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This questions is regarding the behaviour of banks and other financial institutions who deal with FX products and use SABR model volatilities to price options.

How often do they change/tune parameters $\alpha$, $\beta$, $\nu$ and $\rho$?

If a hedge fund is for instance buying USDEUR options and calibrate the model after observing today's market quotes. Will they recalibrate the model tomorrow or use the same parameters?

And finally, some literature suggests that when dealing with FX it is commom to use $\beta = 1$. Why is that?

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  • $\begingroup$ If you don't recalibrate your model parameters, whatever the model, them there's of course a (high) chance you are off from the market. You should recalibrate as often as the data you're receiving allows you to. $\endgroup$ – will Jun 27 '17 at 7:05
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The SABR parameters are typically calibrated daily. Intraday recalibrations may be required on particularly volatile days.

The choice beta = 1 is a popular choice when SABR is used in FX or equity markets, because of the distribution characteristics of the respective asset returns (matched best by beta = 1). In the rates markets, for which SABR was originally developed, beta depends on the option expiration and the underlying tenor.

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  • $\begingroup$ I guess this really depends on the market and the application. For risk management, daily calibrations are probably sufficient. But if you use SABR for market making and calibration to the listed options market, then daily is certainly too slow. $\endgroup$ – LocalVolatility Oct 12 '17 at 7:01

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