Optimal limit methods for computing sensitivities of discontinuous integrals including triggerable derivative securities

Abstract

We introduce an 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 payoffs this minimizes the variance of Monte Carlo sensitivities. An efficient adjoint implementation is discussed, and the method is shown to be effective for a number of natural financial examples including double barrier options and triggerable interest rate derivative securities.