Pricing Bermudan Swaptions in a Stochastic-Volatility LIBOR Market Model

This paper introduces a time-inhomogeneous parameterization of the forward LIBOR volatilities and analyzes its implications for the valuation of Bermudan swaptions. The model approximates the actual term structure of volatilities with a curve from a given set defined by the parametric volatility specification and the structure of a continuous time Markov chain that modulates the volatility function. The first stochastic volatility specification generates jump discontinuities in volatility and shape-preserving evolution of the volatility term structure in thefuture. The second specification allows, in addition, for changes in the shape of the volatility curve. Simulated values of Bermudan swaptions in a LIBOR market model with these volatility structures were obtained and compared to the prices from standard deterministic volatility specifications. The model allows for the assessment of the forward volatility risk of Bermudan swaptions.