  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.
