EUROPEAN BARRIER OPTION PRICING WITH FINITE DIFFERENCE AND ANALYTICAL METHODS - ANGELO (NIM: 10114033), CHRISTOPHER
Pricing Barrier Option is not a simple matter, but of course it is not something impossible to do. With the help of Black Scholes Partial Differential Equation, valuation of Barrier Option becomes possible. In this final project, two methods which are finite difference and analytical methods will be used to solve the Black Scholes Partial Differential Equation until the price of the option is obtained. The Barrier Option that will be discussed is European Down-Out Call. The finite difference methods that will be used are the FTCS and BTCS methods. It is important to check beforehand if those two methods have stable finite difference equations or not. Not only that, Merton analytical method will also be derived in order to check whether the finite difference method is applicable in this matter of pricing or not. After pricing Barrier Option, this project also include the valuation of Moving Curve Barrier analytically. The steps needed to price Moving Curve Barrier are divided into two important things, which are transforming the Black Scholes Partial Differential Equation into heat equation and solving the problem with Fourier Transform and method of images.