SABR Question: Why does the market take the beta parameter as a constant?

External question — Quantitative Finance Stack Exchange Author: Mike Original post: https://quant.stackexchange.com/questions/44273 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. 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.

External answer — Quantitative Finance Stack Exchange Author: AKdemy Original post: https://quant.stackexchange.com/a/63749 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. 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 .