We present a new non-nested approach for computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is possible to early terminate paths once points of optimal exercise have...

We investigate the pricing performance of eight trinomial trees and one binomial tree, which was found to be most effective in an earlier study, under 20 different implementation methodologies for pricing American put options. We conclude that the binomial tree, the Tian third‐order...

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 study the simulation of range accrual coupons when valuing callable range accruals in the displaced-diffusion LIBOR market model (DDLMM). We introduce a number of new improvements that lead to significant efficiency improvements, and explain how to apply the adjoint-improved pathwise method...

We introduce two new methods to calculate bounds for zero-sum game options using Monte Carlo simulation. These extend and generalize upper-bound duality results to the case where both parties of a contract have Bermudan optionality. It is shown that the primal-dual simulation method can still be...

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

We present an extension of the LIBOR market model which allows for stochastic instantaneous volatilities of the forward rates in a displaced-diffusion setting. We show that virtually all the powerful and important approximations that apply in the deterministic setting can be successfully and...

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 compare the bias in binomial trees against that in certain analytical/numerical valuation techniques with which they disagree. We consider the CRR tree, the COS method and the Leisen--Reimer as well as the Prekopa--Szantai exponentially smoothed method. We conclude that the binomial trees are...