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We derive analytic formulae which link $\alpha$, $\nu$ and $\rho$ parameters in Andreasen-Huge style SABR model to the ATM price and option prices at four equally spaced strikes on the sides of ATM. We give two applications. First, we give a characterisation for the SABR parameters in terms of the swap rate forward probability density function. Second, we show how Andreasen-Huge SABR can be combined with other well know analytic SABR formulae to allow consistent use in the non-arbitrage region.

Analytic Calibration in Andreasen-Huge SABR Model