Monte Carlo Simulation in Option Pricing

Abstract

Along with the rapid development of derivatives market in the last several decades, option pricing technique becomes an extremely popular area in academic research, since Black, Scholes and Merton (1973) developed the first option pricing formula. A number of numerical methods can be applied in option valuation. However, they may encounter some difficulties when pricing relatively complicated options like path-dependent or American-style ones, which are quite common in the financial industry. In this thesis, the Least Squares Monte Carlo (LSM) approach to American option valuation by Longstaff and Schwartz (2001) is introduced. Moreover, the mathematical foundation, e.g. the convergence and the robustness of the simulation is provided. Furthermore, we improve this approach by applying the Quasi Monte Carlo, which can enhance the effectiveness, accuracy and computational speed of the simulation. The numerical results show that the improved algorithm works well in pricing American options and outperforms the original one in both effectiveness and accuracy. We have also discussed about the trade-off between the computational time and the precision of the price regarding number of paths in simulation, number of possible exercise time points and different degrees of polynomials in the regression process.