FRED ESPEN BENTH () (Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N0316 Oslo, Norway) RODWELL KUFAKUNESU () (University of Pretoria, Department of Mathematics and Applied Mathematics, Pretoria 0002, South Africa)
Abstract
Based on a non-Gaussian OrnsteinâUhlenbeck model for energy spot, we derive prices for Asian and spread options using Fourier techniques. The option prices are expressed in terms of the Fourier transform of the payoff function and the characteristic functions of the driving noises, being independent increment processes. In many relevant situations, these functions are explicitly available, and fast Fourier transform can be used for efficient numerical valuation. The arithmetic nature of our model implies that only a one-dimensional Fourier transform is required in the computation of the price, contrary to geometric models where transformation along both underlying variables is necessary.
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