Illustrative Hull–White Volatility Parameter Estimates for US Swaps

Summary

The document asks for approximate parameter choices for a Hull–White model used to simulate forward rates on the US swap curve. It specifies an exponentially decaying HJM volatility shape, where alpha sets the scale and gamma controls how quickly volatility declines with the gap between observation and forward dates. The question seeks plausible starting values rather than a precise calibration.

The accepted reply reports alpha of 0.022 and sigma of 0.009, attributing them to a calibration using a named software package and data service. It does not explain the calibration procedure, define the relationship between sigma and the question’s gamma parameter, or provide market dates, curve inputs, fit diagnostics, or validation. The quoted figures are therefore an isolated example, not a general recommendation. Readers would need to confirm parameter conventions and calibrate against their own curve and modeling assumptions before using them.

Key ideas

• The question concerns an exponentially decaying HJM volatility specification for US swap forward rates.
• Alpha controls volatility scale, while gamma governs decay across forward maturities.
• The reply supplies example calibrated values but does not document the fitting method.
• The reported sigma is not reconciled with the question’s gamma notation, so parameter conventions require checking.

Tags

# Reasonable Hull & White parameters


# Reasonable Hull & White parameters












I am using a Hull & White model to simulate forward rates on US swap curve from the 1.10.2012. This is a part of a bigger picture, and I am interested in some reasonable values for the parameters alpha and gamma. Exactly calibrated values are not needed, so I thought it would be faster to ask here :)

i.e. I want alpha and gamma so that the HJM-volatility is

$\sigma(t_i,t_j) = \alpha * e^{-\gamma (t_j-t_i)}$

and gives a reasonable shape. Top of the head-answers are encouraged.

## Answer by matteot (score 0, accepted)

https://quant.stackexchange.com/a/4941

With Fairmat Academic / Data-Link we obtain the following values: alpha=0.022, sigma=0.009.

Fairmat Academic can be freely downloaded from http://www.fairmat.com/downloads

While the code used to calibrate the hull and white model can be found on GitHub: https://github.com/fairmat/InterestRatesModels

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.