| The world of finance has changed significantly in recent years. As many countries struggle to recover from the shock of recent financial crisis, it is obvious that financial institutions do not want to experience another global financial crisis. Nevertheless, it is imperative to study the past behavior of the financial markets in order to prevent future financial crisis. Valuation of stock prices proved to be difficult to determine, and to this day, there is no agreement among financial economists about what the price of a given stock should be. An option is a derivative contract that has a value determined by the price of some underlying risky asset such as a stock. The value of an option is easily obtained from the Black-Scholes (B-S) formula in terms of many quantities which are assumed to be known and fixed. It is important to add that the assumptions underlying the BS formula are unrealistic and restrictive. This thesis relaxes some of the assumptions by empirically motivating the equity price process within the framework of a vector autoregressive (VAR) process using stock indices and the constant risk-free interest rate replaced by a process emanating from a cointegrated VAR model based on treasury securities. In this setup, this thesis estimates the value of the European call options and compares them to the corresponding values from the standard B-S model using Monte Carlo (MC) simulation. Also, the applicability of the antithetic variate as a variance reduction technique to improve the accuracy of our MC estimates is explored. |
