Option Returns Research Articles

Forecasting the Distribution of Option Returns

We propose a method for constructing conditional option return distributions. In our model, uncertainty about the future option return has two sources: Changes in the position and shape of the implied volatility surface that shift option values (holding moneyness and maturity fixed), and changes in the underlying price which alter an option's location on the surface and thus its value (holding the surface fixed). We estimate a joint time series model of the spot price and volatility surface and use this to construct an ex ante characterization of the option return distribution via bootstrap. Our ORB (option return bootstrap) model accurately forecasts means, variances, and extreme quantiles of S&P 500 index conditional option return distributions across a wide range of strikes and maturities. We illustrate the value of our approach for practical economic problems such as risk management and portfolio choice. We also use the model to illustrate the risk and return tradeoff throughout the options surface conditional on being in a high or low risk state of the world. Comparing against our less structured but more accurate model predictions helps identify misspecification of risks and risk pricing in traditional no-arbitrage option models with stochastic volatility and jumps.

Risk-Neutral Moments and Cumulants in the Crude Oil Market

In this paper, we provide a comprehensive study on the higher-order moments and cumulants in the crude oil market, implied by options written on the United States Oil Fund (USO). We find strong evidence of their return predictability on USO excess returns. For example, the monthly adjusted R2 of the innovations in the volatility and the third cumulant are around 11%. In addition, we also find some evidence of their option return predictability by considering two different types of USO option returns. Finally, after sorting portfolios for the selected stocks directly related to crude oil, based on given moment and cumulant risk factors, we find a significantly positive return of the fourth cumulant portfolio in the oil industry, around 2% per month in average (24% per annum) during our sample period from 09 May 2007 to 29 April 2016.

Learning and forecasts about option returns through the volatility risk premium

We use learning in an equilibrium model to explain the puzzling predictive power of the volatility risk premium (VRP) for option returns. In the model, a representative agent follows a rational Bayesian learning process in an economy under incomplete information with the objective of pricing options. We show that learning induces dynamic differences between probability measuresP and Q, which produces predictability patterns from the VRP for option returns. The forecasting features of the VRP for option returns, obtained through our model, exhibit the same behaviour as those observed in an empirical analysis with S&P 500 index options.

Which Index Options Should You Sell?

This paper explores historical return and risk properties of equity-hedged options across the S&P 500 option surface. We evaluate returns by estimating alpha to the S&P 500 index, and we quantify risk using three metrics: return volatility, losses under stress tests, and conditional value at risk. We show that analyzing option risk-adjusted alphas using different risk metrics leads to significantly different conclusions. We find that the most compensated options to sell on the S&P 500 surface per unit of stress-test loss are front-month options with strikes near-the-money and moderately below the index level. We apply these results to evaluate return expectations for short volatility strategies, potential added return from option selection, and implications for variance swaps.

The Skewness and Kurtosis of European Options and the Implications for Trade Sizing

Long vanilla call option positions have unlimited profit potential and limited loss potential, and the opposite is true for short call option positions. Long vanilla puts do not have unlimited profit potential but, for commonly traded strikes, the maximum profit of a long put will be far greater than the maximum loss (the premium of the option). Again, the opposite is true for short put positions: their maximum loss is far greater than the potential gain. Equivalently, option returns are highly skewed and kurtotic. In this note, we calculate the skewness and kurtosis for European calls and puts. Next, using a power series expansion, we derive a simple approximation to the Kelly fraction for optimal trade sizing when returns are non-normal. Taken together, these two results are used to show that the higher order moments of option positions have an economically significant effect on optimal trade sizing when using the Kelly criterion.

Option implied beta and option return

ABSTRACTWe study the information content of option-implied betas for future equity option returns, using data on the S&P 500 index options and all of the component stock options. We find a significantly strong relation between option-implied betas and option returns cross-sectional. The paper presents evidence that call (put) option returns increase (decrease) with the option-implied betas of the underlying stock. A trading strategy of buying high (low) implied beta call (put) option portfolio and selling low (high) implied beta call (put) option portfolio generates a statistically and economically significant return. Our results are robustly persistent even after controlling for various cross-sectional effects and are not explained by the risk factors in asset pricing.

