Estimating probability distributions of future asset prices: empirical transformations from option-implied risk-neutral to real-world density functions
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.
|Date of creation:||21 Jun 2012|
|Contact details of provider:|| Postal: Bank of England, Threadneedle Street, London, EC2R 8AH|
Phone: +44 (0)171 601 4030
Fax: +44 (0)171 601 5196
Web page: http://www.bankofengland.co.uk/
More information through EDIRC
References listed on IDEAS
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.:
- Prasanna Gai & Nicholas Vause, 2006.
"Measuring Investors' Risk Appetite,"
International Journal of Central Banking,
International Journal of Central Banking, vol. 2(1), March.
- Prasanna Gai & Nicholas Vause, 2005. "Measuring investors' risk appetite," Bank of England working papers 283, Bank of England.
- Gai, Prasanna & Vause, Nicholas, 2005. "Measuring Investors' Risk Appetite," MPRA Paper 818, University Library of Munich, Germany.
- 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.
- 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. Full references (including those not matched with items on IDEAS)