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In Heston model, if my intuition is correct, increase in sigma (volatility of volatility parameter) would increase the kurtosis and correlation factor between returns and volatility dictates the skew of the volatility surface. Is it possible to modify it in such a way which could generate a vol surface which has a higher kurtosis on left side of the volatility surface compared to the right side while keeping the original skew intact (Skewness of kurtosis i.e. fifth moment).

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    $\begingroup$ Can you specify what you mean here by 'sigma'? As it stands, I cannot deduce from your question what is it precisely that you're asking, and certainly not how you think the fifth moment has to do with control of left and right wings. I.e. pls add more clarity/details. $\endgroup$
    – Frido
    Commented Aug 30, 2023 at 14:21
  • $\begingroup$ Edited the question. Please let me know if you would like more information. $\endgroup$ Commented Aug 30, 2023 at 14:29
  • $\begingroup$ Well the vol of vol affects the convexity of the IV skew (how curved it is), it affects the perceived correlation (steepness of the skew) through the product $\rho\sigma$ in the PDE for the Heston model, but what truly affects the correlation is of course the correlation parameter $\rho$. You cannot independently control left and right wings in Heston model - it's all inter-related, and I still don't know what the fifth moment has to do with this. $\endgroup$
    – Frido
    Commented Aug 30, 2023 at 14:29
  • $\begingroup$ Okay is there a way to modify the heston model in such a way which gives independent control? $\endgroup$ Commented Aug 30, 2023 at 14:31
  • $\begingroup$ Not that I am aware of. $\endgroup$
    – Frido
    Commented Aug 30, 2023 at 14:56

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