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

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