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Volatility: Expectations and Realizations

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  • Peters, R.
  • van der Weide, R.

    ()
    (World Bank)

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    Abstract

    Embedded in option prices are market expectations regarding future volatility. While the assumption of rational expectations has been a popular paradigm, it is difficult to ignore the subjective nature of expectations. The objective of this paper is to make market expectations visible as they evolve over time, and to price options in line with prevailing expectations, be they rational or non-rational. We put forward an analytically convenient option pricing framework that accommodates both stochastic volatility and asymmetric volatility. Daily estimates of the implied pdf of volatility are obtained by estimating the option pricing model one day at a time. We do not impose too much structure on how expectations are updated over time, but allow market expectations to take their course.

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    File URL: http://www1.fee.uva.nl/cendef/publications/papers/Smile_Dec2011.pdf
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    Bibliographic Info

    Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 12-04.

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    Date of creation: 2012
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    Handle: RePEc:ams:ndfwpp:12-04

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    Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
    Phone: + 31 20 525 52 58
    Fax: + 31 20 525 52 83
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    Web page: http://www.fee.uva.nl/cendef/
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    1. Florian Wagener & Cars Hommes & William Brock, 2006. "More hedging instruments may destabilize markets," Working Papers, Warwick Business School, Finance Group wp06-11, Warwick Business School, Finance Group.
    2. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, Elsevier, vol. 72(2), pages 291-318, May.
    3. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers, Yale School of Management ysm54, Yale School of Management.
    4. Andrea Buraschi & Alexei Jiltsov, 2006. "Model Uncertainty and Option Markets with Heterogeneous Beliefs," Journal of Finance, American Finance Association, American Finance Association, vol. 61(6), pages 2841-2897, December.
    5. René Garcia & Richard Luger & Eric Renault, 2000. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables," Working Papers, Centre de Recherche en Economie et Statistique 2000-56, Centre de Recherche en Economie et Statistique.
    6. Jens Carsten Jackwerth & George M. Constantinaides & Stylianos Perrakis, 2005. "Mispricing of S&P 500 Index Options," CoFE Discussion Paper, Center of Finance and Econometrics, University of Konstanz 05-09, Center of Finance and Econometrics, University of Konstanz.
    7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
    8. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 48-57, January.
    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. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 64(2), pages 253-280.
    11. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, Elsevier, vol. 94(1-2), pages 181-238.
    12. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, American Finance Association, vol. 53(6), pages 2059-2106, December.
    13. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 29(04), pages 589-607, December.
    14. 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.
    15. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers, Yale School of Management ysm65, Yale School of Management.
    16. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, American Finance Association, vol. 52(5), pages 2003-49, December.
    17. Bing Han, 2008. "Investor Sentiment and Option Prices," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 21(1), pages 387-414, January.
    18. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(3), pages 279-302.
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