, Journal of Business, 61, Hasbrouck, J., One security, many markets: Determining the contributions to price discovery. Journal of Finance, 50,

26 John, K., Koticha, A., Narayanan, R., Subrahmanyam, M., 2003, Margin Rules, Informed Trading in Derivatives, and Price Dynamics, Working Paper, New York University. Ju, Nengjiu, and Rui Zhong, 1999, An approximate formula for pricing American options. The Journal of Derivatives 7.2: Kumar, R., Sarin, A., Shastri, K., 1992, The Behavior of Option Price around Large Block Transactions in the Underlying security, Journal of Finance, 47, Luo, H., Kang, S.B., 2014, How does the Crude Oil Market Impound Inventory News Information? A Closer Look at High-frequency Prices and Trading Activities, Working Paper. Manaster, S., Rendleman, R., 1982, Option Prices as Predictors of Equilibrium Stock Prices, Journal of Finance, 37, Muravyev, D., Pearson, N. D., and J. P. Broussard, 2013, Is there price discovery in equity options? Journal of Financial Economics, 107, Stephan, J., Whaley, R., 1990, Intraday Price Change and Trading Volume Relations in the Stock and Stock Option Markets, Journal of Finance, 45, Trolle, Anders B., and Eduardo S. Schwartz, 2009, Unspanned stochastic volatility and the pricing of commodity derivatives. Review of Financial Studies 22.11:

27 Appendix According to Black (1976), the European call and put prices for futures options are given by: [ ] [ ] Where ( ) and. Thus, the following relation must hold: 27

28 Table 1. Descriptive Statistics of Commodity Futures This table summarizes the descriptive statistics of the continuously compounded daily futures return for different maturities and for different commodities: crude oil futures (Panel A), natural gas futures (Panel B), and gasoline futures (Panel C). Panel A. Crude Oil Futures FUT M1 FUT M2 FUT M3 FUT M4 FUT M5 FUT M6 FUT Q1 FUT Q2 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel B. Natural Gas Futures FUT M1 FUT M2 FUT M3 FUT M4 FUT M5 FUT M6 FUT Q1 FUT Q2 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel C. Gasoline Futures FUT M1 FUT M2 FUT M3 FUT M4 FUT M5 FUT M6 FUT Q1 FUT Q2 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N

29 Table 2. Descriptive Statistics of the Implied Volatility Spread (VS) This table summarizes the descriptive statistics of the weighted average implied volatility spread computed for different commodity markets: crude oil, natural gas, and gasoline. The descriptive statistics are summarized for the entire sample and per quintiles of trading volume in the corresponding market of options on commodity futures. In order to get implied volatilities, American option prices are converted to European option prices. The implied volatility is computed by using the method of Bjerksund and Stensland (2002). The implied volatility spread (VS) is computed as the average difference in implied volatilities between call options and put options (with the same strike and maturity) across option pairs. That is, for every day t, the volatility spread (VS) is computed as ( ) where j refers to pairs of put and call options and thus indexes both strike prices and maturities, are weights, there are valid pairs of options on commodity futures on day t, and represents the Black (1976) implied volatility. Option pairs for which either the call or put has zero open interest or bid price of 0 are eliminated. Average open interest in the call and put are used as weights. Panel A. Options on Crude Oil Futures Full Sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel B. Options on Natural Gas Futures Full Sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel C. Options on Gasoline Futures Full Sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N

30 Table 3. Descriptive Statistics of Option Trading Volume This table summarizes the descriptive statistics of the daily option trading volume for options on crude oil futures (Panel A), options on natural gas futures (Panel B), and options on gasoline futures (Panel C). The statistics are presented for the full sample per quintiles of the option trading volume. Panel A. Options on Crude Oil Futures Full sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel B. Options on Natural Gas Futures Full sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N Panel C. Options on Gasoline Futures Full sample Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis N

31 Table 4. Augmented Dickey-Fuller Unit Root Tests This table reports the results of the ADF test for the presence of a unit root in the commodity futures with 1 month maturity (Panel A), and their corresponding implied volatility spread. Panel A. Null hypothesis: FUTret M1 has unit root t-statistic P-value Crude Oil FUTret M *** Natural Gas FUTret M *** Gasoline FUTret M *** Panel B. Null hypothesis: VS has unit root t-statistic P-value Crude Oil *** Natural Gas *** Gasoline ***

32 Table 5. Granger Causality Tests This table reports the Granger Causality Test between commodity futures returns and its corresponding weighted average implied volatility spread computed from options on commodity futures. Panel A reports the results of an F- test. Panel B reports the results of a Wald -statistic, which provides evidence of whether the sum of the lagcoefficients for the causing variable is significantly different from 0. Due to the fact that the sum of the coefficients on the lags of the causing variable is proportional to the long-run impact of that variable, this test can be viewed as a long-run Granger causality test. The sum of the coefficients indicates the direction of the (long-run) relationship, so that the test is associated with a clearer direction in the causation (similar procedure as in Chaboud, Chiquoine, Hjalmarsson, and Vega (2014)). Panel A: F-tests : VS does not Granger Cause FUTret M1 : FUTret M1 does not Granger Cause VS F-Statistic P-value F-Statistic P-value Crude Oil ** *** Natural Gas *** ** Gasoline *** *** Panel B: - tests (based on the VAR models reported in Panels A, B, and C of Table 6) Tests of Futures Return causing Volatility Spread Crude Oil Natural Gas Gasoline Sum of Coefficients on FUTret lags *** ** *** χ 2 (Sum=0) p-value Tests of Volatility Spread causing Futures Returns Sum of Coefficients on VS lags *** *** *** χ 2 (Sum=0) p-value

