European Option Premiums usually expressed as Implied Volatility 3D Surface σ(t, k).
IV shows how the probability distribution of the underlying stock differs from the baseline – the normal distribution. But the normal distribution is quite far away from the real underlying stock distribution. And so to compensate for that discrepancy – IV has complex curvature (smile, wings, asymmetry).
I wonder if there is a better choice of the baseline? Something that has reasonably simple form and yet much closer to reality than the normal distribution? For example something like SkewT(ν(t), λ(t)) with the skew and tail representing the "average" underlying stock distribution?
In theory – this should provide a) simpler and smoother IV surface and so less complicated SV models to fit it and b) better normalisation – making it easier to compare different stocks and spot anomalies c) possibly also easier to analyse visually, spot the patterns.
Wonder if there's any studies on such approach?
P.S.
The IV for the SkewT baseline could be solved numerically.
IV also preferred because of the simplicity and speed of BS computations and nice math formulas. But, with modern computing power and numerical solvers, it's not a problem (with exception of HF trading, but, they are different story).
Posted by h234sd