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

John C. Hull (University of Toronto - Rotman School of Management)

Alexander Sokol (CompatibL)

Alan White (University of Toronto - Rotman School of Management)

In this paper, authors 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, authors 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.

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Related conference presentations

Related research has been presented at several conferences and forums, including:

Calibrating Mean Reversion Skew and Real World Drift for XVA and Regulatory Capital, Alexander Sokol, Global Derivatives, Amsterdam 2014 (pdf).

Using Mean Reversion Skew and Joint Measure Calibration to Model Interest Rates over Long Time Horizons, Alexander Sokol, Barrie & Hibbert Seminar, Edinburgh 2014 (pdf).