In this repository I have all the code for the experiments with the volatility fitting method suggested by Gatheral.
In the Black-Scholes world there is a problem with implied volatility, namely it changes with the strike price. This is not an interpretable more like an artifact of the Black-Scholes model (so called volatility smile). In practice we never have the implied volatility for all option prices we only have a few points. The question is: how can we fit a proper curve to the measured (market) points in a way that the model class implicitly have constraints agains arbitrage. Gatheral solved this question.