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...

We develop an efficient algorithm to implement the adjoint method that computes sensitivities of an interest rate derivative (IRD) with respect to different underlying rates in the co-terminal swap-rate market model. The order of computation per step of the new method is shown to be proportional...

This paper derives the pathwise adjoint method for the predictor-corrector drift approximation in the displaced-diffusion LIBOR market model. We present a comparison of the Greeks between log-Euler and predictor-corrector, showing both methods have the same computational order but the latter to...

We develop new Monte Carlo techniques based on stratifying the stock's hitting-times to the barrier for the pricing and Delta calculations of discretely-monitored barrier options using the Black-Scholes model. We include a new algorithm for sampling an Inverse Gaussian random variable such that...

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...

This paper extends the pathwise adjoint method for Greeks to the displaced-diffusion LIBOR market model and also presents a simple way to improve the speed of the method. The speed improvements of approximately 20% are achieved without using any additional approximations to those of Giles and...

We investigate the pricing performance of eight trinomial trees and one binomial tree, which was found to be most effective in an earlier paper, under twenty different implementation methodologies for pricing American put options. We conclude that the binomial tree, the Tian third order moment...

The pricing of snowball notes in the full-factor LIBOR market model is considered. The primary aspect of the problem considered is the early exercise feature, and it is shown how to characterize a class of sub-optimal points of exercise. By combining this characterization with least-squares...