A Generalized Procedure for Building Trees for the Short Rate

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.