Asymptotic properties of Monte Carlo estimators of derivatives

Asymptotic properties of Monte Carlo estimators of derivatives

0.00 Avg rating0 Votes
Article ID: iaor2008639
Country: United States
Volume: 51
Issue: 11
Start Page Number: 1657
End Page Number: 1675
Publication Date: Nov 2005
Journal: Management Science
Authors: , ,
Keywords: derivatives
Abstract:

We study the convergence of Monte Carlo estimators of derivatives when the transition density of the underlying state variables is unknown. Three types of estimators are compared. These are respectively based on Malliavin derivatives, on the covariation with the driving Wiener process, and on finite difference approximations of the derivative. We analyze two different estimators based on Malliavin derivatives. The first one, the Malliavin path estimator, extends the path derivative estimator of Broadie and Glasserman to general diffusion models. The second, the Malliavin weight estimator, proposed by Fournié et al., is based on an integration by parts argument and generalizes the likelihood ratio derivative estimator. It is shown that for discontinuous payoff functions, only the estimators based on Malliavin derivatives attain the optimal convergence rate for Monte Carlo schemes. Estimators based on the covariation or on finite difference approximations are found to converge at slower rates. Their asymptotic distributions are shown to depend on additional second-order biases even for smooth payoff functions.

Reviews

Required fields are marked *. Your email address will not be published.