# Recalibrating SABR parameters for Swaption ATM volatility

I understand that the ATM volatility of Swaption moves quite frequently and the SABR will need to be recalibrated. Which parameter should I recalibrate?

Is there any financial meanings why we only recalibrate on certain parameters?

Thanks.

## 1 Answer

You will need to recal alpha beta and rho:

\begin{align*} dF_{t}&=\sigma _{t}F_{t}^{\beta }\,dW_{t}\\ d\sigma _{t}&=\alpha \sigma _{t}^{{}}\,dZ_{t}\\ \end{align*} Where $$dW_{t}dZ_{t}=\rho dt$$

• alpha, volvol, lognormal vol of vol param sigma, alpha >= 0.
• beta, skew, closed form soln only if in set {0,1}
• rho, correlation coefficient between two stochastic state variables forward price F and volatility of fwd price, sigma.

Parameters describe smile (richness of out of the money options) and the skew (whether implied vol is upward or downward sloping as a function of strike).

Take a look at Matlab's implementation, which discusses two methods based on closed form, https://www.mathworks.com/help/fininst/calibrating-the-sabr-model.html?s_tid=gn_loc_drop