33 Table 6. VAR models for the commodity markets This table summarizes the estimated results of a VAR model of crude oil futures returns ( and crude oil implied volatility spread (, with 20 lags. The sample period covered is 03/01/1991 to 05/30/2014. Estimates in bold are significant at the 10% level or higher. T-statistics are provided in parentheses beside the estimates. *, **, and *** denote significance at 10 percent, 5 percent, and 1 percent levels, respectively. Panel A. Crude Oil Futures and Options on Crude Oil Futures FUTret t t-stat VS t t-stat FUTret t (-0.47) *** (10.87) FUTret t ** (-2.52) *** (4.55) FUTret t (0.53) *** (4.69) FUTret t (-0.52) ** (2.38) FUTret t ** (-1.97) *** (3.88) FUTret t ** (-2.13) ** (2.12) FUTret t (-0.71) ** (2.31) FUTret t (-0.55) * (1.95) FUTret t (-1.52) (1.02) FUTret t (0.70) ** (2.33) FUTret t (-0.66) (1.49) FUTret t (1.18) ** (2.56) FUTret t * (1.92) ** (2.49) FUTret t *** (3.42) *** (3.31) FUTret t ** (2.24) (0.67) FUTret t *** (2.77) ** (2.53) FUTret t (-1.57) (0.58) FUTret t (-0.69) (-0.93) FUTret t (-0.27) (-0.30) FUTret t (0.99) ** (-2.28) 2

34 Table 5 Panel A contd. FUTret t t-stat VS t t-stat VS t (-0.98) *** (31.93) VS t (1.03) *** (13.90) VS t (0.43) *** (5.40) VS t (-0.53) *** (3.30) VS t (0.16) * (1.74) VS t (-1.18) (0.22) VS t ** (2.11) (1.05) VS t (0.26) (0.00) VS t (0.65) ** (2.07) VS t ** (-2.53) (-1.33) VS t ** (-2.16) (-1.07) VS t * (1.73) (-1.57) VS t (-1.07) (0.70) VS t (-0.22) (1.21) VS t (-0.04) (0.64) VS t (-0.96) (-0.18) VS t (1.61) (1.59) VS t (1.63) *** (2.58) VS t (0.31) (1.22) VS t (-0.69) * (1.88) intercept (1.26) *** (3.63) R % 79.13% 3

35 Panel B. Natural Gas Futures and Options on Natural Gas Futures FUTret t t-stat VS t t-stat FUTret t *** (-4.98) ** (2.50) FUTret t (0.20) * (1.83) FUTret t (-0.47) *** (2.58) FUTret t (0.04) (-0.10) FUTret t (-1.32) (1.00) FUTret t (-1.67) (-0.33) FUTret t (0.31) (-0.05) FUTret t (-1.50) (-0.66) FUTret t (0.93) (0.70) FUTret t * (1.78) (0.62) FUTret t (-1.32) ** (2.44) FUTret t *** (2.74) (1.10) FUTret t (0.67) (0.58) FUTret t (1.60) (1.13) FUTret t (-1.11) (0.35) FUTret t (0.53) (1.67) FUTret t (0.22) (1.67) FUTret t (1.22) (0.39) FUTret t ** (2.11) (1.30) FUTret t * (1.78) (0.40) 4

36 Table 5 Panel B contd. FUTret t t-stat VS t t-stat VS t ** (2.18) *** (18.06) VS t *** (-5.76) *** (3.87) VS t (1.21) *** (-8.39) VS t *** (3.01) *** (6.81) VS t (-0.18) *** (6.20) VS t *** (-3.99) *** (-15.62) VS t *** (3.55) *** (7.52) VS t ** (-2.39) *** (-2.90) VS t (-0.47) *** (-3.07) VS t (0.5) ** (2.43) VS t (-1.50) (0.16) VS t (-0.40) *** (-3.00) VS t * (1.87) *** (8.06) VS t (0.08) (1.50) VS t (-1.17) *** (-6.96) VS t (-0.97) *** (-3.94) VS t *** (-3.52) *** (-9.25) VS t (0.46) *** (7.32) VS t ** (2.52) * (1.82) VS t (-1.42) *** (-3.34) intercept (0.50) ** (2.54) R % 17.86% 5

