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.