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

摘要

Subdiffusion is a well established phenomenon in physics. In this paper we apply the sub-diffusive 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 & ndash;Scholes (B & ndash;S) model. Two computational methods for valuing American options in the considered model are proposed -the weighted finite difference (FD) and the Longstaff & ndash;Schwartz method. In the article it is also shown how to valuate numerically wide range of barrier options using the FD approach.(c) 2020 Elsevier B.V. All rights reserved.