A General Pricing Technique Based on Theta-Calculus and Sparse Grids

Abstract

In [An Introduction to Theta-calculus (2005)], Dirnstorfer introduced the Theta-notation for modeling financial contracts consistently by a sequence of operators. This easy-to-use modeling for financial engineers together with Monte Carlo methods is already applied successfully for option pricing. We combined the idea of Theta-calculus with an approach based on partial differential equations (PDE) to get a higher accuracy. In this paper, we give a short introduction to Theta-calculus and deduce the resulting pricing algorithm that is – in contrast to common PDE based pricing techniques – general and independent from the type of product. With the use of sparse grids, this method also works for higher dimensional problems. Thus, the approach allows an easy access to the numerical pricing of various types of multi-dimensional problems.