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The Hull and White Model of the Short Rate: An Alternative Analytical Representation
Author(s) -
Grant Dwight,
Vora Gautam
Publication year - 2002
Publication title -
journal of financial research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.319
H-Index - 49
eISSN - 1475-6803
pISSN - 0270-2592
DOI - 10.1111/1475-6803.00031
Subject(s) - trinomial , hull , short rate model , mean reversion , vasicek model , representation (politics) , monte carlo method , interest rate , mathematics , arbitrage , econometrics , computer science , statistics , economics , financial economics , volatility (finance) , combinatorics , engineering , marine engineering , politics , political science , monetary economics , law
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.