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

19 Pages Posted: 2 Mar 2014 Last revised: 3 Jul 2014

See all articles by John C. Hull

John C. Hull

University of Toronto - Rotman School of Management

Alexander Sokol

CompatibL

Alan White

University of Toronto - Rotman School of Management

Date Written: June 2014

Abstract

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

Hull, John C. and Sokol, Alexander and White, Alan, Modeling the Short Rate: The Real and Risk-Neutral Worlds (June 2014). Rotman School of Management Working Paper No. 2403067. Available at SSRN: https://ssrn.com/abstract=2403067 or http://dx.doi.org/10.2139/ssrn.2403067

John C. Hull

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
(416) 978-8615 (Phone)
416-971-3048 (Fax)

Alexander Sokol (Contact Author)

CompatibL ( email )

100 Overlook Center
Second Floor
Princeton, NJ 08540
United States

HOME PAGE: http://www.compatibl.com

Alan White

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
416-978-3689 (Phone)
416-971-3048 (Fax)

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