Variance reductions using the control variates in the monte carlo simulation

Abstract

Equity Linked Securities is an over-the-counter derivative which is introduced in Korea at 2003 and actively traded among investors. Since various option features are embedded in a single ELS, they have a variety of structure, according to the embedded option feature designed for the needs of investors. The purpose of this thesis is to find a reasonable estimate of price, especially step-down type, and is to reduce its variance, by choosing a control variate which has an analytic expectation. The variance of Monte Carlo Simulation using control variate is compared to crude simulation and the variance reduction rate is evaluated. In addition, through tables and graphs, we confirm the fact that variance reduction rate grows up as the rate of an underlying stock price to the reference price increases, or as the time is close to maturity.