Physical and Risk-Neutral Moments in Option Pricing Models

Summary

The document raises a question about whether option pricing models can estimate physical moments, such as skewness and kurtosis, separately from risk-neutral moments. It contrasts this possibility with model-free methods such as the VIX methodology, whose outputs are risk-neutral, and mentions the Heston and Bates models as examples of models discussed in the cited research.

The text contains the question but no answer or derivation. It therefore introduces a useful distinction between moments under the real-world probability measure and those implied by option prices, without explaining how a model would identify or calculate each set. It supplies no data, estimation procedure, empirical findings, or caveats about model assumptions. Readers should treat it as a prompt for further study rather than a complete method for computing physical skewness or kurtosis.

Key ideas

• The document asks how option models can produce physical moments separately from risk-neutral moments.
• It specifically identifies physical skewness and kurtosis as the quantities of interest.
• It contrasts model-based approaches with model-free option measures that yield risk-neutral quantities.
• No answer, estimation procedure, or empirical evidence is provided.

Tags

# Computing Physical and Risk-Neutral Moments in a Model-Based Fashion


# Computing Physical and Risk-Neutral Moments in a Model-Based Fashion












In Christoffersen et al. (2013), the authors state that it is possible to compute both physical and risk-neutral moments separately in a model-based fashion. Some examples of option pricing models that can do these are Heston (1993) and Bates (2000).

I am quite surprised because even in Model-Free implementation (such as in the VIX methodology), the outputs are risk-neutral. How is it possible that models are able to produce physical moments?

To be specific, I think the authors are referring to physical skewness and kurtosis.

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