Abstract
SummaryThis paper develops a new class of option price models and applies it to options on the Australian S&P200 Index. The class of models generalizes the traditional Black‐Scholes framework by accommodating time‐varying conditional volatility, skewness and excess kurtosis in the underlying returns process. An important property of these more general pricing models is that the computational requirements are essentially the same as those associated with the Black‐Scholes model, with both methods being based on one‐dimensional integrals. Bayesian inferential methods are used to evaluate a range of models nested in the general framework, using observed market option prices. The evaluation is based on posterior parameter distributions, as well as posterior model probabilities. Various fit and predictive measures, plus implied volatility graphs, are also used to rank the alternative models. The empirical results provide evidence that time‐varying volatility, leptokurtosis and a small degree of negative skewness are priced in Australian stock market options.
Highlights
The Black and Scholes (1973) model for pricing options is founded on two important assumptions: first, that the distribution of returns on the asset on which the option is written is normal, and second, that the volatility of returns is constant
For reviews of the relevant literature see Bollerslev, Chou and Kroner (1992) and Pagan (1996). Associated with this misspecification of the Black-Scholes (BS) model is the occurrence of implied volatility smiles, or smirks, whereby the implied volatility backed out of observed option prices via the BS model varies across the degree of moneyness of the option contract
In this paper we develop a more general framework for pricing options that accommodates the empirical features of the underlying returns process, namely time-varying conditional volatility as well as conditional skewness and excess kurtosis
Summary
The Black and Scholes (1973) model for pricing options is founded on two important assumptions: first, that the distribution of returns on the asset on which the option is written is normal, and second, that the volatility of returns is constant. As in Lim, Martin and Martin (2002a and b) a distribution is specified for the return over the life of the option, with the option priced by evaluating the expected payoff using simple univariate numerical quadrature In this way, the computational burden is comparable to that associated with the BS price, which involves evaluation of a one-dimensional normal integral. The results provide strong evidence that the option market has factored in the assumption of non-constant volatility in returns, plus excess kurtosis in the conditional distribution. There is clear evidence that the non-BS models are more accurate predictors of future market prices and that the parameterization of higher order moments in returns does serve to reduce the extent of the volatility smiles
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