Bootstrap-based budget allocation for nested simulation

Operations Research and Operations Management

Kun Zhang, Guangwu Liu, and Shiyu Wang

Operations Research, forthcoming

Nested simulation has been an important computational tool in financial risk measurement, especially for large-scale portfolios that consist of sophisticated financial derivatives. Budget allocation is a central issue of nested simulation that has received in recent years a significant amount of attention from both researchers and practitioners in the financial industries. 

Budget allocation aims to allocate a given computational budget to the simulation procedure efficiently so as to provide accurate risk estimates within an affordable time frame. In this paper, we develop an efficient budget allocation rule based on a resampling technique called bootstrap, in conjunction with in-depth analysis of the problem structure of nested simulation and its asymptotic behaviors. An attractive feature of the proposed allocation rule is that it leverages the samples generated by simulation and guides an efficient allocation that is proven to be asymptotically optimal. Numerical examples have demonstrated that it may serve as a viable tool for risk measurement of financial portfolios in practice.