Comonotonic Monte Carlo Simulation and Its Applications in Option Pricing and Quantification of Risk

Abstract

For many kinds of derivative valuation problems, especially those that try for greater realism using return processes that are more consistent with empirical evidence, Monte Carlo simulation is the only feasible solution technique. Among the well-known strategies to improve its efficiency, the use of a well-chosen control variate is often very effective. But a good selection can make a lot of difference. This article explains how the mathematical concept of comonotonicity can be applied as a new way to create a control variate. A remarkable improvement in performance can be achieved using the comonotonic upper bound as the control variate. The article illustrates the power of Comonotonic Monte Carlo simulation in estimating tail value at risk and pricing arithmetic Asian options.