Narrow Results

A new approach to the problem of computing risk sensitivities of Bermuda swaptions in a lattice, or PDE, framework is presented. The algorithms developed perform the task much faster and more accurately that the traditional approach in which the Greeks are computed numerically by shocking the appropriate inputs and revaluing the instrument. The time needed to execute the tradition scheme grows linearly with the number of Greeks required, whereas our approach computes any number of Greeks for a Bermuda swaption in nearly constant time. The new method explores symmetries in the structure of Bermuda swaptions to derive recursive relations between different Greeks, and is essentially model-independent. These recursive relations allow us to represent risk sensitivities in a number of ways, in particular as integrals over the "survival" density. The survival density is obtained as a solution to a forward Kolmogorov equation. This representation is the basis for practical applications of our approach.

This paper describes an American Monte Carlo approach for obtaining fast and accurate exercise policies for pricing of callable LIBOR Exotics (e.g., Bermudan swaptions) in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM). SGBM is a bundling and regression based Monte Carlo method where the continuation value is projected onto a space where the distribution is known. We also demonstrate an algorithm to obtain accurate and tight lower–upper bound values without the need for nested Monte Carlo simulations.