Fast Monte-Carlo Greeks for Financial Products with Discontinuous Pay-Offs

41 Pages Posted: 11 Jan 2010 Last revised: 28 Nov 2010

See all articles by Jiun Hong Chan

Jiun Hong Chan

University of Melbourne - Centre for Actuarial Studies

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Multiple version iconThere are 2 versions of this paper

Date Written: November 5, 2009

Abstract

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

Chan, Jiun Hong and Joshi, Mark, Fast Monte-Carlo Greeks for Financial Products with Discontinuous Pay-Offs (November 5, 2009). Available at SSRN: https://ssrn.com/abstract=1500343 or http://dx.doi.org/10.2139/ssrn.1500343

Jiun Hong Chan

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies (deceased) ( email )

Melbourne, 3010
Australia

Register to save articles to
your library

Register

Paper statistics

Downloads
707
rank
34,123
Abstract Views
3,166
PlumX Metrics