Efficient pricing of European options on two underlying assets by frame duality

Abstract

The PROJ method for pricing European options on one underlying asset was proposed by J. Lars Kirkby and then was applied to price Bermudan and Asian options. In this paper, we extend the method to higher dimensions, especially two-dimensions in which some exotic options can be priced. Our method does not rely on a-priori truncation of the integration range and exhibits excellent performance compared with other state-of-the-art methods, particularly for fatter-tailed short maturity models. We also discuss the errors introduced in each approximation and give corresponding error bounds. Numerical results on implementation of this method to price for popular two-assets options, under both the geometric Brownian Motion and Variance-Gamma dynamics, demonstrate remarkable accuracy and robustness.