Option Returns Research Articles

Trading Activity and Bid-Ask Spreads of Individual Equity Options

We empirically examine the impact of trading activities on the liquidity of individual equity options measured by the proportional bid-ask spread. There are three main findings. First, the option return volatility, defined as the option price elasticity times the stock return volatility, has a much higher power in explaining the spread variations than the commonly considered liquidity determinants such as the stock return volatility and option trading volume. Second, after controlling for all the liquidity determinants, we find a maturity-substitution effect due to expiration cycles. When medium-term options (60-90 days maturity) are not available, traders use short-term options as substitutes whose higher volume leads to a smaller bid-ask spread or better liquidity. Third, we also find a moneyness-substitution effect induced by the stock return volatility. When the stock return volatility goes up, trading shifts from in-the-money options to out-of-the-money options, causing the latter's spread to narrow.

Overpriced Puts Puzzle in KOSPI 200 Options Market

The purpose of this paper is to examine the argument that the put options traded in the exchanges are too high, compared to the asset prices based on the classical CAPM model, and thus the short position of the put option would make a significant profit from trading. In order to explore the earlier report, this paper, using the KOSPI 200 index options market price, estimates the historical rate of return on several option trading strategies such as naked option, protective put, covered call, straddle, and strangle. Secondly this paper compares the historical rates of return on the option trading strategies and Sharpe ratios with those generated by Monte-Carlo simulation and examines whether the historical option returns are inconsistent with Black-Scholes model, Jump-diffusion model, Stochastic Volatility model, or Stochastic Volatility with Jump model. Thirdly, this paper computes the optimal asset allocation ratio among the risk-free asset, risky assets, and option trading strategies in the viewpoint of rational investors who maximize the CRRA utility function. The results show that the historical returns on short position of ATM and OTM puts are too high to explain based on the classical CAPM, and the optimal allocation ratios among put, risky asset, and the risk-free asset are different from those derived using Monte-Carlo simulation.

Expected Call Option Returns: A Reconciliation of Stock and Index Options and the Significance of Holding Period

Coval and Shumway (2001) show that under certain simple assumptions the expected returns to call options should be higher than the expected returns to their underlying assets, and increasing in the strike price. The authors find empirical support for these predictions by studying index option returns over the January 1990 to October 1995 period. Ni (2008), however, demonstrates that this does not hold empirically for stock options, where returns are relatively low and decreasing in the strike price. The author finds some evidence that a preference for idiosyncratic skewness in returns might explain this result. In this paper I show that the different results documented in these two papers are related to the differences in methods used to determine the moneyness of the options and the holding periods used to calculate the returns. Furthermore, when the bid-ask spread is included in the calculation of holding period returns a consistent pattern of low returns which are decreasing in the strike price emerges for both stock and index Calls.

The Price of Correlation Risk: Evidence from Equity Options

ABSTRACTWe study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the cross‐section of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limits‐to‐arbitrage interpretation of our finding of a high price of correlation risk.

Understanding Index Option Returns

This paper studies the returns from investing in index options. Previous research documents significant average option returns, large CAPM alphas, and high Sharpe ratios, and concludes that put options are mispriced. We propose an alternative approach to evaluate the significance of option returns and obtain different conclusions. Instead of using these statistical metrics, we compare historical option returns to those generated by commonly used option pricing models. We find that the most puzzling finding in the existing literature, the large returns to writing out-of-themoney puts, is not even inconsistent with the Black-Scholes model. Moreover, simple stochastic volatility models with no risk premia generate put returns across all strikes that are not inconsistent with the observed data. At-the-money straddle returns are more challenging to understand, and we find that these returns are not inconsistent with explanations such as jump risk premia, Peso problems, and estimation risk.

The Weekend Effect in Equity Option Returns

We find that option returns are significantly lower over nontrading periods, the vast majority of which are weekends. Our evidence suggests that nontrading returns cannot be explained by risk, but are rather the result of widespread and highly persistent option mispricing driven by the incorrect treatment of non-smoothness in stock return variance. The size of the effect implies that the broad spectrum of finance research involving option prices should account for nontrading effects and non-smoothness in variance more generally. Our study further suggests how alternative industry practices could improve the efficiency of option markets in a meaningful way.

Short-Put Exposures in Hedge Fund Returns: Are They Really There?

Previous studies have shown that systematic risk in hedge fund returns is partly captured by short positions in put option returns. This is suggestive of a potential ‘peso problem’ in hedge fund returns: a series of steady returns may alternate with an occasional crash. In this paper, we analyze whether equity option-exposures are actually there, and find they are not. Although some hedge fund indices show some exposure to put or call-returns, several robustness analysis as well as an analysis of individual hedge fund returns show that exposures are not consistent with fundamental characteristics of options, such as put-call parity and the positive relation between option prices and volatility.

