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The Forecasting Performance of German Stock Option Densities


Author Info

  • Keller, Joachim
  • Glatzer, Ernst
  • Craig, Ben R.
  • Scheicher, Martin


In this paper we will be estimating risk-neutral densities (RND) for the largest euro area stock market (the index of which is the German DAX), reporting their statistical properties, and evaluating their forecasting performance. We have applied an innovative test procedure to a new, rich, and accurate data set. We have two main results. First, we have recorded strong negative skewness in the densities. Second, we find evidence for significant differences between the actual density and the risk-neutral density, leading to the conclusion that market participants were surprised by the extent of both the rise and the fall of the DAX. -- In dieser Arbeit werden "risikoneutrale" Dichtefunktionen über künftige DAXIndexstände aus täglich beobachteten Preisen europäischer Kauf- und Verkaufsoptionen mit verschiedenen Restlaufzeiten abgeleitet. Das hierbei verwendete Berechnungsverfahren beruht auf der Mischung von zwei Log-Normalverteilung, bei dem fünf Parameter (der Mischungsparameter, zwei Mittelwerte und zwei Standardabweichungen) so bestimmt werden, dass der quadratische Abstand zwischen beobachteten und impliziten Optionspreisen minimal ist. Die Preisnotierungen für die Derivative werden der Eurex entnommen und der Untersuchungszeitraum erstreckt sich von Dezember 1995 bis Mai 2002, also sowohl über die Boom- als auch über die Niedergangsphase des DAX. Die Vorhersagehorizonte der Dichten sind auf Grund der Datenlage auf sechs bis acht Wochen begrenzt. Die Vorhersagegüte dieser Dichten wird über verschiedene neuartige statistische Evaluierungsverfahren abgeschätzt. Im Ergebnis stellt sich folgendes heraus: Erstens: Die Dichten weisen im Durchschnitt eine negative Schiefe (negatives drittes Moment) auf, so dass das linke Ende der Dichte "dicker" ist als das rechte und die Marktteilnehmer somit einen bestimmten prozentualen Kursverlust als wahrscheinlicher einschätzten als einen Kursgewinn. Zweitens: Die Evaluierungstests für die Dichten machen deutlich, dass die tatsächlichen Dichten im Mittel deutlich von den risikoneutralen Dichten abweichen. Dabei kann ausgeschlossen werden, dass es sich lediglich um einen "Mittelwert"fehler handelt. Vielmehr scheinen die Markteilnehmer sowohl in der Aufschwung- als auch in der Abschwungphase von den Kursbewegungen des DAX überrascht worden zu.

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2003,17.

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Date of creation: 2003
Date of revision:
Handle: RePEc:zbw:bubdp1:4214

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Keywords: option prices; risk-neutral density; density evaluation; overlapping data;

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  1. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(2-3), pages 381-422, March.
  2. Jondeau, Eric & Rockinger, Michael, 1998. "Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2009, C.E.P.R. Discussion Papers.
  3. Söderlind, Paul & Svensson, Lars E.O., 1996. "New Techniques to Extract Market expectations from Financial Instruments," Working Paper Series in Economics and Finance 142, Stockholm School of Economics.
  4. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 97-37, Wharton School Center for Financial Institutions, University of Pennsylvania.
  5. 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, Elsevier, vol. 102(1), pages 67-110, May.
  6. Keller, Joachim G. & Craig, Ben R., 2002. "The Empirical Performance of Option Based Densities of Foreign Exchange," Discussion Paper Series 1: Economic Studies 2002,07, Deutsche Bundesbank, Research Centre.
  7. Clements, Michael P. & Smith, Jeremy, 2001. "Evaluating forecasts from SETAR models of exchange rates," Journal of International Money and Finance, Elsevier, Elsevier, vol. 20(1), pages 133-148, February.
  8. Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(2-3), pages 323-345, March.
  9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  10. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 32(01), pages 91-115, March.
  11. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  12. Ben R. Craig & Joachim G. Keller, 2002. "The Empirical Performance of Option Based Densities of Foreign Exchange," Working Papers, Oesterreichische Nationalbank (Austrian Central Bank) 60, Oesterreichische Nationalbank (Austrian Central Bank).
  13. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 51(5), pages 1611-32, December.
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Cited by:
  1. Belén Nieto & Gonzalo Rubio, 2007. "Measuring time-varying economic fears with consumption-based stochastic discount factors," Economics Working Papers 1029, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2007.
  2. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2009. "Option-implied preferences adjustments, density forecasts, and the equity risk premium," Spanish Economic Review, Springer, Springer, vol. 11(2), pages 141-164, June.
  3. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2005. "Testing the forecasting performace of IBEX 35 option implied risk neutral densities," Banco de Espa�a Working Papers 0504, Banco de Espa�a.
  4. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2006. "Option-implied preferences adjustments, density forecasts, and the equity risk premium," Banco de Espa�a Working Papers 0630, Banco de Espa�a.


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