The Risk-Neutral Distribution of Option Returns

Options provide a payoff structure that is very attractive to lottery investors. Despite the growing importance of options in investors' portfolios, little is known about the actual distribution of option returns. We derive solutions for the risk-neutral variance, skewness, and kurtosis of call and put option returns and document several properties of these ex-ante moments. We find that the volatility, skewness, and kurtosis of both call and put returns are higher (lower) for options that are further out-of-the-money (in-the-money). The risk-neutral volatility of call returns is higher for options with shorter times to expiration, while the risk-neutral skewness and kurtosis are higher for calls with longer times to expiration. For put options, all three moments are higher for short-maturity options. The risk-neutral moments of call returns are increasing in the volatility of the underlying security, while the opposite is true for put returns. Risk-neutral call return moments exhibit strong positive time-series correlation, as do put return moments. Call return moments have strong negative time-series correlation with put return moments. Comparing the risk-neutral return moments to physical return moments, we find that the magnitudes of the risk-neutral and physical moments differ substantially, indicating risk premia associated with option return moments.

Learning and Forecasts about Option Returns through the Volatility Risk Premium

We use learning in an equilibrium model to explain the puzzling predictive power of the volatility risk premium (VRP) for option returns. In the model, a representative agent follows a rational Bayesian learning process in an economy under incomplete information with the objective of pricing options. We show that learning induces dynamic differences between probability measures P and Q, which produces predictability patterns from the VRP for option returns. The forecasting features of the VRP for option returns, obtained through our model, exhibit the same behaviour as those observed in an empirical analysis with S&P 500 index options.

Volatility and expected option returns: A note

We show analytically that the relationship between asset volatility and expected option return is ambiguous. Numerical results elaborate how the direction and magnitude of the relationship depend on asset beta and volatility levels, and option moneyness and maturity.

Call-Put Volatility Spreads and Option Returns in the KOSPI 200 Index Options Market

This study analyzes whether KOSPI200 option returns can be predicted by call-put implied volatility spreads. Doran et al. (2013) show that call-put implied volatility spreads predict the option returns of a specific moneyness as well as underlying asset returns in the US options market. Our study examines whether the same results are shown in the KOSPI200 options market, which has different characteristics in investor compositions and trading behaviors. According to the results, the call-put implied volatility spreads cannot predict the future returns of the underlying index significantly in the KOSPI200 options market. Only, the call-put spreads can predict the future option returns. More specifically, the increase in implied volatility spreads is able to predict the decrease in call option returns and the increase in put option returns in the KOSPI200 options market. This supports the overreaction hypothesis in all ranges of option moneyness, which is in contrast to the result of Doran et al. (2003).

Macroeconomic factors and index option returns

This study empirically investigates whether macroeconomic factors are priced in the cross-section of index option returns. Macroeconomic factors are extracted from a large panel of 132 economic activity indicators using dynamic factor analysis. The empirical analysis employs linear factor methodology with a factor structure including market return and macroeconomic factors. The results show that the risk premia on inflation, term spread, industrial production, and housing factors are significant. Further, business sales is a useful conditioning factor that drives variation in market betas. These extracted macroeconomic factors provide information that is not fully captured by Fama and French's (2015) investment and profitability factors.

Moneyness, Total, Systematic, and Idiosyncratic Volatility, and the Cross-Section of European Option Returns

We use a stochastic discount factor model to show that the expected returns of European options are not unambiguously positively or negatively related to their underlying asset’s volatility, a conclusion strikingly different from those derived in the prior literature. Higher idiosyncratic volatility always lowers (raises) expected call (put) returns through increasing the chance of non-zero option payoffs in high (low) stochastic discount factor states. Higher systematic volatility can raise or lower the expected call or put return since it produces both the above option-payoff effect, but also an oppositely-signed effect arising through a higher underlying asset risk. The strike price modulates the strengths of the oppositely-signed effects and thus determines the signs of both the effects of systematic volatility and of total volatility on expected option returns. Single-stock call option data strongly confirm the testable implications of our European option pricing theory.

Volatility and Expected Option Returns: A Note

Are options on more volatile assets expected to provide higher or lower return? Using analytics, we show the ambiguous nature of the answer when the volatility differential is due to the systematic/priced risk. Here the difference in the expected return of the assets also matters and has an effect on expected option return that is opposite to the case of idiosyncratic/unpriced risk. Our numerical results, based on more than 13 million parameter combinations, elaborate how the direction and magnitude of the net effect depends on the levels of asset beta and volatility and the moneyness and maturity of options. Accordingly, in analyzing the cross-section of returns on traded options, securities with embedded options, and other nonlinear derivatives, one should pay attention to the source of volatility differential, and the sample range/mix of betas, volatilities, and option moneyness and maturity.

Earnings announcements and option returns

Abstract While prior studies find that returns on option straddles are generally negative, we show that returns on straddles purchased prior to earnings announcements are actually positive. The earnings announcement impact is compounded when the pre-portfolio formation volatility is low (high) and the pre-expiration realized volatility is high (low). Apparently, the average option trader underestimates future volatility before forthcoming earnings announcements, particularly after a period of relatively low volatility, and overestimates future volatility after recent earnings announcements, particularly after a period of relatively high volatility. The overestimation of future volatility after recent earnings announcements also increases with the magnitude of the earnings surprise.

