Limit Proxy Methods for Fast Monte-Carlo Greeks
by Jiun Hong Chan
Abstract: We introduce a new class of numerical schemes for discretizing processesâ€¨ driven by Brownian motions. These allow the rapid computation of â€¨sensitivities of discontinuous integrals using pathwise methods even when â€¨the underlying densities post-discretization are singular. The two new â€¨methods presented in this paper allow Greeks for financial products with â€¨trigger features to be computed in the LIBOR market model with similarâ€¨ speed to that obtained by using the adjoint method for continuousâ€¨ pay-offs. The methods are generic with the main constraint being that theâ€¨ discontinuities at each step must be determined by a one-dimensionalâ€¨ function: the proxy constraint. They are also generic with the sole â€¨interaction between the integrand and the scheme being the specificationâ€¨ of this constraint.
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