Efficient Risk Estimation via Nested Sequential Simulation

Authors:
Mark Broadie;Yiping Du;Ciamac C. Moallemi
Affiliations:
Graduate School of Business, Columbia University, New York, New York 10027;Industrial Engineering and Operations Research, Columbia University, New York, New York 10027;Graduate School of Business, Columbia University, New York, New York 10027
Venue:
Management Science
Year:
2011

Citing 12
Cited 3

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Abstract

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimator in each scenario. Theoretical results are given to show that the risk estimator has a faster convergence order compared to the conventional uniform inner sampling approach. Numerical results consistent with the theory are presented. This paper was accepted by Gérard Cachon, stochastic models and simulation.