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Estimating probability distributions of future asset prices: empirical transformations from option-implied risk-neutral to real-world density functions

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  • de Vincent-Humphreys, Rupert

    (Bank of England)

  • Noss, Joseph

    (Bank of England)

Abstract

The prices of derivatives contracts can be used to estimate ‘risk-neutral’ probability density functions that give an indication of the weight investors place on different future prices of their underlying assets, were they risk-neutral. In the likely case that investors are risk-averse, this leads to differences between the risk-neutral probability density and the actual distribution of prices. But if this difference displays a systematic pattern over time, it may be exploited to transform the risk-neutral density into a ‘real-world’ density that better reflect agents’ actual expectations. This work offers a methodology for performing this transformation. The resulting real-world densities may better represent market participants’ views of future prices, and so offer an enhanced means of quantifying the uncertainty around financial variables. Comparison with their risk-neutral equivalents may also reveal new and useful information as to how attitudes towards risk are affecting pricing.

Suggested Citation

  • de Vincent-Humphreys, Rupert & Noss, Joseph, 2012. "Estimating probability distributions of future asset prices: empirical transformations from option-implied risk-neutral to real-world density functions," Bank of England working papers 455, Bank of England.
    • Handle: RePEc:boe:boeewp:0455
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    References listed on IDEAS

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    8. Josep Puigvert-Gutiérrez & Rupert Vincent-Humphreys, 2012. "A Quantitative Mirror on the Euribor Market Using Implied Probability Density Functions," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 2(1), pages 1-31, June.
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    Citations

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    Cited by:

    1. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    2. Roberto Casarin & Fabrizio Leisen & German Molina & Enrique ter Horst, 2014. "A Bayesian Beta Markov Random Field Calibration of the Term Structure of Implied Risk Neutral Densities," Papers 1409.1956, arXiv.org.
    3. Michel Dacorogna & Juan-José Francisco Miguelez & Marie Kratz, 2016. "Risk neutral versus real-world distribution on puclicly listed bank corporations," Working Papers hal-01373071, HAL.
    4. Ricardo Crisóstomo & Lorena Couso, 2018. "Financial density forecasts: A comprehensive comparison of risk‐neutral and historical schemes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(5), pages 589-603, August.
    5. repec:wsr:wpaper:y:2019:i:189 is not listed on IDEAS
    6. 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.
    7. Julius Loermann, 2021. "The impact of CHF/EUR exchange rate uncertainty on Swiss exports to the Eurozone: evidence from a threshold VAR," Empirical Economics, Springer, vol. 60(3), pages 1363-1385, March.
    8. Jukka Sihvonen & Sami Vähämaa, 2014. "Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(4), pages 346-373, April.
    9. Jaqueline Terra Moura Marins, 2024. "Predictability of Exchange Rate Density Forecasts for Emerging Economies in the Short Run," Working Papers Series 588, Central Bank of Brazil, Research Department.
    10. Wagner Piazza Gaglianone & Jaqueline Terra Moura Marins, 2014. "Risk Assessment of the Brazilian FX Rate," Working Papers Series 344, Central Bank of Brazil, Research Department.
    11. Andres Trujillo-Barrera & Philip Garcia & Mindy L Mallory, 2018. "Short-term price density forecasts in the lean hog futures market," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 45(1), pages 121-142.
    12. Gaglianone, Wagner Piazza & Marins, Jaqueline Terra Moura, 2017. "Evaluation of exchange rate point and density forecasts: An application to Brazil," International Journal of Forecasting, Elsevier, vol. 33(3), pages 707-728.
    13. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    14. Smith, Tom, 2012. "Option-implied probability distributions for future inflation," Bank of England Quarterly Bulletin, Bank of England, vol. 52(3), pages 224-234.
    15. Jaqueline Terra Moura Marins, 2020. "Option-Based Risk Aversion Indicators for Predicting Currency Crises in Emerging Markets," Working Papers Series 515, Central Bank of Brazil, Research Department.

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    More about this item

    Keywords

    Asset prices; derivatives; expectations; options; option-implied density; risk premia; probability density forecasting; probability measure;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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