Expected Option Returns and the Structure of Jump Risk Premia

The paper analyzes expected option returns in a model with stochastic volatility and jumps. A comparison with empirically documented returns shows that the ability of the model to explain these returns can dier significantly depending on the holding period and depending on whether we consider call or put options. Furthermore, we show that the size of the jump risk premium and its decomposition into a premium for jump intensity risk, jump size risk, and jump variance risk has a significant impact on expected option returns. In particular, expected returns on OTM calls can even become negative if e.g. jump variance risk is priced.

Effect of Non-Normality Dynamics on the Expected Return of Options

The author shows that, somewhat surprisingly, the real world expected value of an at-the-money call option does not increase when stock index returns are assumed to follow a more realistic process that than of geometric Brownian motion. Thus, the fact that instantaneous stock returns are not normally distributed does not detract from the efficacy of covered call (CC) strategies (relative to the stock index), which employ at-the-money call options. The analysis presented in this article concentrates on the efficacy of stock index CC strategies. The stock index process used by the author incorporates stochastic volatility, jumps in returns, and jumps in volatility. <b>TOPICS:</b>Equity portfolio management, statistical methods, volatility measures

The Weekend Effect in Equity Option Returns

The Weekend Effect in Equity Option Returns

Volatility Mean Reversion and the Cross-Section of Option Returns

Volatility Mean Reversion and the Cross-Section of Option Returns

The Information Content of Implied Skewness and Kurtosis Changes Prior to Earnings Announcements for Stock and Option Returns

We explore whether changes in stock return skewness and kurtosis, as implied in option prices preceding earnings announcements, provide information about subsequent stock and option returns through the announcement. We demonstrate that the change in skewness and kurtosis can be related to changing jump risk premiums, where jump risk can be associated with the uncertainty around the direction and size of the stock price response to the earnings announcement. As such, implied skewness (kurtosis) should capture the direction (magnitude) of a stock jump if option prices change as a result of changing jump risk size and intensity. Examining changes in implied skewness and kurtosis preceding over 74,000 earnings announcements for over 4700 firms, we find that both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to skewness. Thus, prior to earnings announcements, option prices contain information about future security returns.

Futures and Option Prices After the Stock Market Close: Evidence from the Korean Markets

In the KOSPI2oo futures and option markets. additional fifteen minutes (15 : 00∼15 개5) after the underlying stock market close are given tor the adjustments of the futures and option positions. During the first five minutes. 15: 00∼15 : 05. a continuous auction trading is made. while the trading at a single clearing price is made for the remaining ten minutes. 15: 05∼15: 15. Previous studies focused on the synchronous trading in terms of transaction time in the analysis of the lead-lag relationship. truncating the futures and option data during 15 : 00∼15 : 15. In this article. we explore how the KOSPI2oo futures and option returns for the extra fifteen minutes impact the next day's KOSPI200 cash returns, We also examine the lead-lag relationship during the reggular trading hours (9 : 00∼15 : 00) and the impact of the cash returns during 14 : 20∼15 : 00 on futures and option returns during 15 : 00∼15: 15. Our main findings are summarized as follows. First. the KOSPI200 futures and option returns during 15 : 00∼15 : 15 lead the close-to-open KOSPI200 cash return, even though the trading volume and return volatility during 15: 00∼15: 15 are lower relative to the regular stock market session (9 : 00∼15: 00). The impact of the futures and option returns on the cash return lasts hlK) minutes and one minute‘ repectively. after the next day open. Second. the option return during the continuous auction trading session (15 : 00∼ 15 : 05) leads the close-to-open cash return. while the futures return of trading at a single clearing price during 15 : 05∼15 : 10 impacts the close-to-open cash return. Third, we found that the lead-lag relationships among the KOSPI200 futures, option, and cash returns are not constant during the reg비ar stock market session‘ In partieular. the impact of the KOSPI200 cash ret un during 14 : 40∼15 : 00 on the futures and option retuns for the 15 : 00∼15: 15 Interval is much stronger. compared with other time zones. Finally. the KOSPI200 cash return during the last ten minutes of trading at a Single clearing price (14 : 50∼15 : 00). significantly impacts the option return during 15: 00∼15: 05. while there is no impact on the futures return (15 : 00∼15: 15).

Explaining the Level of Credit Spreads: Option-Implied Jump Risk Premia in a Firm Value Model

We study whether option-implied jump risk premia can explain the high observed level of credit spreads. We use a structural jump-diffusion firm value model to assess the level of credit spreads generated by option-implied jump risk premia. Prices and returns of equity index and individual options are used to estimate the jump parameters. We further calibrate the model to historical information on default risk and the equity premium. The results show that incorporating option-implied jump risk premia brings predicted credit spread levels much closer to observed levels. The introduction of jumps also helps to improve the fit of the volatility of credit spreads and equity returns.

