A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates

Abstract

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.Monte Carlo simulation, control variate, discretization bias, variance reduction, compound options, stochastic interest rates,

Utilizing Monte Carlo Simulation for Valuation: the Case of Barrier Options under Stochastic Interest Rates

“…It is also easy to implement. Related use of the control variate technique for Asian options is considered in Fu et al (1998) and for different price processes by Lindset & Lund (2007). The chapter is organized as follows: In section 2 we present the economic set-up.…”