Implementing the principle of maximum entropy in option pricing

The Black-Scholes option pricing model has been the foundation of option pricing analysis. Yet as well known as the model itself, its empirical deficiencies are also well documented. Option prices generated by the Black-Scholes formula are often found to systematically differ from observed prices. The patterns of mispricing are generally believed to result from violations of one or more assumptions underlying the Black-Scholes option pricing model, such as the natural logarithm of the underlying stock price following a normal distribution with a variance that increases exactly linearly with time. This dissertation concerns an evaluation of the Principle of Maximum Entropy as a method for recovering a probability density function from stock index option prices. Theoretically, the resulting probability density is "the least prejudiced estimate since it is maximally noncommittal with respect to missing or unknown information." Empirically, this dissertation demonstrates that entropy valuation gives much stronger performance than does the Black-Scholes model in pricing stock index options on the S & P 500 and on the Dow Jones Industrial Average.