37 Panel C. Gasoline Futures and Options on Gasoline Futures FUTret t t-stat VS t t-stat FUTret t (-0.87) *** (6.19) FUTret t (0.22) (0.98) FUTret t (-1.38) (-0.12) FUTret t * (1.81) (0.97) FUTret t (1.05) ** (2.53) FUTret t (0.06) (-1.36) FUTret t (0.44) (0.67) FUTret t (0.95) (-0.38) FUTret t ** (2.01) ** (2.14) FUTret t *** (3.63) *** (2.86) FUTret t ** (2.08) *** (2.94) FUTret t (0.88) (0.38) FUTret t (0.70) ** (2.19) FUTret t (0.23) (0.13) FUTret t (-1.18) (0.07) FUTret t (1.35) (0.55) FUTret t (-0.17) (0.02) FUTret t (0.42) (-1.47) FUTret t (0.10) * (-1.88) FUTret t (-0.28) *** (-2.58) 6

38 Table 5 Panel C contd. FUTret t t-stat VS t t-stat VS t (-0.21) *** (3.27) VS t *** (3.55) *** (5.88) VS t *** (-3.71) *** (-3.87) VS t * (-1.90) ** (-2.12) VS t (1.63) * (1.84) VS t (-0.04) (1.22) VS t (-0.07) (-0.02) VS t (0.50) (-0.64) VS t (-0.67) (0.87) VS t (-1.63) *** (-2.82) VS t ** (2.42) ** (2.46) VS t (1.50) ** (1.96) VS t (0.53) (0.56) VS t (1.40) ** (2.56) VS t *** (-4.01) *** (-2.74) VS t (0.34) (-1.21) VS t (0.88) (1.20) VS t * (1.73) *** (3.29) VS t (-1.46) *** (-3.37) intercept (0.53) (0.88) R % 87.41% 7

39 Table 7. The Average Implied Volatility (IV) Spread during Low vs. High Option Liquidity This table summarizes the estimated results from testing the difference in the means of Implied Volatility (IV) Spread during low and high option liquidity. The liquidity is proxied by the trading volume of the options written on crude oil futures (panel A), natural gas futures (Panel B), or gasoline futures (Panel C). The sample period covered is 03/01/1991 to 05/30/2014 for the options written on crude oil futures, 10/09/1992 to 05/30/2014 for the options written on natural gas futures, and 05/16/2006 to 05/30/2014 for options written on gasoline futures. The choice of the sample period in each case is driven by the availability of options and futures data. Estimates in bold are significant at the 10% level or higher. *, **, and *** denote significance at 10 percent, 5 percent, and 1 percent levels, respectively. Option Volume Panel A. Crude Oil Futures and Options on Crude Oil Futures Mean of IV Spread Low Option Volume High Option Volume (Low Volume-High Volume ) *** Equality of Means t Value Pr > t Pooled (Variances are Equal) <.0001 Satterthwaite (Variances are Unequal) <.0001 Equality of Variances F Value Pr > F Folded F Panel B. Natural Gas Futures and Options on Natural Gases Futures Option Volume Mean of IV Spread Low Option Volume High Option Volume (Low Volume-High Volume ) *** Equality of Means t Value Pr > t Pooled (Variances are Equal) Satterthwaite (Variances are Unequal) Equality of Variances F Value Pr > F Folded F <

40 Panel C. Gasoline Futures and Options on Gasoline Futures Option Volume Mean of IV Spread Low Option Volume High Option Volume (Low Volume-High Volume ) *** Equality of Means t Value Pr > t Pooled (Variances are Equal) <.0001 Satterthwaite (Variances are Unequal) <.0001 Equality of Variances F Value Pr > F Folded F 2.07 <

41 Table 8. Test while accounting for Option Liquidity This table reports the results of a Wald -statistic, which provides evidence of whether the relation between commodity futures returns and its corresponding weighted average implied volatility spread computed from options on commodity futures becomes stronger in presence of high option liquidity. is a dummy variable taking values of 1 for days when the trading volume of the commodity futures options is greater than its sample median, and 0 otherwise. Due to the fact that the sum of the coefficients on the lags of the causing variable is proportional to the long-run impact of that variable, this test can be viewed as a long-run Granger causality test (similar procedure as in Chaboud, Chiquoine, Hjalmarsson, and Vega (2014)). Tests of Futures Return causing Volatility Spread Crude Oil Natural Gas Gasoline χ 2 (Sum Coeff. FUTret lags =0) 97.04*** 22.82*** 24.09*** χ 2 (Sum Coeff. FUTret* lags =0) Tests of Volatility Spread causing Futures Returns χ 2 (Sum Coeff. VS lags =0) ** 33.89*** χ 2 (Sum Coeff. VS* lags =0) 37.85***

42 Figure 1 This figure plots the continuously compounded returns of commodity futures contracts (crude oil futures- in Panel A, natural gas futures- in Panel B, and gasoline futures- in Panel C) with maturity one month (M1). Panel A. Futures Returns of 1 Month WTI Crude Oil Futures Contract Panel B. Futures Returns of 1 Month Natural Gas Futures Contract 11

43 Panel C. Futures Returns of 1 Month Gasoline Futures Contract 12