How Does Stochastic Basis Change Mean Reversion? A Study on Bermudan Swaptions

Abstract

The main goal of this work is to analyse the impact of the stochastic nature of basis spreads in the price of Bermudan swaptions. In this paper we find a relationship between the effect of stochastic basis spreads and an effective mean reversion of the traditional one-factor Hull-White model. We develop an extended Hull-White model which considers two different curves: one used to discount and the other used to estimate cash-flows, with a stochastic basis spread between both curves. We derive formulas for the Libor rate and the stochastic discount factor. We also derive semi-analytical formulas for Euopean swaptions used to calibrate the model. The impact of stochastic basis spreads in Bermudan swaptions is analysed for different volatility and correlation scenarios. We show that the impact may clearly become non-negligible and is captured in a natural way by means of an effective mean reversion in the simplest one-factor Hull-White model. This permits to manage positions in an effective way, incorporating stochastic basis spreads automatically.