Abstract

The prices of traded financial assets incorporate a rich information set regarding payoffs and investor risk preferences in equilibrium. Arrow-Debreu prices, or in continuous states, the state price density (SPD) summarise this information. This study applies a nonparametric kernel regression technique that estimates an option pricing function from observed data. Inferred from the estimated pricing function is the nonparametric SPD estimator. From a pricing perspective the SPD is a `sufficient' statistic. The SPD estimator is applied to the pricing of European `exotic' options. The existing literature is extended by outlining a method of incorporating the important data features of the nonparametric estimator into a trinomial tree for the purpose of pricing path dependent derivatives. These data features encompass negative skewness in stock price returns and implied volatility `smiles' from option prices, that are observed in the sample of common stock options. Monte Carlo analysis and a bootstrap statistical test provide evidence of the nonparametric model's robustness and the SPD estimator's deviation from the Black-Scholes lognormal.