Applications of randomized low discrepancy sequences to the valuation of complex securities

This paper deals with a recent modification of the Monte Carlo method known as quasi-random Monte Carlo. Under this approach, one uses specially selec ted deterministic sequences rather than random sequences as in Monte Carlo. These special sequences are known as low discrepancy sequences and have th e property that they tend to be evenly dispersed throughout the unit cube. For many applications in finance, the use of low discrepancy sequences seem s to provide more accurate answers than random sequences. One of the main d rawbacks of the use of low discrepancy sequences is that there is no obviou s method of computing the standard error of the estimate. This means that i n performing the calculations, there is no clear termination criterion for the number of points to use. We address this issue here and consider a part ial randomization of Owen's technique for overcoming this problem. The prop osed method can be applied to much higher dimensions where it would be comp utationally infeasible for Owen's technique. The efficiency of these proced ures is compared using a particular derivative security. The exact price of this security can be calculated very simply and so we have a benchmark aga inst which to test our calculations. We find that our procedures give promi sing results even for very high dimensions. Statistical tests are also cond ucted to support the confidence statement drawn from these procedures. (C) 2000 Elsevier Science B.V. All rights reserved. JEL classification: C15; C6 3; G13.