Modeling the Short Rate: The Real and Risk-Neutral Worlds
19 Pages Posted: 2 Mar 2014 Last revised: 3 Jul 2014
Date Written: June 2014
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.
Keywords: Real World Measure, Market Price of Risk, PFE, CVA, Limits, Liquidity, Solvency II, Interest Rate Models, Short Rate, Monte Carlo, Long Term Simulation, Potential Future Exposure, Joint Measure
JEL Classification: G13, E43, E44
Suggested Citation: Suggested Citation