Fast Monte-Carlo Greeks for Financial Products with Discontinuous Pay-Offs
41 Pages Posted: 11 Jan 2010 Last revised: 28 Nov 2010
Date Written: November 5, 2009
We introduce a new class of numerical schemes for discretizing processes driven by Brownian motions. These allow the rapid computation of sensitivities of discontinuous integrals using pathwise methods even when the underlying densities post-discretization are singular. The two new methods presented in this paper allow Greeks for financial products with trigger features to be computed in the LIBOR market model with similar speed to that obtained by using the adjoint method for continuous pay-offs. The methods are generic with the main constraint being that the discontinuities at each step must be determined by a one-dimensional function: the proxy constraint. They are also generic with the sole interaction between the integrand and the scheme being the specification of this constraint.
Keywords: Price Sensitivities, Monte-Carlo Greeks, Partial Proxy Simulation Scheme, Minimal Partial Proxy Simulation Scheme, Pathwise Partial Proxy Method, Pathwise Minimal Partial Proxy Method, Discontinuous Pay-offs, Digital Options, Target Redemption Notes, LIBOR Market Model
JEL Classification: C15, G13
Suggested Citation: Suggested Citation