In the framework of the displaced-diffusion LIBOR market model, we derive the pathwise adjoint method for the iterative predictor-corrector and Glasserman-Zhao drift approximations in the spot measure. This allows us to compute fast deltas and vegas under these schemes. We compare the...

In this paper, we present a generic framework known as the minimal partial proxy simulation scheme. This framework allows for a stable computation of the Monte-Carlo Greeks for financial products with trigger features via finite difference approximation. The minimal partial proxy simulation...

We demonstrate how to compute first- and second-order sensitivities of portfolio credit derivatives such as synthetic collateralized debt obligation (CDO) tranches using algorithmic Hessian methods developed in Joshi and Yang (2010) in a single-factor Gaussian copula model. Our method is correct...

We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the...

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...

In this paper, we present an efficient approach to compute the first and the second order price sensitivities in the Heston model using the algorithmic differentiation approach. Issues related to the applicability of the pathwise method are discussed in this paper as most existing numerical...

Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued...

The calculation of prices and sensitivities of exotic interest rate derivatives in the LIBOR market model is often very time consuming. One approach that has been previously suggested is to use a Markov-functional model as a control variate for prices and deltas but not vegas. We present a new...

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...

We introduce a new arbitrage-free interpolation scheme for the displaced-diffusion LIBOR market model. Using this new extension, and the Piterbarg interpolation scheme, we study the simulation of range accrual coupons when valuing callable range accruals in the displaced-diffusion LIBOR market...