Stock Return Predictability of Out-of-the-Money Option Trading

This paper provides evidence of the market segmentation of stock and options. We find that informed out-of-the money (OTM) option trading measure, which is publicly available, predicts the returns of underlying stock and its at-the-money (ATM) options, but not the returns of OTM options. Specifically, higher OTM put-call trading volume ratio predicts negative returns of stock and ATM calls while predicting positive returns of ATM puts. The results are robust in large stock and not driven by short-selling costs. Using the OTM put-call volume ratio, we propose an implementable investment strategy that offers 20 bp weekly risk-adjusted stock returns (i.e., about 10% annually). Our findings support the segmentation between stock and option markets and between the option contracts in the same class.

Margin Requirements and Equity Option Returns

In equity option markets, traders face margin requirements both for the options themselves and for hedging-related positions in the underlying stock market. We show that these requirements carry a significant margin premium in the cross-section of equity option returns. The sign of the margin premium depends on demand pressure: If end-users are on the long side of the market, option returns decrease with margins, while they increase otherwise. Our results are statistically and economically significant and robust to different margin specifications and various control variables. We explain our findings by a model of funding-constrained derivatives dealers that require compensation for satisfying end-users’ option demand.

Contrasting patterns of environmental fluctuation contribute to divergent life histories among amphibian populations

Because it modulates the fitness returns of possible options of energy expenditure at each ontogenetic stage, environmental stochasticity is usually considered a selective force in driving or constraining possible life histories. Divergent regimes of environmental fluctuation experienced by populations are expected to generate differences in the resource allocation schedule between survival and reproductive effort and outputs. To our knowledge, no study has previously examined how different regimes of stochastic variation in environmental conditions could result in changes in both the temporal variation and mean of demographic parameters, which could then lead to intraspecific variation along the slow-fast continuum of life history tactics. To investigate these issues, we used capture-recapture data collected on five populations of a long-lived amphibian (Bombina variegata) experiencing two distinct levels of stochastic environmental variation: (1) constant availability of breeding sites in space and time (predictable environment), and (2) variable spatio-temporal availability of breeding sites (unpredictable environment). We found that female breeding propensity varied more from year to year in unpredictable than in predictable environments. Although females in unpredictable environments produced on average more viable offspring per year, offspring production was more variable between years. Survival at each ontogenetic stage was slightly lower and varied significantly more from year to year in unpredictable environments. Taken together, these results confirm that increased environmental stochasticity can modify the resource allocation schedule between survival and reproductive effort and outputs and may lead to intraspecific variation along the slow-fast continuum of life history tactics.

Order Flow and Expected Option Returns

ABSTRACTI show that the inventory risk faced by market‐makers has a first‐order effect on option prices. I introduce a simple approach that decomposes the price impact of trades into inventory risk and asymmetric information components. While both components are large for option trades, the inventory risk component is larger. Using the full panel of daily option returns, I find that option order imbalances attributable to inventory risk have five times larger impact on option prices than previously thought. Finally, I find that past order imbalances have greater predictive power than any other commonly used predictor of option returns.

Understanding Foreign Exchange Option Returns: The Information Content Of Volatility

According to general asset pricing theory, options should reward their holders for the systematic risk they are bearing. In this paper, we study the returns of foreign exchange options. We find that, by sorting options according to the distance of their implied volatility from the historical volatility, we obtain portfolios with positive average monthly returns. These returns are not explained by standard aggregate risk factors, which suggest either that additional risk factors should be accounted for, or that investors behavior differs from the traditional paradigm of rational agents.

The Determinants of the KOSPI200 Index Option Returns

This study examines the effects of crisis-related factors on the returns of KOSPI200 index options using a factor model, which was introduced by Constantinides, Jackwerth and Savov (2013). Three factors incorporating price jumps, changes in volatility, and volatility jumps are considered as the crisis-related factors. With the data for the period from 2004 to 2015, we find followings : First, most of the crisis-related factor premia are statistically significant, and their signs are consistent with those expected. Second, these crisis-related factors contribute to improve the understanding of the cross-sectional variation in KOSPI200 index option returns. Third, the crisis-related factor premia became much more significant after the global financial crisis in 2008. Finally, our empirical findings are robust to whether the long options and the in-the-money options are included in the sample or not, and to whether the factor premia are constrained to equal the corresponding premia estimated from the cross-section of equities.