Choosing Normal or Lognormal Short-Rate Models

Summary

The document asks how to choose between normal short-rate models, such as Hull–White, and lognormal models, such as Black–Karasinski, when the aim is to reproduce market data. It notes the familiar limitation that a lognormal rate cannot become negative, then asks whether other criteria distinguish the distributions.

The response says distribution choice is only one part of selecting a short-rate process. It points to references on interest-rate models and notes that pricing models have often favored lognormal specifications when more precise distributional properties were needed. However, it gives no calibration procedure, data comparison, or specific criteria for judging fit beyond that broad observation. The excerpt therefore offers background rather than a decision rule; the appropriate model remains dependent on the market behavior and pricing task being represented.

Key ideas

• Normal and lognormal short-rate models differ in their allowed rate distributions.
• A lognormal rate specification cannot represent negative short rates.
• Distribution choice alone does not determine which short-rate model best fits market data.
• The response notes a historical preference for lognormal models when distributional precision mattered.
• The excerpt gives no empirical model comparison or practical selection procedure.

Tags

# Normal vs Lognormal Short Rate models


# Normal vs Lognormal Short Rate models












Are there any general arguments to decide whether it is better to use a model with a normal or a lognormal distribution of the short rate? E.g. Hull-White with a normal and Black-Karasinski with a lognormal, is there a way to judge which is better? I am aware of the fact that lognormal models don't describe negative interest rates, but are there any other criteria? By "better" I mean the model's better ability to reproduce actual market data.

## Answer by Lucas Morin (score 4, accepted)

https://quant.stackexchange.com/a/8491

General knowledge:

The reference for short rates models is: Interest Rate Models, by D. Brigo & F. Mercurio, Springer Worth the cost.

You can find a summary of the propeties of the "dr" models p15 & p19: Interest Rate Models: Paradigm shifts in recent years, D. Brigo, Columbia University Seminar

You will see the quote p19: "Pricing models need to be more precise in the distribution properties so lognormal models were usually preferred". Normal Versus Lorgnormal is not the only thing involved in the process of choosing the models.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.