Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options

This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the risk-neutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed. This paper explains the presence and evolution of risk-neutral skewness over time and in the cross-section of individual stocks.

[1]  M. Rubinstein..  The Fundamental Theorem of Parameter-Preference Security Valuation , 1973, Journal of Financial and Quantitative Analysis.

[2]  E. Fama,et al.  Risk, Return, and Equilibrium: Empirical Tests , 1973, Journal of Political Economy.

[3]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[4]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[5]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[6]  M. Rubinstein..  Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .

[7]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[8]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[9]  S. Beckers.  The Constant Elasticity of Variance Model and Its Implications For Option Pricing , 1980 .

[10]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[11]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[12]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[13]  David S. Bates.  The Crash of ʼ87: Was It Expected? The Evidence from Options Markets , 1991 .

[14]  Kaushik I. Amin,et al.  Option Valuation with Systematic Stochastic Volatility , 1993 .

[15]  Ravi Jagannathan,et al.  Assessing Specification Errors in Stochastic Discount Factor Models , 1994 .

[16]  M. Rubinstein..  Implied Binomial Trees , 1994 .

[17]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[18]  F. Longstaff.  Option Pricing and the Martingale Restriction , 1995 .

[19]  J. Jackwerth.  Recovering Risk Aversion from Option Prices and Realized Returns , 1998 .

[20]  M. Stutzer.  A Simple Nonparametric Approach to Derivative Security Valuation , 1996 .

[21]  M. Broadie,et al.  American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods , 1996 .

[22]  K. Toft.,et al.  Options on Leveraged Equity: Theory and Empirical Tests , 1997 .

[23]  Eric Ghysels,et al.  A study towards a uni " ed approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation q , 1997 .

[24]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[25]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[26]  N. Prabhala,et al.  The relation between implied and realized volatility , 1998 .

[27]  P. Carr,et al.  The Variance Gamma Process and Option Pricing , 1998 .

[28]  B. Dumas,et al.  Implied volatility functions: empirical tests , 1996, IEEE Conference on Computational Intelligence for Financial Engineering & Economics.

[29]  B. Dumas,et al.  Implied Volatility Smiles: Empirical Tests , 1998 .

[30]  Jeff Fleming.  The quality of market volatility forecasts implied by S&P 100 index option prices , 1998 .

[31]  D. Madan,et al.  Spanning and Derivative-Security Valuation , 2000 .

[32]  P. Veronesi,et al.  Option Prices with Uncertain Fundamentals Theory and Evidence on the Dynamics of Implied Volatilities Alexander David Board of Governors of the Federal Reserve System , 1999 .

[33]  Jun Pan,et al.  Transform Analysis and Asset Pricing for AÆne Jump-Di usions , 1999 .

[34]  W. Ferson,et al.  How Much Do Expected Stock Returns Vary Over Time? Answers From the Options Markets , 1999 .

[35]  Jun Pan.  Integrated Time-Series Analysis of Spot and Option Prices , 1999 .

[36]  Campbell R. Harvey,et al.  Current Version : April 6 , 1999 Autoregressive Conditional Skewness , 1999 .

[37]  E. Ghysels,et al.  A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation , 2000 .

[38]  Campbell R. Harvey,et al.  Conditional Skewness in Asset Pricing Tests , 1999 .

[39]  David S. Bates.  Post-'87 crash fears in the S&P 500 futures option market , 2000 .

[40]  S. Mayhew,et al.  Implied Volatility Smiles : Evidence From Options on Individual Equities 1 , 2000 .

[41]  Jun Pan.  The Jump-Risk Premia Implicit in Options : Evidence from an Integrated Time-Series Study , 2001 .

[42]  Dilip B. Madan,et al.  Optimal positioning in derivative securities , 2001 .

[43]  Jun Pan.  Integrated Time-Series Analysis of Spot and Option Prices , 2022 .