Pricing European Options Using Monte Carlo Simulation With Stochastic Interest Rate

Abstract

Over the decades, Black-Scholes formula exploited its efficiency in valuing derivatives. Since that, many mathematicians tried to extend this formula by considering additional risk such as interest rate risk. There were published papers investigated pricing formula with stochastic interest rate. These formulas are quite complicated and take long time to be proved. Therefore, objective of this study is to simplify the way pricing European options with stochastic interest rate by Monte Carlo simulation in MATLAB. We first use simulation to compute option value when interest rate is constant and compare with results obtained from Black-Scholes formula. Then, we focus on involving stochastic interest rate into model. After getting results, we compare result in two cases to recognize the impact of changing interest rate on option values. Besides, we apply our method to real data to check its validity. Historical data taken is S&P500 index and Fed Fund rate, with length of time being 423 trading days. Our simulation give outcomes with high degree of accuracy due to small standard erros and short length of confidence interval. Our empirical results support the view that option pricing model under stochastic interest rate has a significant improvement. Key words: European options, stochastic interest rate, Monte Carlo simulation, Black-Scholes formula, S&P500 index