Efficient Control Variates and Strategies for Bermudan Swaptions in a LIBOR Market Model

Pricing Bermudan Swaptions in the LIBOR Market Model

Pricing Bermudan Swaptions on the LIBOR Market Model using the Stochastic Grid Bundling Method

We examine using the Stochastic Grid Bundling Method (SGBM) to price a Bermudan swaption driven by a one-factor LIBOR Market Model (LMM). Using a wellknown approximation formula from the finance literature, we implement SGBM with one basis function and show that it is around six times faster than the equivalent Longstaff–Schwartz method. The two methods agree in price to one basis point, and th...

Bounding Bermudan Swaptions in a Swap-rate Market Model

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 swaption prices on the number of instantaneous factors used in the model. We also establish an equivalence w...

On the joint calibration of the Libor market model to caps and swaptions market volatilities

In this paper we consider several parametric assumptions for the instantaneous covariance structure of the Libor market model. We examine the impact of each different parameterization on the evolution of the term structure of volatilities in time, on terminal correlations and on the joint calibration to the caps and swaptions markets. We present a number of cases of calibration in the Euro mark...

Different Covariance Parameterizations of the Libor Market Model and Joint Caps/Swaptions Calibration

In this paper we consider several parametric assumptions for the instantaneous covariance structure of the Libor market model. We examine the impact of each different parameterization on the evolution of the term structure of volatilities in time, on terminal correlations and on the joint calibration to the caps and swaptions markets. We present a number of cases of calibration in the Euro mark...