A Generalized Linear Transformation Method for Simulating Meixner Lévy Processes

In this paper, we consider an enhanced quasi-Monte Carlo (QMC) method for pricing derivative securities when the underlying asset price follows an exponential Lévy process. In particular, we focus on a special family of the Lévy process known as the Meixner process. The enhanced QMC is based on a generalization of the linear transformation (LT) method of Imai and Tan (2006). The generalized LT method can be used to simulate general stochastic processes and hence has a wider range of application than the original LT which only applies to the Gaussian process. Using some option examples with dimensions ranging from 4 to 250 as test cases, the numerical results suggest that the generalized LT-based QMC substantially outperforms the standard applications of quasi-Monte Carlo and Monte Carlo methods.