Pricing Asian Options by Numerical Path Integration with Advanced Lévy Dynamics
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In this thesis I combine the strengths of the Path Integration method and the Fast Fourier transform to price discretely monitored, path dependent, fixed strike Asian options in a fast and accurate manner. The presented method can be used to accurately price various types of exotic options with greatly improved computation speed compared to the frequently used Monte Carlo simulations.The method, in the form it is presented here, is implemented for underlying assets modelled by advanced Lévy processes; namely the Normal Inverse-Gaussian process and the Variance Gamma process in addition to the simpler Geometric Brownian Motion for comparison. Some interesting characteristics of these processes are uncovered and discussed.