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Modelling the implied probability of stock market movements

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Author Info
Martin Scheicher () (European Central Bank, Postfach 160319, 60311 Frankfurt am Main, Germany.)
Ernst Glatzer () (Austrian National Bank - Economic Studies Division, POB 61, Otto Wagner Platz 3, A-1011 Vienna, Austria.)
Abstract

In this paper we study risk-neutral densities (RNDs) for the German stock market. The use of option prices allows us to quantify the risk-neutral probabilities of various levels of the DAX index. For the period from December 1995 to November 2001, we implement the mixture of log-normals model and a volatility-smoothing method. We discuss the time series behaviour of the implied PDFs and we examine the relations between the moments and observable factors such as macroeconomic variables, the US stock markets and credit risk. We find that the risk-neutral densities exhibit pronounced negative skewness. Our second main observation is a significant spillover of volatility, as the implied volatility and kurtosis of the DAX RND are mostly driven by the volatility of US stock prices. JEL Classification: C22; C51; G13; G15.

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Paper provided by European Central Bank in its series Working Paper Series with number 212.

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Length: 39 pages
Date of creation: Jan 2003
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Handle: RePEc:ecb:ecbwps:20030212

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Related research
Keywords: Option prices; risk-neutral density; volatility; spillover.;

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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.:
  1. 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. [Downloadable!] (restricted)
  2. Jondeau, Eric & Rockinger, Michael, 1998. "Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities," CEPR Discussion Papers 2009, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  3. Amado Peiro, Javier Quesada, Ezequiel Uriel, 1998. "Transmission of movements in stock markets," European Journal of Finance, Taylor and Francis Journals, vol. 4(4), pages 331-343, December. [Downloadable!] (restricted)
  4. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266. [Downloadable!] (restricted)
  5. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July. [Downloadable!] (restricted)
  6. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311. [Downloadable!] (restricted)
  7. Peiro, Amado, 1999. "Skewness in financial returns," Journal of Banking & Finance, Elsevier, vol. 23(6), pages 847-862, June. [Downloadable!] (restricted)
  8. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March. [Downloadable!] (restricted)
  9. Sergio Nicoletti Altimari, 2001. "Does money lead inflation in the euro area?," Working Paper Series 063, European Central Bank. [Downloadable!]
  10. Mark J. Flannery & Aris A. Protopapadakis, 2002. "Macroeconomic Factors Do Influence Aggregate Stock Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(3), pages 751-782.
  11. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May. [Downloadable!] (restricted)
  12. Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 323-345, March. [Downloadable!] (restricted)
  13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  14. Joseph Chen & Harrison Hong & Jeremy C. Stein, 2000. "Forecasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Prices," NBER Working Papers 7687, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Hisashi Nakamura & Shigenori Shiratsuka, 1999. "Extracting market expectations from option prices: case studies in Japanese option markets," Working Paper Series WP-99-1, Federal Reserve Bank of Chicago. [Downloadable!]
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  16. Pierre Collin-Dufresne, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December. [Downloadable!] (restricted)
  17. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
  18. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. D. Johannes Juttner & Wayne Leung, 2004. "Towards Decoding Currency Volatilities," Research Papers 0405, Macquarie University, Department of Economics. [Downloadable!]
  2. Lutz Kilian & Atsushi Inoue, 2003. "On the selection of forecasting models," Working Paper Series 214, European Central Bank. [Downloadable!]
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