Fast and Accurate Exercise Policies for Bermudan Swaptions in Libor Market Model

Abstract

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.

Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

“…The sensitivity of the continuation value with respect to the model parameters for the paths at t m−1 is computed using the relation in Equation (10) and with respect to the state space is computed using the relation in Equation (19), where…”