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Simple and reliable way to compute option-based risk-neutral distributions

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  • Allan M. Malz

Abstract

This paper describes a method for computing risk-neutral density functions based on the option-implied volatility smile. Its aim is to reduce complexity and provide cookbook-style guidance through the estimation process. The technique is robust and avoids violations of option no-arbitrage restrictions that can lead to negative probabilities and other implausible results. I give examples for equities, foreign exchange, and long-term interest rates.

Suggested Citation

  • Allan M. Malz, 2014. "Simple and reliable way to compute option-based risk-neutral distributions," Staff Reports 677, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:677
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
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    4. Ruijun Bu & Kaddour Hadri, 2007. "Estimating option implied risk-neutral densities using spline and hypergeometric functions," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 216-244, July.
    5. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
    6. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    7. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
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    Citations

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    Cited by:

    1. Sonalika Sinha & Bandi Kamaiah, 2017. "Estimating Option-implied Risk Aversion for Indian Markets," IIM Kozhikode Society & Management Review, , vol. 6(1), pages 90-97, January.
    2. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
    3. Fabien Le Floc’h & Cornelis W. Oosterlee, 2019. "Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II," Risks, MDPI, vol. 7(1), pages 1-21, March.
    4. Dossani, Asad, 2021. "Central bank tone and currency risk premia," Journal of International Money and Finance, Elsevier, vol. 117(C).
    5. Iain J. Clark & Saeed Amen, 2017. "Implied Distributions from GBPUSD Risk-Reversals and Implication for Brexit Scenarios," Risks, MDPI, vol. 5(3), pages 1-17, July.
    6. Ahmadov, Vugar & Huseynov, Salman & Mammadov, Fuad & Karimli, Tural, 2015. "Brent nefti opsiyonlarından neytral riskli ehtimal paylanmasının əldə olunması [Extracting risk-neutral probability distribution from Brent oil options]," MPRA Paper 65704, University Library of Munich, Germany.
    7. Matthew Greenwood-Nimmo & Daan Steenkamp & Rossouw van Jaarsveld, 2022. "CaninformationonthedistributionofZARreturnsbeusedtoimproveSARBsZARforecasts," Working Papers 11035, South African Reserve Bank.
    8. Mirkov, Nikola & Pozdeev, Igor & Söderlind, Paul, 2019. "Verbal interventions and exchange rate policies: The case of Swiss franc cap," Journal of International Money and Finance, Elsevier, vol. 93(C), pages 42-54.
    9. Bressan, Silvia & Weissensteiner, Alex, 2021. "The financial conglomerate discount: Insights from stock return skewness," International Review of Financial Analysis, Elsevier, vol. 74(C).
    10. Taboga, Marco, 2016. "Option-implied probability distributions: How reliable? How jagged?," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 453-469.
    11. Mr. Fabio Comelli & Mrs. Esther Perez Ruiz, 2016. "To Bet or Not to Bet: Copper Price Uncertainty and Investment in Chile," IMF Working Papers 2016/218, International Monetary Fund.
    12. Agarwalla, Sobhesh Kumar & Varma, Jayanth R. & Virmani, Vineet, 2021. "The impact of COVID-19 on tail risk: Evidence from Nifty index options," Economics Letters, Elsevier, vol. 204(C).
    13. Nicolás Álvarez & Antonio Fernandois & Andrés Sagner, 2018. "Medida de aversión al Riesgo Mediante Volatilidades Implícitas Realizadas," Working Papers Central Bank of Chile 818, Central Bank of Chile.
    14. Hanke, Michael & Kosolapova, Maria & Weissensteiner, Alex, 2020. "COVID-19 and market expectations: Evidence from option-implied densities," Economics Letters, Elsevier, vol. 195(C).
    15. Hardeep Singh Mundi, 2023. "Risk neutral variances to compute expected returns using data from S&P BSE 100 firms—a replication study," Management Review Quarterly, Springer, vol. 73(1), pages 215-230, February.

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    More about this item

    Keywords

    option pricing; risk-neutral distributions;

    JEL classification:

    • G01 - Financial Economics - - General - - - Financial Crises
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation

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