American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach

Nan Chen () and Yanchu Liu ()
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Nan Chen: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong
Yanchu Liu: Lingnan (University) College, Sun Yat-Sen University, Guangzhou, 510275, China

Operations Research, 2014, vol. 62, issue 3, 616-632

Abstract: In this paper, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be reformulated as how to perform sensitivity analysis for a stochastic optimization problem with model uncertainty. We introduce a generalized infinitesimal perturbation analysis (IPA) approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The IPA estimators are unbiased if the optimal decisions are explicitly known. To quantify the estimation bias caused by intractable exercising policies in the case of pricing American options, we also provide an approximation guarantee that relates the sensitivity under the optimal exercise policy to that computed under a suboptimal policy. The price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high-dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. Our generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need path-wise continuity to apply it.

Keywords: finance; asset pricing; American option; price sensitivities; simulation; applications; dynamic programming; applications; optimal stopping (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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