Nonparametric Option Pricing by Transformation

This paper develops a nonparametric option pricing theory and numerical method for European, American and path-dependent derivatives. In contrast to the nonparametric curve fitting techniques commonly seen in the literature, this nonparametric pricing theory is more in line with the canonical valuation method developed Stutzer (1996) for pricing options with only a sample of asset returns. Unlike the canonical valuation method, however, our nonparametric pricing theory characterizes the asset price behavior period-by-period and hence is able to price European, American and path-dependent derivatives. This nonparametric theory relies on transformation to normality and can deal with asset returns that are either i.i.d. or dynamic. Applications to simulated and real data are provided and implications discussed.