  We discuss modelling of SPX and DAX index option prices using the Shifted
Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR
model. We found out that for SPX options, an example of strongly skewed option
prices, SLN can produce a quite accurate fit. Moreover, for both types of index
options, the SLN model is giving a good fit of near-at-the-forward strikes.
Such a near-at-the-money fit allows us to calculate precisely the skew
parameter without involving directly the 3rd moment of the related probability
distribution. Eventually, we can follow with a procedure in which the skew is
calculated using the SLN model and further smile effects are added as a next
iteration/perturbation. Furthermore, we point out that the SLN trajectories are
exact solutions of the SABR model for rho = +/-1.
