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Nested Simulation in Portfolio Risk Measurement

Michael B. Gordy and Sandeep Juneja
Management Science
Vol. 56, No. 10 (October 2010), pp. 1833-1848
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/40864742
Page Count: 16
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Nested Simulation in Portfolio Risk Measurement
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Abstract

Risk measurement for derivative portfolios almost invariably calls for nested simulation. In the outer step, one draws realizations of all risk factors up to the horizon, and in the inner step, one reprices each instrument in the portfolio at the horizon conditional on the drawn risk factors. Practitioners may perceive the computational burden of such nested schemes to be unacceptable and adopt a variety of second-best pricing techniques to avoid the inner simulation. In this paper, we question whether such short cuts are necessary. We show that a relatively small number of trials in the inner step can yield accurate estimates, and we analyze how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator. Finally, we introduce a jackknife procedure for bias reduction.

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