An Accelerating Quasi-Monte Carlo Method for Option Pricing Under the Generalized Hyperbolic Lévy Process

In this paper, we develop a simple and yet practically efficient simulation algorithm for derivative pricing. Our method is based on an extension of the Imai and Tan’s linear transformation method which is originally proposed in the context of simulating a Gaussian process. By generalizing this method to other stochastic processes and exploiting the numerical inversion method of Hormann and Leydold, this method can be used to enhance quasi-Monte Carlo method in a wide range of applications. We demonstrate the relative efficiency of our proposed simulation technique using option examples for which the underlying asset price follows an exponential generalized hyperbolic Lévy process. We also illustrate the impact of our proposed method on dimension reduction.

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