Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

Kamonchat Trachoo, Wannika Sawangtong, and Panumart Sawangtong

To study the financial derivative in the market, the Black Scholes model proposed by Black and Scholes in 1973 is used. The concept of their model is hedging and eliminating the risk of option pricing for purchasing and selling of underlying assets. The European call option price of this model varies over time and stocks price. In addition, the price of assets is modelled by a geometric Brownian motion with a constant drift and volatility. the Black Scholes equation was used to investigate the behavior of the option pricing. Since the option pricing in a market is dependent on other markets, the multidimensional Black Scholes equation is more efficient than the one dimensional version. In this article, we consider the two-dimensional Black Scholes equation based on European call option. By using the LHPM, we obtain the explicit solution of the problem in the form of a special function, namely the Mellin–Ross function. The advantage of LHPM for this problem is that this explicit solution can be easily implemented to simulate the European call option depending on two stock prices in order to apply in a real life situation for financial markets.