The Term Structure of Simple Forward Rates with Hidden Markov Jump Risk

Abstract

Markov jump diffusion models have been proposed to address leptokurtic feature of the asset return distribution, volatility smile, the effects of volatility clustering phenomenon and long memory. In this study, we develop a term structure of forward LIBOR rates with hidden Markov jump risk, a extend model of pure jump risk, and characterize the arbitrage-free dynamics of simple forward rates with hidden Markov jump diffusion risk. According to no-arbitrage framework, the closed forma formulas for a caplet and swaption are derived for the interest rate derivatives. When the jump size follows a specific distribution, such as a lognormal distribution or a default probability, we devise explicit analytic formulas for no-arbitrage prices. In the future, through proposed models and derived formulas, we investigate the empirical phenomenon in fixed-income markets and illustrate the effect of jumps, via stochastic intensity, on implied volatility and volatility surface as well as sensitivity analysis.