Instantaneous Forward Rates and Hull–White Calibration

Summary

The note explains why a market instantaneous forward rate is not a directly observable Bloomberg quote. An instantaneous forward rate is a theoretical curve quantity whose value depends on the model and assumptions used to infer it, so separate implementations can yield different estimates.

It distinguishes calibration under the physical measure from risk-neutral calibration. For physical-measure mean reversion, the answer suggests using a short-term interest rate, such as bill rates, as a proxy. For risk-neutral calibration, it recommends fitting to quoted market instruments, such as bonds or swaps, chosen to match the curve being modeled. The response is brief and gives no data, derivation, or comparison of proxy quality, so the suitability of any instrument depends on the calibration objective.

Key ideas

• An instantaneous forward rate is a model-derived quantity rather than a directly quoted market input.
• Different models or implementations can produce different instantaneous forward curves.
• For physical-measure mean-reversion estimation, short-term rates may serve as proxies.
• Risk-neutral calibration should use market instruments consistent with the curve being fitted.

Tags

# Instantaneous Forward Rate from Bloomberg


# Instantaneous Forward Rate from Bloomberg












I am calibrating the Hull-White model which involves finding the level of mean-reversion from the market instantaneous forward rate? Is the market instantaneous forward rate directly available from Bloomberg? Thank you.

## Answer by Helin (score 2)

https://quant.stackexchange.com/a/34982

"Instantaneous forward rate" is a theoretical construct. Two different models produce vastly different forwards; in fact, two different researchers using the same model may produce different forwards. So short answer is no, this is not available from Bloomberg.

Assuming you're trying to get mean-reversion params for the physical measure, you can just use a short-term interest rate (e.g., short-term bill rates) as a proxy. Assuming you're calibrating in the risk neutral measure, then use quoted instruments (bonds or swaps, depending on what curve you're fitting).

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