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Risk-Neutral Densities: A Review

Author

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  • Stephen Figlewski

    (New York University Stern School of Business, New York, NY 10012-1126, USA)

Abstract

Trading in options with a wide range of exercise prices and a single maturity allows a researcher to extract the market's risk-neutral density (RND) over the underlying price at expiration. The RND contains investors’ beliefs about the true probabilities blended with their risk preferences, both of which are of great interest to academics and practitioners alike. With a particular focus on US equity options, I review the historical development of this powerful concept, practical details of fitting an RND to options market prices, and the many ways in which investigators have tried to distill true expectations and risk premia from observed RNDs. I briefly discuss areas of active current research including the pricing kernel puzzle and the volatility surface, and offer thoughts on what has been learned about RNDs so far and fruitful directions for future research.

Suggested Citation

  • Stephen Figlewski, 2018. "Risk-Neutral Densities: A Review," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 329-359, November.
    • Handle: RePEc:anr:refeco:v:10:y:2018:p:329-359
    DOI: 10.1146/annurev-financial-110217-022944
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    Citations

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    Cited by:

    1. Chen, Qiang & Han, Yu, 2023. "Options market ambiguity and its information content," Journal of Financial Markets, Elsevier, vol. 64(C).
    2. Bressan, Silvia & Weissensteiner, Alex, 2021. "The financial conglomerate discount: Insights from stock return skewness," International Review of Financial Analysis, Elsevier, vol. 74(C).
    3. Li, Yifan & Nolte, Ingmar & Pham, Manh Cuong, 2024. "Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures," Journal of Econometrics, Elsevier, vol. 241(2).
    4. Bian, Timothy Yang & Wang, Tianyi & Zhou, Zipeng, 2021. "Measuring investors’ risk aversion in China’s stock market," Finance Research Letters, Elsevier, vol. 42(C).
    5. Shan Lu, 2019. "Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(12), pages 1587-1612, December.
    6. George Dotsis, 2024. "A New Index of Option Implied Absolute Deviation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(9), pages 1543-1555, September.
    7. Ben Boukai, 2021. "On the RND under Heston's stochastic volatility model," Papers 2101.03626, arXiv.org.
    8. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    9. Sanford, Anthony, 2024. "Information content of option prices: Comparing analyst forecasts to option-based forecasts," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    10. Ben Boukai, 2021. "The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility model," Papers 2108.07937, arXiv.org, revised Aug 2021.

    More about this item

    Keywords

    risk-neutral densities; option risk premia; implied volatility; option pricing;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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