A Generalized Procedure for Building Trees for the Short Rate and Its Application to Determining Market Implied Volatility Functions

33 Pages Posted: 23 Feb 2014 Last revised: 9 Apr 2017

See all articles by John C. Hull

John C. Hull

University of Toronto - Rotman School of Management

Alan White

University of Toronto - Rotman School of Management

Date Written: June 1, 2014

Abstract

One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate models can be accommodated. It shows how a piecewise linear volatility function can be calibrated to market data and, using market data from days during the period 2004 to 2013, finds that the best fit to cap prices is provided by a function remarkably similar to that estimated by Deguillaume et al (2013) from historical data.

Keywords: Interest Rate Models, Short Rate, Trees, Derivatives

JEL Classification: G13

Suggested Citation

Hull, John C. and White, Alan, A Generalized Procedure for Building Trees for the Short Rate and Its Application to Determining Market Implied Volatility Functions (June 1, 2014). Rotman School of Management Working Paper No. 2399615. Available at SSRN: https://ssrn.com/abstract=2399615 or http://dx.doi.org/10.2139/ssrn.2399615

John C. Hull (Contact Author)

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)

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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