Optimal quasi-Monte Carlo valuation of derivative securities

For many applications of computational finance, the use of quasirandom sequences seems to provide a faster rate of convergence than pseudorandom sequences. However, at present there are only a few choices of quasirandom sequences. By scrambling a quasirandom sequence we can produce a family of related quasirandom sequences. Finding an optimal quasirandom sequence within this family is an interesting problem, as such optimal quasirandom sequences can be quite useful in applications. The process of finding such optimal quasirandom sequences is called the derandomization of a randomized (scrambled) family. In this paper, we summarize aspects of this technique and explore applications of optimal quasirandom sequences to evaluate a particular derivative security. We find that the optimal quasirandom sequences give promising results even for high dimensions.