Monte Carlo Greeks, Old and New
The problem of calculating Greeks (price sensitivities) is central to financial engineering. Complex models often require Monte Carlo methods for valuation and thus raise difficulties associated with estimating sensitivities through Monte Carlo. After a brief review of the traditional pathwise and likelihood ratio methods, we discuss two recent developments. First, we discuss results (joint with Nan Chen) showing the connection between estimators derived from Malliavin calculus and more traditional methods. Second, we present an adjoint method (joint with Mike Giles) that can dramatically accelerate the calculation of pathwise estimates.
Paul Glasserman, Columbia University