American Option Sensitivities Estimation via a Generalized IPA Approach
نویسندگان
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.
منابع مشابه
European and American put valuation via a high-order semi-discretization scheme
Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...
متن کامل2001: Graphical Representation of Ipa Estimation
Infinitesimal Perturbation Analysis (IPA) estimators of the response gradient for a discrete event stochastic simulation are typically developed within the framework of Generalized semi-Markov processes (GSMPs). Unfortunately, while mathematically rigorous, GSMPs are not particularly useful for modeling real systems. In this paper we describe a procedure that allows IPA gradient estimation to b...
متن کاملSensitivity Analysis for Ruin Probabilities: Canonical Risk Model
The surplus process of an insurance portfolio is defined as the wealth obtained by the premium payments minus the reimboursements made at the times of claims. When this process becomes negative (if ever), we say that ruin has occurred. The general setting is the Gambler’s Ruin Problem. In this paper we address the problem of estimating derivatives (sensitivities) of ruin probabilities with resp...
متن کاملThe phantom SPA method: an inventory problem revisited
It is widely accepted today that the Infinitesimal Perturbation Analysis (IPA) method for estimating sensitivities is the preferred method, when it is applicable. The major problem with IPA is handling certain kinds of discontinuities, such as thresholds. The Smoothed Perturbation Analysis (SPA) method was conceived applying a conditional expectation to a dynamic system, similar to the Filtered...
متن کاملOptimal Importance Sampling in Securities Pricing
To reduce variance in estimating security prices via Monte Carlo simulation, we formulate a parametric minimization problem for the optimal importance sampling measure, which is solved using in nitesimal perturbation analysis (IPA) and stochastic approximation (SA). Compared with existing methods, the IPA estimator we derive is more universally applicable and more computationally e cient. Under...
متن کامل