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Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics

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  • Amadeo Alentorn

    ()

  • Sheri Markose

    ()

Abstract

When studying a time series of implied Risk Neutral Densities (RNDs) or other implied statistics, one is faced with the problem of maturity dependence, given that option contracts have a fixed expiry date. Therefore, estimates from consecutive days are not directly comparable. Further, we can only obtain implied RNDs for a limited set of expiration dates. In this paper we introduce two new methods to overcome the time to maturity problem. First, we propose an alternative method for calculating constant time horizon Economic Value at Risk (EVaR), which is much simpler than the method currently being used at the Bank of England. Our method is based on an empirical scaling law for the quantiles in a log-log plot, and thus, we are able to interpolate and extrapolate the EVaR for any time horizon. The second method is based on an RND surface constructed across strikes and maturities, which enables us to obtain RNDs for any time horizon. Removing the maturity dependence of implied RNDs and related statistics is useful in many applications, such as in (i) the construction of implied volatility indices like the VIX, (ii) the assessment of market uncertainty by central banks (iii) time series analysis of EVaR, or (iv) event studies.

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Bibliographic Info

Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 609.

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Date of creation: 22 Feb 2006
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Handle: RePEc:esx:essedp:609

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References

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  1. Shiratsuka, Shigenori, 2001. "Information Content of Implied Probability Distributions: Empirical Studies of Japanese Stock Price Index Options," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(3), pages 143-170, November.
  2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  3. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
  4. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
  5. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393.
  6. Ncube, Mthuli, 1996. "Modelling implied volatility with OLS and panel data models," Journal of Banking & Finance, Elsevier, vol. 20(1), pages 71-84, January.
  7. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
  8. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  9. Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
  10. William R. Melick & Charles P. Thomas, 1996. "Using options prices to infer PDF'S for asset prices: an application to oil prices during the Gulf crisis," International Finance Discussion Papers 541, Board of Governors of the Federal Reserve System (U.S.).
  11. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
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Cited by:
  1. Sheri M. Markose & Yue Peng & Amadeo Alentorn, 2012. "Forecasting Extreme Volatility of FTSE-100 With Model Free VFTSE, Carr-Wu and Generalized Extreme Value (GEV) Option Implied Volatility Indices," Economics Discussion Papers 713, University of Essex, Department of Economics.

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