SABR Question

Why does the market take the $\beta$ parameter as a "constant"?

  • I see most brokers quoting SABR parameters nowadays.
  • I've seen many banks use $\beta$=0.5 as a rule.
  • I've seen quants select a $\beta$ based on best fit to calibration instruments.

What is most correct to the spirit of the paper, and explain any issues to anticipate with IMR/IPV processes.


1 Answer 1


Managing Smile risk from Hagan et. al.

Generally if you pre-select $\beta$, it is from a priori considerations.

  • $\beta = 1$ corresponds to stochastic lognormal
  • $\beta = 0$ is stochastic normal
  • $\beta=1/2$ CIR

In the SABR model, beta is usually calibrated first, followed by the other 3 parameters. Frequently, instead of calibrating beta, it is simply assumed to have $\beta=1/2$ (since CIR is widely used). That said, JPY it is also natural to select 0 for JPY due to negative rates.
The paper explains both. "Aesthetic" consideration (a priori - fixed) or determined form historical observations.

Click here for an intuitive explanation of the SABR model. How to estimate $\beta$ can be seen in this answer.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.