The skewness premium: option pricing under asymmetric processes

This paper develops distribution-specific theoretical constraints on relative prices of out-of-the-money European call and put options that are also valid for American options on futures. The constraints can be used to identify which distributional hypotheses can and cannot explain observed moneyness biases. An application to S&P 500 futures options over 1983-1993 illustrates the inability of standard distributional hypotheses to explain observed moneyness biases -especially those observed following the stock market crash of 1987. Some distribution-specific extensions to exotic option pricing are also discussed. *The Wharton School, University of Pennsylvania and National Bureau of Economic Research. 5GG $NCEM /CE$GVJ CPF /GTXKNNG CPF 4WDKPUVGKP HQT ECNNU QP %$1' UVQEMU UGG CNUQ VJG ETKVKEKUOU D[ )GUMG CPF 4QNN CPF 9JCNG[ 5GG $NQOG[GT CPF ,QJPUQP HQT RWVU QP %$1' UVQEMU 5GG 9JCNG[ CPF $CVGU 5GG $QFWTVJC CPF %QWTVCFQP 5GG %JGUPG[ CPF 5EQVV Option pricing models such as Black and Scholes (1973) premised upon the underlying asset price following geometric Brownian motion have been found to exhibit serious specification error when fitted to market data. A "moneyness" or "striking price" bias is ubiquitous: model prices as a (monotone) function of the strike price are typically "tilted" relative to observed options prices, so that the residuals for low strike prices tend to be opposite in sign from the residuals for high strike prices. Such biases have been found in American call and put options on stocks traded on the Chicago Board Options Exchange; in American calls and puts on S&P 500 futures traded on the Chicago Mercantile 1 Exchange; in American foreign currency call options traded on the Philadelphia Stock Exchange; and in European 2 3 Swiss franc-denominated call options on the dollar traded in Geneva. The biases are not in the same direction for all 4 markets, nor are they constant over time. The biases have been especially egregious in stock and stock index options since the stock market crash of 1987. Observed moneyness biases and considerable time series evidence against the hypothesis that log-differenced asset prices are homoskedastic and normally distributed have spurred the development of option pricing models for alternative stochastic processes. The constant elasticity of variance (CEV) option pricing model of Cox and Ross (1976) and Cox and Rubinstein (1985) relaxed the constant volatility assumption and allowed the instantaneous conditional volatility of asset returns to depend deterministically upon the level of the asset price. Special cases include both arithmetic and geometric Brownian motion. The recent “implied binomial tree” models of &WRKTG &GTOCP CPF -CPK CPF 4WDKPUVGKP can be viewed as flexible generalizations of the CEV model. The stochastic volatility option pricing models of Hull and White (1987), Scott (1987), and Wiggins (1987) permitted more general patterns of evolution for conditional volatility, parallelling the development of time series models such as ARCH and GARCH that were concerned with the same issue. The recogn ition that asset returns are leptokurtic, particularly for short holding periods, motivated Merton's (1976) model for pricing options on jump-diffusion