Monte Carlo methods for derivatives of options with discontinuous payoffs

Authors:
Jérôme Detemple;Marcel Rindisbacher
Affiliations:
School of Management, Boston University and CIRANO, USA;Rotman School of Management, University of Toronto and CIRANO, 105 St. George, Toronto M5S 3E6, Canada
Venue:
Computational Statistics & Data Analysis
Year:
2007

Citing 3
Cited 0

A unified view of the IPA, SF, and LR gradient estimation techniques

Management Science
Estimating security price derivatives using simulation

Management Science
Pricing and Hedging Path-Dependent Options Under the CEV Process

Management Science

Quantified Score

Hi-index	0.03

Visualization

Abstract

Various Monte Carlo methods have been proposed to estimate the derivatives of contingent claims prices. The Monte Carlo approximate likelihood ratio estimator is studied. Recent convergence results are extended in order to show that the Monte Carlo approximate likelihood ratio derivative estimator is asymptotically equivalent, up to a second-order bias component, to an estimator based on a covariation approximation, the Monte Carlo Covariation estimator. Both converge slower than the Monte Carlo Malliavin derivative estimators. Theoretical convergence results are illustrated in a numerical experiment dealing with the risk management of digital options in a CEV model.