In this paper, we derive and empirically test a regime-shifting dynamic term structure model for pricing interest rate caps. The central state variables are the target rate of the Federal Reserve and its latent regime in which it fluctuates. These state variables are driven by a discrete time inhomogeneous Markov chain that captures the timing of FOMC meetings. The Fed Funds rate and the slope of the Libor-swap term structure complete the set of state variables. Their dynamics exhibit regime-shifts based on the latent regime of the target rate in both the physical and risk-neutral measures. The modelling approach for pricing at-the-money cap prices leads to an exponential affine analytical form where the regime-shift risk is priced. Allowing for this feature significantly helps the model to empirically match cap prices. The empirical analysis also indicates that the stable regime where the target rate is frequently at inertia is a state where market operators exhibit a higher level of risk aversion. It is also in this regime that the term structure of the mean Black implied volatilities is the highest and where cap price changes are the most sensitive to jumps in the target rate.
Published June 2012 , 30 pages