Τιμολόγηση δικαιωμάτων προαίρεσης μέσω Monte Carlo
Monte Carlo methods for option pricing
Through this master thesis attempts to present methods of pricing options using the Monte Carlo simulation method. Initially, basic concepts of Probability theory and Stochastic Processes are introduced so that the reader is able to understand the Simple and Geometric Brownian motion. The Black & Scholes method is presented and so the way to solve the model equation and its solution. All the theoretical backgrounds are stated for the understanding of the Black & Scholes model via Monte Carlo simulation method using the MATLAB program. Also at the end an example of option pricing is given. Through MATLAB codes, which are presented in the Appendix A, we simulate the paths of the price of an «exchange» option. At the end, an extension of the Black & Scholes model is presented, called “Jump Diffusion Model”. This extension involves the addition of random changes (jumps) to the model of Black & Scholes.