Option Returns and Disagreement Risk

We study the relation between beliefs disagreement among investors and the cross-sectional differences in option returns. Writers of index options earn high returns due to a significant and high volatility risk premium but writers of options in single-stock markets earn lower returns. We develop a structural model using an incomplete information economy with multiple assets and explain endogenously the different volatility risk premia of index and single-stock options. We show that higher disagreement increases the volatility of stock returns and the volatility premia of individual options. At the same time, it generates a higher endogenous correlation of stock returns that further increases the volatility premium of index options relative to single-stock options. In equilibrium, this different exposure to disagreement risk is compensated for in the cross-section of options and model-implied trading strategies exploiting differences in disagreement earn substantial excess returns. We test the model predictions in a set of panel regressions, by merging three datasets of firm-specific information on analysts' earning forecasts, options data on S&P 100 index options, options on all constituents, and stock returns. We find that beliefs disagreement is the most powerful determinant of volatility risk premia in individual and index options. Sorting stocks based on differences in beliefs, we find that volatility trading strategies exploiting different exposures to disagreement risk in the cross-section of options earn high Sharpe ratios. The results are robust to stock risk-characteristics and are not subsumed by other theories explaining the volatility risk premia.

The Price of Market Volatility Risk

We analyze the volatility risk premium by applying a modified two-pass Fama-MacBeth procedure to the returns of a large cross section of the returns of options on individual equities. Our results provide strong evidence of a volatility risk premium that is increasing in the level of overall market volatility. This risk premium provides compensation for risk stemming both from the characteristics of the option contract and the riskiness of the underlying equity. We also show with a large scale Monte Carlo simulation that measurement error in option prices and violations of arbitrage bounds induce highly economically significant biases in the mean returns of options. In fact, our simulation results demonstrate that biases can be up to several percentage points per day. These large biases can lead researchers to faulty conclusions with respect to both the magnitude of the volatility risk premium and the sign of expected option returns.

Lead-Lag Relationship between Return and Volume in the KOSPI200 Spot and Option Markets

This study explores the Granger causal relationship between return and volume in the KOSPI200 spot and option markets for the period from December 13. 2002 to December 9. 2004. using minute-by-minute data. Specifically, we examine the lead-lag relationship among OPtion volume, option return, cash volume, and cash return to determine whether option volume and return impact cash return. Our results show that option volume has no direct impact on cash return as cash return unilaterally leads option volume‘ While option volume impacts cash volume. cash return unilaterally leads cash volume. implying no indirect impact of option volume on cash return. However, there is evidence that option return impacts cash return directly, given a bilateral causality between option return and casll return. Option return also impacts cash volume, but again cash volume has no impact on cash return. meaning no indirect impact of option return on cash return. Our findings were generally robust across days of the week and different maturities. Finally, we analyzed lead-lag relationship within the option market. and found a bilateral causality between option volume and option return. This implies that option volume may impact cash return indirectly via option return.

Option returns versus asset-pricing theory: Evidence from the European option market

Against the background of standard asset-pricing theory, this paper empirically investigates returns of index call and put options traded at the Eurex (European Exchange). We find that option returns are not fully consistent even with a very general asset-pricing framework. Under comparatively stronger Black–Scholes/CAPM assumptions, returns deviate significantly from expected values, though results are sensitive to option type, moneyness, and time-to-maturity. We also provide evidence that short positions in suitably chosen zero-beta straddle portfolios yield remarkable positive (excess) returns on average.

On the Negative Market Volatility Risk-Premium: Bridging the Gap Between Option Returns and the Pricing of Options

Existing evidence indicates that (i) average returns of purchased delta-hedged options are negative, implying options are expensive, and (ii) volatility is the most important extra risk that is factored into option prices. Therefore, a natural extension is to explain the cross-section of average delta-hedged option returns in a stochastic volatility model. This paper solves this problem by introducing a measure of option overprice, which quantifies the impact on option prices of the volatility risk premium. It is an application of option-pricing in incomplete markets under stochastic volatility. An extensive numerical exercise shows the option overprice is consistent with the cross-section of average delta-hedged returns of calls, puts, and straddles reported by the literature for the S&P 500 index, except for expensive short-term out-of-the-money puts. In a stochastic volatility model, the volatility risk of at- and, especially, out-of-the-money calls and puts is several times larger than market volatility, which explains large negative volatility risk premiums if volatility risk is negative priced.

Model Specification and Risk Premia: Evidence from Futures Options

ABSTRACTThis paper examines model specification issues and estimates diffusive and jump risk premia using S&amp;P futures option prices from 1987 to 2003. We first develop a time series test to detect the presence of jumps in volatility, and find strong evidence in support of their presence. Next, using the cross section of option prices, we find strong evidence for jumps in prices and modest evidence for jumps in volatility based on model fit. The evidence points toward economically and statistically significant jump risk premia, which are important for understanding option returns.