Our main goal is to investigate the question of which interest-rate options valuation models are better suited to support the management of interest-rate risk. We use the German market to test seven spot-rate and forward-rate models with one and two factors for interest-rate warrants for the period from 1990 to 1993. We identify a one-factor forward-rate model and two spot-rate models with two factors that are not significantly outperformed by any of the other four models. Further rankings are possible if additional criteria are applied.A VALUATION MODEL FOR INTEREST-RATE derivatives represents the core of any system designed to measure, control, and supervise interest-rate risk. This is true regardless of whether a value-at-risk methodology, sensitivity analysis, stress test, or scenario technique is applied. Unfortunately, there is no empirical evidence that evaluates the performance of the most popular competing pricing models using the same data from a risk management perspective. This paper provides such empirical evidence using data from the German market for interest-rate warrants for the period from 1990 to 1993.The more recent valuation models are dominated by two groups of models, forward-rate and spot-rate models. The approach of the first group, pioneered by Ho and Lee~1986! and Heath, Jarrow, and Morton~HJM!~1992!, directly uses the arbitrage-free dynamics of the entire zero bond price curve or, equivalently, the term structure of forward rates to price interest-rate derivatives. We refer to this approach as the forward-rate~or HJM! model. The approach of the second group~e.g., see Hull and White~1990, 1993!, Black, Derman, and Toy~1990!, Black and Karasinski~1991!, Jamshidiañ 1991!, and Sandmann and Sondermann~1993!! is based on the dynamics of * Bühler and Uhrig-Homburg are from the University of Mannheim, Germany. Walter is at Deutsche Genossenschaftsbank, Germany. Weber is at Infinity Financial Technology, London. We thank Michael Dempster, Darrell Duffie, Stewart Hodges, Wolfgang Schmidt, and Dieter Sondermann. We are especially grateful for the comments by Stephen Figlewski, Olaf Korn, and Stuart Turnbull. The paper has also greatly benefited from comments made at the Warwick Option Conference 1995, the European Financial Management Association Conference 1997, and the Finance seminars at Ecole Supérieure des Sciences Economiques et Commerciales, Paris; Eidgenössische Hochschule, Zürich; and Erasmus University, Rotterdam. Additional thanks go to an anonymous referee and René Stulz for helping us to sharpen our focus. THE JOURNAL OF FINANCE • VOL. LIV, NO. 1 • FEBRUARY 1999 269 the instantaneous spot interest rate. The second group's papers follow a suggestion by Cox, Ingersoll, and Ross~1985! and fit the endogenous term structure~and volatility structure! of interest rates to the observed term structure. This fitting is achieved through time-dependent parameters of the stochastic factor processes. Both approaches that model the stochastic behavior of the term structure of interest r...

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