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 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 develop a new method for finding upper bounds for Bermudan swaptions in a swap-rate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bid-offer spread. As an application, we study the dependence of Bermudan...

We introduce a new calibration methodology that allows perfect fitting of the displaced diffusion LIBOR market model to caplets and co-terminal swaptions, whilst avoiding global optimizations. The approach works by regarding a forward rate as a difference of swap rates and then bootstrapping...

A new binomial approximation to the Black-Scholes model is introduced. It is shown that, for digital options and vanilla European call and put options, a complete asymptotic expansion of the error in powers of n-1 exists. This is the first binomial tree for which an asymptotic expansion has been...

We present four new methods for approximating the drift in the LIBOR market model when performing very long steps. These are compared with a variety of existing methods, including PPR, Glasserman-Zhao and predictor-corrector. We find that two of them, which use correlation adjustments to better...