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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)

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    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.

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    File URL: http://www.bankofengland.co.uk/research/Documents/workingpapers/2012/wp455.pdf
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    Bibliographic Info

    Paper provided by Bank of England in its series Bank of England working papers with number 455.

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    Length: 39 pages
    Date of creation: 21 Jun 2012
    Date of revision:
    Handle: RePEc:boe:boeewp:0455

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    Related research

    Keywords: Asset prices; derivatives; expectations; options; option-implied density; risk premia; probability density forecasting; probability measure;

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    1. Inkinen, Mika & Stringa, Marco & Voutsinou, Kyriaki, 2010. "Interpreting equity price movements since the start of the financial crisis," Bank of England Quarterly Bulletin, Bank of England, vol. 50(1), pages 24-33.
    2. Liu, Xiaoquan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2007. "Closed-form transformations from risk-neutral to real-world distributions," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1501-1520, May.
    3. Shackleton, Mark B. & Taylor, Stephen J. & Yu, Peng, 2010. "A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2678-2693, November.
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