Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics
AbstractWhen 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 InfoPaper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 609.
Date of creation: 22 Feb 2006
Date of revision:
Postal: Discussion Papers Administrator, Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, U.K.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-11 (All new papers)
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- 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.
- Jean-Pierre Zigrand & Jon Danielsson, 2003. "On time-scaling of risk and the square–root–of–time rule," FMG Discussion Papers dp439, Financial Markets Group.
- 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.
- Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
- Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393.
- 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.
- Whitney K. Newey & Kenneth D. West, 1986.
"A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix,"
NBER Technical Working Papers
0055, National Bureau of Economic Research, Inc.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
- 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.).
- 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.
- 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.
- Ncube, Mthuli, 1996. "Modelling implied volatility with OLS and panel data models," Journal of Banking & Finance, Elsevier, vol. 20(1), pages 71-84, January.
- Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor and Francis Journals, vol. 2(1), pages 45-60.
- 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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