Use of the Monte Carlo Simulation in Valuation of European and American Call Options

This thesis examines the valuation methods used for pricing European and American call options. Options are financial instruments that play an important role in the financial industry and are used in hedging, speculating and arbitraging. Because options are widely used in investing, there is a need for valuation methods that are as precise as possible. Options have been perceived as obscure financial instruments due to the lack of valuation techniques in the past. However, with the discovery of Black-Scholes Model in 1973, the first option valuation method, option trading escalated. In this thesis, the fair market value of S&P 500 index with European exercise style, The Google Option Contract and Apple Option Contract will be obtained by using the Black-Scholes Model, the General Monte Carlo Simulation, The Combined Method and the Least-Squares Monte Carlo. The results from three models will be compared and contrasted in order to determine the best valuation method