A Numerical Procedure for the General One-Factor Interest Rate Model

Hull and White (1993) considered a general one-factor interest rate model and developed a numerical procedure involving the use of trinomial trees so that the model is consistent with initial market data. Their procedure is very effective for some particular types of volatility functions, but may not be effective for others. The purpose of this article is to develop an alternative trinomial tree associated with the general one-factor term structure model based on the Kijima-Nagayama procedure (1994). Our procedure is simple but efficient and does not assume any particular form of volatility function. This is important because we can test the effect of a wide range of different assumptions on volatility by the same procedure. Numerical examples are given to support the usefulness of our results