Modeling the Short Rate : The Real and Risk-Neutral Worlds

In this paper, we propose a way to construct a single forward-looking model for interest rates, which represents their evolution under both the Q-measure and P-measure (a joint measure model). As is well known, the market prices of contingent claims are independent of investor risk preferences. This means that risk preferences, and therefore real world processes, cannot be obtained from market prices alone. Using a new concept, the local price of risk, we present a simple way in which historical data can be used in conjunction with market prices to create a joint measure model for the short rate and estimate the real world drift in interest rates. The local price of risk can be used for a wide range of interest rate models