Extending the universality of the Heath–Jarrow–Morton model

Dwight Grant and Gautam Vora

Review of Financial Economics, 2006, vol. 15, issue 2, 129-157

Abstract: Heath, Jarrow, and Morton (HJM) developed an important model of the evolution of interest rates. A key assumption of the model is that interest rate changes are normally distributed in continuous time. Implementing the HJM‐method of evolution of interest rates in discrete time for more complex volatility functions remains a significant challenge. In this article, we present a relatively simple and flexible method of implementation, that extends the usefulness of the HJM model. The derivation assumes that the distribution of interest rates is stable, but not necessarily identical, for each discrete time period. This allows us to identify the drift‐adjustment terms necessary to build interest rate lattices and trees and Monte Carlo simulations that satisfy exactly the no‐arbitrage and volatility conditions, even complex ones, of the model. The much more difficult discrete‐time implementation methods suggested in the literature (Heath, Jarrow, and Morton (1991) [Heath, D., Jarrow, R. & Morton, A. (1991). Contingent claim valuation with a random evolution of interest rates. Review of Futures Markets, 54–76.] and Jarrow (1996) [Jarrow, R. (1996). Modeling fixed income securities and interest rate options. New York, NY: McGraw‐Hill Companies Inc.]) do not accomplish that. We illustrate our analytical implementation with three examples of volatility functions and demonstrate its superiority to other methods of implementation.

Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1016/j.rfe.2005.04.003

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:revfec:v:15:y:2006:i:2:p:129-157

Access Statistics for this article

More articles in Review of Financial Economics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().