On the Comparative Study of Some Numerical Methods for Vanilla Option Valuation

This paper presents some numerical methods for vanilla option valuation namely binomial tree model, Crank Nicolson method and Monte Carlo method. Binomial model is widely used in the finance community for numerical valuation of a wide variety of option models, due primarily to its ease of implementation and pedagogical appeal. Crank Nicolson approach seeks the discretization of the differential operators in the continuous Black Scholes model. Monte Carlo method simulates the random movement of the asset prices and provides a probabilistic solution to the option pricing models. We discuss the strengths, drawbacks and the performance of the methods under consideration. However, binomial model is the most accurate and converges faster than its two counterparts; Crank Nicolson method and Monte Carlo method

On a New Technique for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

This paper presents a new technique for the solution of the Black-Scholes partial differential equation for European call option using a method based on the modified Mellin transform. We also used the modified Mellin transform method to determine the price of European call option. The modified Mellin transform method is mutually consistent and agrees with the values of Black-Scholes model as shown i