American Option Sensitivities Estimation via a Generalized IPA Approach

نویسندگان

  • Nan Chen
  • Yanchu Liu
  • Jeremy Staum
  • Lixin Wu
  • David D. Yao
چکیده

In this paper, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated 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 untractable exercising policies in the case of pricing American options, we also provide an approximation guarantee which 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 pathwise continuity to apply it.

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تاریخ انتشار 2014