A weighted finite difference method for American and Barrier options in subdiffusive Black-Scholes Model
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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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