In this study, we attempt to calculate the term structure of the interest rate under partial information using a model in which the mean reversion level of the short rate changes in accordance with a regime shift in the economy. Under partial information, an investor observes the history of only the short rate and not a regime shift; hence, calculating the term structure of the interest rate is reduced to the problem of filtering the current regime from observable short rates. Therefore, we calculate it using the filtering theory that estimates a stochastic process from noisy observations, and investigate the effects of the regime shift under partial information on the market price of risk and the volatility of a bond price compared with those under full information, in which the regime is assumed to be observable. We find that, under partial information, the regime-shift risk converts into the diffusion risk. As a result, we find that both the market price of diffusion risk and the volatility of a bond price under partial information become stochastic, even though these under full information are constant.
Regime-Switching Behavior of the Term Structure of Forward Markets
