Variance Reduction Techniques for Monte Carlo Valuation of Financial Derivatives
Open Access
Author:
Korostin, Stan A
Area of Honors:
Risk Management
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Ron Gebhardtsbauer, Thesis Supervisor Ron Gebhardtsbauer, Thesis Honors Advisor Lisa Lipowski Posey, Faculty Reader
Keywords:
Monte Carlo Variance Control Variate Antithetic Stratified Quasi-Monte Carlo Asian Actuarial Derivative Financial
Abstract:
Monte Carlo simulations rely on repeated random sampling to represent real events. They have
become a pivotal tool for valuating financial derivatives that do not have a closed form pricing formula. These simulations often take a long time to execute, especially when considering portfolios with thousands of options. There exist methods that mathematically alter the formulas for Monte Carlo simulation to reduce the variance and ultimately minimize the convergence time. This paper applies the naïve, control
variate, antithetic, and stratified methods to Asian call options to examine which of the techniques quickens convergence to the true price. This paper also introduces quasi-Monte Carlo methods as efficient sequences for simulation. While the analysis focuses on Asian options specifically, the Monte Carlo methodology has many actuarial applications.
