A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model

Abstract

This paper is focused on American option pricing in the subdiffusive Black Scholes model. Two methods for valuing American options in the considered model are proposed. The weighted scheme of the finite difference (FD) method is derived and the main properties of the method are presented. The Longstaff-Schwartz method is applied for the discussed model and is compared to the previous method. In the article it is also shown how to valuate wide range of Barrier options using the FD approach. The proposed FD method has 2 − α order of accuracy with respect to time, where α ∈ (0, 1) is the subdiffusion parameter, and 2 with respect to space. The paper is a continuation of [13], where the derivation of the governing fractional differential equation, similarly as the stability and convergence analysis can be found.

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“…Since European option can be used only at the time of its expiry S , its American analogue can be exercised at any time between 0 and S . The American option is the one most listed in United States and is one of the most popular derivatives in the rest of the world (see [9] and references therein).…”