In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

We are concerned with a model for asset prices introduced by Koichiro Takaoka, which extends the well known Black-Scholes model. For the pricing of contingent claims, partial differential equation (PDE) is derived in a special case under the typical delta hedging strategy. We present an exact pricing formula by way of solving the equation.

This paper gives a connection between the theory of semigroups of operators (functional analysis) and mathematical finance through the Black-Scholes equation. Besides using this theory obtain the solution of this equation via the infinitesimal generator of a group of evolution. Mathematics Subject Classification: Primary 91G80; Secondary 47D06

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at ha...

In the Black-Scholes option price model Brownian motion and the underlying Normal distribution play a fundamental role. Empirical evidence however shows that the normal distribution is a very poor model to fit real-life data. In order to achieve a better fit we replace the Brownian motion by a special Lévy process: the Meixner process. We show that the underlying Meixner distribution allows an ...

The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been ...

In this paper two different methods are presented to approximate the solution of the fractional BlackScholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the applic...