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Testing Option Pricing Models: Complete and Incomplete Markets

This paper examines the empirical performance of several complete and incomplete market models of stock price dynamics using S&P 500 options and stock market data. The main contribution of this work is that it suggests and implements an empirical approach to estimating a complete model with uncertain volatility, and then judges it against other popular option pricing processes. The performance of alternative models is evaluated from four perspectives: (1) in-sample fit to stock returns data, (2) in-sample fit to options data, (3) consistency of physical and risk-neutral parameter estimates and (4) out-of-sample option pricing. Overall, the complete model with uncertain volatility is found to .t the data much better than models with constant and price-level-dependent volatilities, and the variance gamma process, and its performance is comparable to that of a stochastic volatility model.