Optimal Limit Methods for Computing Sensitivities of Discontinuous Integrals Including Triggerable Derivative Securities

95 Pages Posted: 27 Feb 2012 Last revised: 13 Aug 2014

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)

Date Written: February 27, 2012

Abstract

We introduce a new approach to computing sensitivities of discontinuous integrals. The methodology is generic in that it only requires knowledge of the simulation scheme and the location of the integrand's singularities. The methodology is proven to be optimal in terms of minimizing the variance of the measure changes. For piecewise constant pay-offs this minimizes the variance of the Greek. An efficient adjoint implementation is discussed, and the method is shown to be effective for a number of natural examples including double barrier options and triggerable interest rate derivative securities.

Keywords: price sensitivities, Monte-Carlo Greeks, partial proxy simulation scheme, minimal partial proxy simulation scheme, optimal partial proxy simulation scheme, discontinuous pay-offs, digital options, target redemption notes, LIBOR market model

JEL Classification: C15, G13

Suggested Citation

Chan, Jiun Hong and Joshi, Mark, Optimal Limit Methods for Computing Sensitivities of Discontinuous Integrals Including Triggerable Derivative Securities (February 27, 2012). Available at SSRN: https://ssrn.com/abstract=2011690 or http://dx.doi.org/10.2139/ssrn.2011690

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

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