Quasi‐MonteCarlo Methods

AbstractThis article presents a survey of quasi‐Monte Carlo methods for multidimensional numerical integration and their applications to computational finance. Quasi‐Monte Carlo methods are deterministic versions of Monte Carlo methods, which outperform Monte Carlo methods for many types of integrals. First, a general background on quasi‐Monte Carlo methods is given. Then we describe principles for the construction of low‐discrepancy sequences, which are basic ingredients of any implementation of quasi‐Monte Carlo methods. Special emphasis is placed on the currently most powerful constructions based on the digital method and the theory of (T,s)‐sequences. Next, the important concept of effective dimension is discussed. One section is devoted to scrambling schemes for low‐discrepancy sequences. A review of applications to pricing problems, in particular for mortgage‐backed securities and options, concludes the article.