Closed-form approximations in derivatives pricing: The Kristensen-Mele approach

Abstract

Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some known auxiliary model. Since the resulting approximation formula has closed-form it is straightforward to obtain approximations of greeks. In this thesis I will introduce Kristensen and Mele's methods and apply it to a variety of stochastic volatility models of European style options as well as a model for commodity futures. The focus of this thesis is the effect of different model choices and different model parameter values on the numerical stability of Kristensen and Mele's approximation.