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

Abstract

Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American and barrier option pricing in the subdiffusive Black–Scholes (B–S) model. Two computational methods for valuing American options in the considered model are proposed - the weighted finite difference (FD) and the Longstaff–Schwartz method. In the article it is also shown how to valuate numerically wide range of barrier options using the FD approach.