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Published in:
2009 | OriginalPaper | Chapter
Sensitivity Estimates for Compound Sums
Authors : Paul Glasserman, Kyoung-Kuk Kim
Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher: Springer Berlin Heidelberg
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We derive unbiased derivative estimators for expectations of functions of random sums, where differentiation is taken with respect to a parameter of the number of terms in the sum. As the number of terms is integer valued, its derivative is zero wherever it exists. Nevertheless, we present two constructions that make the sum continuous even when the number of terms is not. We present a locally continuous construction that preserves continuity across a single change in the number of terms and a globally continuous construction specific to the compound Poisson case. This problem is motivated by two applications in finance: approximating Lévy-driven models of asset prices and exact sampling of a stochastic volatility process.