Pricing and hedging multiasset spread options using a three-dimensional Fourier cosine series expansion method

Abstract

The aim of this paper is to show the benefit of applying a three-dimensional Fourier cosine series expansion method in order to price and hedge multi-asset spread options. The approach consists of approximating the probability density function by its Fourier cosine series expansion in a truncated domain. The Fourier coefficients associated with the payoff function are then approximated via the so-called discrete cosine transform. The main advantage associated with the numerical approach proposed in this paper is the level of accuracy reached with respect to the Monte Carlo method, not only for the option price but especially for the most important Greeks, namely deltas and gammas. This is not the case for the other approaches available in the literature. Our numerical examples show that the three-dimensional cosine series method can be seen as an alternative pricing technique, which can deal with multiasset option problems of medium-sized dimensionality. The main contribution of our work is a concrete application of the COS method to option problems whose dimension is higher than two.