The paper Skewness and Kurtosis Adjusted Black-Scholes Model: A Note on Hedging Performance by Sami Vähämaa discusses the hedging performance of skewness and kurtosis adjusted models for the pricing of options. According to the paper, these models price options more accurately, but their performance for hedging is worse than that of vanilla Black-Scholes. The measures they use are Mean Absolute Heding Error and Room Mean Squared Hedging Error, and the adjusted models perform worse in both measures according to their data, across all moneyness and maturities.What explanations are there for this? The only time the paper seems to delve into this is at the very end, where it states:QuoteA potential explanation might be that, although the Black-Scholes delta is likely to be biased, the estimation error in the delta is relatively small due to the simplicity of the model.Also, does anyone have any idea if their data covered periods of extreme/black swan events? Has the author considered that perhaps while the delta hedging performance is worse during steadier periods, but improved during the black swan periods that the adjusted models are trying to account for?

I´ll try an explanation:If i´m not mistaken, approaches like Corrado and Su, only deal with the final (acumulated) distribution. They do not imply there´s a difusion that could generate this distribution. If there´s no difusion, there´s no proper dynamic delta hedge.

Thank you. Has there ever been a diffusion proposed to model the fat tail/leptokurtic distribution?