An Accelerating Quasi-Monte Carlo Method for Option Pricing Under the Generalized Hyperbolic L[e-acute]vy Process

In this paper, we develop a simple and yet practically efficient algorithm for simulating high-dimensional exotic options. Our method is based on an extension of 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 exotic option examples including Asian, lookback, barrier, and cliquet options for which the underlying asset price follows an exponential generalized hyperbolic Levy process. We also illustrate the impact of our proposed method on dimension reduction.