I am faced with having to fit skew/smile to option quotes with different strike and same maturity. In order to keep things reasonably simple and to avoid potential artifacts from fitting higher order polynomials, I thought of using a quadratic polynomial.
Is there a consensus on which functions to use, resp. a paper discussing what makes most sense ?
Answer
@Lisa Ann: Typing an answer to my own post, mostly to share my "findings" for the benefit of anyone coming across this.
Looking at the paper of Brigo, Mercurio and Rapisarda, they fit using a single forward price. This comes at the expense of being able to fit only smiles, where the minimum is ATMF. I asked why, and got the answer that choosing different forward prices for the individual fit functions (as does Bahra) will allow for fitting smiles with non-ATMF minima (which I often find in the markets I am concerned with), however it may result in results that allow for arbitrage. While for $\lim_{K \to 0}$ and $\lim_{K \to \infty}$ there is no issue. However, I have indeed observed that CDF values <0 resp. >1 do occur.
Looks like shifting the distributions as described in the Brigo paper is called for ...
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