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

• Published in: Communications in nonlinear science & numerical simulation 2021-05, Vol.96, p.105676, Article 105676
• Main Authors: Krzyżanowski, Grzegorz, Magdziarz, Marcin
• Format: Article
• Language: English
• Subjects: Algorithms; American option numerical evaluation; Diffusion; Diffusion barriers; Finite difference method; Finite element analysis; Fluid dynamics; Mathematical analysis; Physics; Schwartz method; Subdiffusion; Time fractional Black–Scholes model; Weighted finite difference method
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105676

•The system describing the fair price of American put option in subdiffusive Black–Scholes model is derived.•The weighted finite difference method for the class of problems is introduced.•The formula for the optimal choice of discretization parameter is given.•The Longstaff–Schwartz method is inefficient for the subdiffusive models. 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.