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  model. Two computational 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 numerically wide range of barrier options using the FD approach . The proposed FD method has 2-\alpha order of accuracy with respect to time, where \alpha\in(0,1) is the subdiffusion parameter, and 2 with respect to space .
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 .
A
(B-S)
R
. The weighted scheme of the
- the weighted
R
method is derived and the main properties of the method are presented. The
and the
D
is applied for the discussed model and is compared to the previous method
D
. The proposed FD method has 2-\alpha order of accuracy with respect to time, where \alpha\in(0,1) is the subdiffusion parameter, and 2 with respect to space