Estimating probability distributions of future asset prices: empirical transformations from option-implied risk-neutral to real-world density functions
AbstractThe 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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Bibliographic InfoPaper provided by Bank of England in its series Bank of England working papers with number 455.
Length: 39 pages
Date of creation: 21 Jun 2012
Date of revision:
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Asset prices; derivatives; expectations; options; option-implied density; risk premia; probability density forecasting; probability measure;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-08 (All new papers)
- NEP-FOR-2012-07-08 (Forecasting)
- NEP-UPT-2012-07-08 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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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