Generating quasi-random paths for stochastic processes

被引:50
作者
Morokoff, WJ [3 ]
机构
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA
[2] C ATS Software, Palo Alto, CA USA
[3] Goldman Sachs & Co, New York, NY 10005 USA
关键词
quasi-Monte Carlo; stochastic process simulation; computational finance;
D O I
10.1137/S0036144597317959
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The need to simulate stochastic processes numerically arises in many fields. Frequently this is done by discretizing the process into small time steps and applying pseudorandom sequences to simulate the randomness. This paper addresses the question of how to use quasi-Monte Carlo methods to improve this simulation. Special techniques must be applied to avoid the problem of high dimensionality which arises when a large number of time steps is required. Two such techniques, the generalized Brownian bridge and particle reordering, are described here. These methods are applied to a problem from finance, the valuation of a 30-year bond with monthly coupon payments assuming a mean reverting stochastic interest rate. When expressed as an integral, this problem is nominally 360 dimensional. The analysis of the integrand presented here explains the effectiveness of the quasi-random sequences on this high-dimensional problem and suggests methods of variance reduction which can be used in conjunction with the quasi-random sequences.
引用
收藏
页码:765 / 788
页数:24
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