Some Control Variates for exotic options

TL;DR

This paper explores the use of control variates to reduce variance in Monte Carlo simulations for valuing complex exotic options like Asian and lookback options, providing new inequalities for estimator comparison.

Contribution

It introduces specific control variates for exotic options valuation and presents an inequality for comparing correlation-based estimators in variance reduction.

Findings

Control variates improve Monte Carlo estimation accuracy.

New inequality aids in comparing variance reduction estimators.

Results demonstrate effectiveness for Asian and lookback options.

Abstract

There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo Simulation approach, amongst other numerical methods, to estimate the value of these options. The problem which then arises with this method is one of variance reduction. Control variates are often used, and we present some results concerning these control variables, for the valuation of Asian and lookback options. An inequality on functions of correlations useful for comparing estimators in variance reduction procedures is also provided.