Subsampling and other considerations for efficient risk estimation in large portfolios

Michael B. Giles; Abdul-Lateef Haji-Ali

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The authors use random sub-sampling to devise efficient estimators for pricing derivatives or computing risk measures on large portfolios.
Multilevel Monte Carlo and adaptive sampling are used to deal with the problem of nested expectation.
Several control variates and variance reduction techniques can be combined in a unified framework for efficient computation of risk measures in large financial portfolios.

Abstract

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem both because it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and because evaluating the loss of the portfolio is expensive and the cost increases with portfolio size. We apply multilevel Monte Carlo simulation with adaptive inner sampling to this problem and discuss several practical considerations. In particular, we discuss a subsampling strategy whose computational complexity does not increase with the size of the portfolio. We also discuss several control variates that significantly improve the efficiency of multilevel Monte Carlo in our setting.

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