When HJM Models Improve on Short-Rate Models for Derivatives

Summary

The document explains why a Heath–Jarrow–Morton forward-curve model may be preferable to a short-rate model for pricing complex interest-rate derivatives. For simpler instruments, a short-rate model can capture the main source of variance. However, its assumptions impose structure on the shape of forward volatility and often on forward-curve tilt, which may not match observed market behavior.

When a derivative's value is sensitive to changes in forward volatility or curve tilt, a multifactor framework such as HJM can represent those dynamics more flexibly. Bermudan swaptions are given as an example of an instrument that can benefit from this added structure. The answer offers a qualitative model-selection principle, not a comparison of calibration procedures, numerical results, or pricing performance; it also does not specify which HJM implementation is appropriate for a given product.

Key ideas

• Short-rate models can capture the key variance for relatively simple instruments.
• Short-rate model assumptions constrain forward-volatility shapes and may impose unrealistic curve tilt.
• Derivatives sensitive to forward volatility or tilt may need a multifactor forward-curve model.
• Bermudan swaptions are an example where HJM-style flexibility can be useful.

Tags

# HJM or Short rates model?


# HJM or Short rates model?












When market practitioners do prefer HJM models to short rates models when it comes to pricing derivatives (other than swaptions and caps, let say light exotics to exotics) ?

To be more specific, what are the features of the derivatives that's make forward curve models more appealing than short rate models ?

## Answer by Brian B (score 2)

https://quant.stackexchange.com/a/41508

If you have a simple instrument, short rate models capture all the key variance, but they impose structure on the shape of forward volatility curves (and, usually, forward tilt) that is often far from realistic.

If you have instruments whose value is sensitive to what might happen with tilt or forward volatility, you need a multifactor model like HJM. Bermudan swaptions are a good example.

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.