Efficient Risk Estimation via Nested Sequential Simulation
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.
Volume (Year): 57 (2011)
Issue (Month): 6 (June)
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- Vadim Lesnevski & Barry L. Nelson & Jeremy Staum, 2007. "Simulation of Coherent Risk Measures Based on Generalized Scenarios," Management Science, INFORMS, vol. 53(11), pages 1756-1769, November.
- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
- Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
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