Variance Reduction in Monte Carlo Option Pricing: A Comparative Analysis of Control Variates, Multiple Control Variates and Antithetic Variates

Abstract

Monte-Carlo Simulation is a method to solve many financial problems but the convergence rate of the simple Monte-Carlo method tends to be low. In Monte-Carlo Simulation, variance reduction is a technique to reduce the accuracy of the simulation in order to increase the efficiency and accuracy of the simulation. This paper aims to investigate and compare the methods which reduce the variance for the Monte Carlo simulation. Three variance reduction techniques, involving control variates, multiple control variates and antithetic variates, are implemented to Monte Carlo simulation for option pricing, including European and Power put and call options. Multiple control variates is a linear combination of variates in control variates. Black-Scholes Model are used as a benchmark for the validation of the accuracy and effectiveness of three methods in an initial condition. Various scenarios, compromising different Strike Prices, Risk-Free Interest Rates and Volatilities, are used to analyse their impact on the performance of three methods and to compare the effectiveness of these techniques in different occasions. Sufficient simulation paths are set to be 1 million, which ensures statistical stability. The results demonstrate that multiple control variates perform as the best technique in most cases, while in some cases antithetic shows a better performance than the other 2 methods. Moreover, control variates sometimes give a similar effectiveness in variance reduction compared to multiple control variates, but it performs worse in most experimental occasions than multiple control variates.