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Option-implied preferences adjustments, density forecasts, and the equity risk premium

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  • Francisco Alonso

    ()
    (Banco de España)

  • Roberto Blanco

    ()
    (Banco de España)

  • Gonzalo Rubio

    ()
    (Euskal Herriko Unibertsitatea
    Universitat Pompeu Fabra)

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    Abstract

    The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two lognormals and several alternative risk adjustments: the power, exponential and habit inspired based stochastic discount factors. Moreover, by allowing additional flexibility in the shape of the stochastic discount factor, two other ad hoc time varying risk aversion adjustments are also employed. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at four and eight week horizons. When forecasting through risk adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. Somehow surprisingly, all risk adjusted densities generate similar forecasting statistics. Finally, from October 1996 to December 2004, the ex ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18 percent higher than the premium required to compensate the same investors for the realised volatility in stock market returns.

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    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/06/Fic/dt0630e.pdf
    File Function: First version, Nobember 2006
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    Bibliographic Info

    Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0630.

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    Length: 44 pages
    Date of creation: Nov 2006
    Date of revision:
    Handle: RePEc:bde:wpaper:0630

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    Keywords: risk-adjustments; option-implied densities; forecasting performance; equity-risk premium;

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    1. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    2. Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
    3. Kang, Byung Jin & Kim, Tong Suk, 2006. "Option-implied risk preferences: An extension to wider classes of utility functions," Journal of Financial Markets, Elsevier, vol. 9(2), pages 180-198, May.
    4. Ben Craig & Ernst Glatzer & Joachim Keller & Martin Scheicher, 2003. "The forecasting performance of German stock option densities," Working Paper 0312, Federal Reserve Bank of Cleveland.
    5. Cochrane, John H. & Campbell, John, 1999. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Scholarly Articles 3119444, Harvard University Department of Economics.
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    7. 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, vol. 32(01), pages 91-115, March.
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    9. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
    10. Alonso, Francisco & Blanco, Roberto & Rubio Irigoyen, Gonzalo, 2005. "Testing the Forecasting Performance of Ibex 35 Option-implied Risk-neutral Densities," DFAEII Working Papers 2005-09, University of the Basque Country - Department of Foundations of Economic Analysis II.
    11. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    12. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
    13. Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers RPF-265, University of California at Berkeley.
    14. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    15. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
    16. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
    17. Keller, Joachim & Glatzer, Ernst & Craig, Ben R. & Scheicher, Martin, 2003. "The Forecasting Performance of German Stock Option Densities," Discussion Paper Series 1: Economic Studies 2003,17, Deutsche Bundesbank, Research Centre.
    18. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
    19. Nave, Juan & Rubio Irigoyen, Gonzalo & León, Angel, 2005. "The Relationship between Risk and Expected Return in Europe," DFAEII Working Papers 2005-08, University of the Basque Country - Department of Foundations of Economic Analysis II.
    20. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
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