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

摘要

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 multiasset 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 of 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, in particular, 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 that can deal with multiasset option problems of medium 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 2.