On the Stability and Accuracy of Finite Difference Method for Options Pricing

This paper presents finite difference methods for options pricing. These methods are useful to solve partial differential equations and provide a general numerical solution to the valuation problems, as well as an optimal early exercise strategy and other physical sciences. The methods considered are the basic implicit and Crank Nicolson finite difference methods. The stability and accuracy of each of the methods were considered. Crank Nicolson method is more accurate and converges faster than implicit method. Key words: Convergence, Crank Nicolson Method, European Option, Finite Difference Method, Implicit Method, Option, Stability

ON THE STRENGTH AND WEAKNESS OF BINOMIAL MODEL FOR PRICING VANILLA OPTIONS

This paper presents binomial model for pricing vanilla options. Binomial model can be used to accurately price American style options than the Black-Scholes model as it takes into consideration the possibilities of early exercise and other factors like dividends. The strength and weakness of this model were considered. This model is both computationally efficient and accurate but not adequate to deal with path dependent options

On Some Numerical Methods for Solving Initial Value Problems in Ordinary Differential Equations

This work presents numerical methods for solving initial value problems in ordinary differential equations. Euler's method is presented from the point of view of Taylor's algorithm which considerably simplifies the rigorous analysis while Runge Kutta method attempts to obtain greater accuracy and at the same time avoid the need for higher derivatives by evaluating the given function at selected points on each subinterval. We discuss the stability and convergence of the two methods under consideration and result obtained is compared to the exact solution. The error incurred is undertaken to determine the accuracy and consistency of the two methods