Dimension Reduction Approach To Simulating Exotic Options In A Meixner Levy Market

In the past decade, quasi-Monte Carlo (QMC) method has become an important numerical tool in computational finance. This is driven, in part, by the sophistication of the models and, in part, by the complexity of the derivative securities. In this paper, we consider an enhanced QMC method recently proposed by Imai and Tan (2009). This method is known as the generalized linear transformation (GLT) and it increases the efficiency of QMC via dimension reduction. GLT can be used to simulate general stochastic processes and hence has a much wider range of applications. By assuming that the dynamics of the underlying asset price follows an exponential Meixner Lévy process and by resorting to some exotic options including average options and lookback options, we demonstrate the effectiveness and robustness of GLT and it substantially outperforms the standard applications of QMC and Monte Carlo methods.