State Price Density, Esscher Transforms, and Pricing Options on Stocks, Bonds, and Foreign Exchange Rates

The state price density is modeled as an exponential function of the underlying state variables, and the Esscher transform is used to specify the forward-risk-adjusted measure. With the aid of state price densities, Esscher transforms, and characteristic functions, this paper provides a consistent framework for pricing options on stocks, interest rates, and foreign exchange rates. The framework discussed is quite general and is related to many popular models.