Pricing and Hedging Multi-Asset Spread Options by a Three-Dimensional Fourier Cosine Series Expansion Method

The aim of this paper is to show the bene fit 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 simulation, 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 multi-asset option problems of medium-sized dimensionality. The main contribution of our work is a concrete application of the Fourier cosine series expansion method to option problems whose dimension is higher than two.