No abstract

In this article, the researchers obtained a recursive formula for the price of discrete single barrier option based on the Black-Scholes framework in which drift, dividend yield and volatility assumed as deterministic functions of time. With some general transformations, the partial differential equations (PDEs) corresponding to option value problem, in each monitoring time interval, were converted into wellknown Black-Scholes PDE with constant coefficients. Finally, an innovative numerical approach was proposed to utilize the obtained recursive formula efficiently. Despite some claims, it has considerably low computational cost and could be competitive with the other introduced method. In addition, one advantage of this method, is that the Greeks of the contracts were also calculated.

In this paper, we propose some analytical solutions of stochastic differential equations related to Martingale processes. In the first resolution, the answers of some stochastic differential equations are connected to other stochastic equations just with diffusion part (or drift free). The second suitable method is to convert stochastic differential equations into ordinary ones that it is tried to omit diffusion part of stochastic equation by applying Martingale processes. Finally, solution focuses on change of variable method that can be utilized about stochastic differential equations which are as function of Martingale processes like Wiener process, exponential Martingale process and differentiable processes.

No abstract