主 题: Malliavin Greeks without Malliavin Calculus
报告人: 陈南 博士 (香港中文大学)
时 间: 2007-10-29 下午 3:00 - 4:00
地 点: 理科一号楼 1560
We derive and analyze Monte Carlo estimators of price sensitivities
(``Greeks\'\') for contingent claims priced in a diffusion model. There
have traditionally been two categories of methods for estimating
sensitivities: methods that differentiate paths and methods that
differentiate densities. A more recent line of work derives estimators
through Malliavin calculus.
The purpose of this article is to investigate connections between
Malliavin estimators and the more traditional and elementary pathwise method
and likelihood ratio method. Malliavin estimators have been derived
directly for diffusion processes, but implementation typically requires
simulation of a discrete-time approximation. This raises the question
of whether one should discretize first and then differentiate, or
differentiate first and then discretize. We show that in several
important cases the first route leads to the same estimators found through Malliavin calculus, but using only elementary techniques. Time-averaging of
multiple estimators emerges as a key feature in achieving convergence
to the continuous-time limit.
This is a joint work with Prof. Paul Glasserman at Columbia University.
