A Generalized Procedure for Building Trees for the Short Rate
John Hull and Alan White（看到John Hull 的大名果断下载了）
Joseph L. Rotman School of Management
University of Toronto
January 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 finds that the best fit to cap prices at the end of 2013 was
provided by a function remarkably similar to that estimated by Deguillaume et al (2013) from
historical data.
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