We introduce a set of improvements which allow the calculation of very tight lower bounds for Bermudan derivatives using Monte Carlo simulation. These tight lower bounds can be computed quickly, and with minimal hand-crafting. Our focus is on accelerating policy iteration to the point where it...

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 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 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...

We present a new method for truncating binomial trees based on using a tolerance to control truncation errors and apply it to the Tian tree together with acceleration techniques of smoothing and Richardson extrapolation. For both the current (based on standard deviations) and the new (based on...

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...

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...

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 a fast method to price and hedge CMS spread options in the displaced-diffusion co-initial swap market model. Numerical tests demonstrate that we are able to obtain sufficiently accurate prices and Greeks with computational times measured in milliseconds. Further, we find that CMS...