A Rbsdes Approach for the Numerical Evaluation of the American Option Pricing Problem

Abstract

The problem of pricing American type options is a typical example of a non linear problem characterized by the absence of closed expressions for its evaluation. Therefore, during recent years, such an issue has been approached , both deterministically and randomly, from the algorithmic point of view, trying to derive suitable numerical approximations. In this paper, starting from the aforementioned solutions, we review some computational, stochastic inspired, methods, mainly based on the the existing link between the above recalled pricing task, and the theory of Reflected Backward Stochastic Differential Equations (BSDEs).In particular we show how suitable numerical schemes can be developed within the SBDEs framework by mean of quantization techniques as well as considering Monte Carlo methods. AMS Subject Classification: 60H15, 60H35, 90-08, 91G20, 91G80, 91B25