Forward-Rate Volatility Specifications in the HJM Framework

Summary

The document asks about common specifications for forward-rate volatility in the Heath–Jarrow–Morton (HJM) framework, with particular interest in two- and three-factor models used in industry. It gives one example: instantaneous forward-rate volatility represented as a sum of two exponentially decaying components, and relates this form to the G2++ model. It also asks for guidance on calibration references.

No model equations beyond that brief example, calibration procedure, cited references, market evidence, or model comparison are supplied. The text is a request for pointers rather than a developed explanation, so it offers only a starting point for studying parametric term-structure volatility. The example indicates that factor count and the shape of volatility across forward maturities are specification choices, but the document does not discuss fit, parameter estimation, or limitations of any particular choice.

Key ideas

• The document asks which forward-rate volatility specifications are commonly used with HJM models.
• It identifies two- and three-factor models as candidates of interest.
• It gives a sum of two exponentially decaying components as an example for instantaneous forward-rate volatility.
• It requests references on model calibration but provides no calibration method or sources.

Tags

# Vol specifications under Heath Jarrow Morton framework


# Vol specifications under Heath Jarrow Morton framework












What are some of the common forward vol specifications under HJM framework used in the industry. I guess most common would be 2 and 3 factor models, but any pointers to more details would be very useful. An example would be - parametric instantaneous forward rate vol as sum of two exponential decaying vols (same as G2++ model).

PS: could you please also point to any references on the model calibration as well.

Thanks for your help!

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