Option pricing and higher order moments of the risk-neutral probability density functio

For over twenty years the Black-Scholes model has been the pre-eminent model used by financial economists and option market participants for pricing derivatives. The model assumes that the log-return of an asset over any time period is normally distributed conditional on the current asset price and that log-returns over equal non-overlapping periods of time are iid. Research has shown that both of these assumptions are incorrect. This dissertation develops option pricing models that are consistent with these observed characteristics of asset returns.;In Chapter Two an Edgeworth expansion is used to approximate the risk-neutral pdf of the log return of an asset. Using a kth order Edgeworth expansion, which allows for skewness and fat-tails, an explicit formula for pricing European options is developed, of which the Black-Scholes option pricing formula is a special case.;In Chapter Three estimates of the implied risk-neutral pdf of the log-return on the S&P 500 index are obtained using high frequency prices of S&P 500 index futures and options written on the futures. Risk-neutral pdfs are estimated for each option maturity on every trading day during the time period 1990 to 1996. Consistent with previous findings, the results show that the implied conditional risk-neutral pdfs are left-skewed and leptokurtic. Further, the data suggest that daily log-returns are not iid through time.;In Chapter Four, a general autoregressive conditional density model is estimated for daily log-returns on the S&P 500 index. This model allows for skewness and kurtosis in the conditional actual log-returns and autoregressive conditional skewness, in addition to autoregressive conditional volatility. The success of this model for capturing the behavior of actual log-returns leads us to develop a similar model for risk-neutral log-returns.;Parameters of the dynamic process for one-week risk-neutral log-returns are obtained using a time series of prices of S&P 500 index futures and options for the period 1990 to 1996. The estimated weekly risk-neutral pdf is found to be left-skewed, exhibit volatility clustering and persistence, asymmetric volatility, fat tails and clustering and persistence in the third central moment. The dynamic model is found to outperform the Black-Scholes model out-of-sample.