 The value formula_36 denotes a conveniently chosen midpoint between formula_8 and formula_26 (such as the geometric average formula_39 or the arithmetic average formula_40).We have also set

and

The function formula_44 entering the formula above is given by

Alternatively, one can express the SABR price in terms of the normal Black's model.Then the implied normal volatility can be asymptotically computed by means of the following expression