In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for fractional diffusion equation. We also show stability convergence analysis fully discrete scheme a Crank–Nicolson time. A Black–Scholes equation is proposed tested numerically. Some numerical experiments are carried out to confirm a...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

For the pricing of options on equity shares, the Black-Scholes equation has become an indispensable tool for agents on the financial market. Under the assumption that the value of the underlying share evolves in time according to a stochastic differential equation and some further assumptions on the financial market, the equation can be derived by an application of Itô’s calculus. It represents...