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The Hull and White Model of the Short Rate: An Alternative Analytical Representation

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  • Dwight Grant
  • Gautam Vora

Abstract

Hull and White extend Ho and Lee's no‐arbitrage model of the short interest rate to include mean reversion. This addition eliminates the problem of negative interest rates and has found wide application. To implement their model, Hull and White employ a sequential search process to identify the mean interest rate in a trinomial lattice at each date. In this article we extend Hull and White's work by developing an analytical solution for the mean interest rate at each date. This solution applies equally well to trinomial lattices, interest rate trees, and Monte Carlo simulation. We illustrate the analytical result by applying it to an example originally used by Hull and White and then for valuing an option on a bond.

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  • Dwight Grant & Gautam Vora, 2002. "The Hull and White Model of the Short Rate: An Alternative Analytical Representation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 25(4), pages 463-476, December.
    • Handle: RePEc:bla:jfnres:v:25:y:2002:i:4:p:463-476
    DOI: 10.1111/1475-6803.00031
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    Cited by:

    1. Dwight Grant & Gautam Vora, 2006. "Extending the universality of the Heath–Jarrow–Morton model," Review of Financial Economics, John Wiley & Sons, vol. 15(2), pages 129-157.
    2. Grant, Dwight & Vora, Gautam, 2006. "Extending the universality of the Heath-Jarrow-Morton model," Review of Financial Economics, Elsevier, vol. 15(2), pages 129-157.

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