How Heston Parameters Shape Volatility Skew and Surface Wings

Summary

The document asks whether the Heston stochastic volatility model can produce a volatility surface with more pronounced kurtosis on the left wing than on the right while preserving the existing skew. It identifies volatility of volatility as a driver of kurtosis and the correlation between returns and volatility as a driver of skew, then frames the desired asymmetry in the fifth moment as an open modeling question.

No modification or calibrated example is supplied, so the document does not establish a method for achieving that shape or demonstrate that the stated parameter effects are sufficient. It is useful as a question about the limits of the standard Heston specification: matching skew and overall kurtosis may not independently control asymmetry between the two wings. Further model details or empirical evidence would be needed to assess possible extensions.

Key ideas

• Volatility of volatility is raised as a possible control for return kurtosis in Heston.
• Return-volatility correlation is identified as a driver of implied-volatility skew.
• The question seeks stronger left-wing than right-wing kurtosis while retaining the original skew.
• The document proposes no model extension or evidence that achieves the requested surface shape.

Tags

# How to modify the Heston Model such that we can modify the wings of the volatility surface?


# How to modify the Heston Model such that we can modify the wings of the volatility surface?












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.