Interest Rate Models Implied Volatility Function Stochastic Movements

Thomas S. Y. Ho and Blessing Mudavanhu

Volume 5, Number 4, Fourth Quarter 2007

This paper presents a one-factor and a two-factor arbitrage-free interest rate models with parsimonious implied volatility functions. The models are empirically tested on the entire swaption surface in three currencies (US dollar, Euro, and Japanese yen) over a 5-year period. They are shown to be robust in explaining the swaption values, and the implied volatility functions are shown to exhibit a three-factor movement in all three currencies. The results show that the observed swaption prices incorporate the market conditional expectations of the correlations of the key interest rates and the stochastic process of the yield curve, and the interest rate models should be calibrated to such market information to provide accurate relative valuation. Further this paper describes a modeling approach that has important implications on hedging interest rate derivatives dynamically taking the stochastic volatility risks into account.