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Jump and volatility risk premiums implied by VIX

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  • Duan, Jin-Chuan
  • Yeh, Chung-Ying
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    Abstract

    An estimation method is developed for extracting the latent stochastic volatility from VIX, a volatility index for the S&P 500 index return produced by the Chicago Board Options Exchange (CBOE) using the so-called model-free volatility construction. Our model specification encompasses all mean-reverting stochastic volatility option pricing models with a constant-elasticity of variance and those allowing for price jumps under stochastic volatility. Our approach is made possible by linking the latent volatility to the VIX index via a new theoretical relationship under the risk-neutral measure. Because option prices are not directly used in estimation, we can avoid the computational burden associated with option valuation for stochastic volatility/jump option pricing models. Our empirical findings are: (1) incorporating a jump risk factor is critically important; (2) the jump and volatility risks are priced; (3) the popular square-root stochastic volatility process is a poor model specification irrespective of allowing for price jumps or not. Our simulation study shows that statistical inference is reliable and not materially affected by the approximation used in the VIX index construction.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 34 (2010)
    Issue (Month): 11 (November)
    Pages: 2232-2244

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    Handle: RePEc:eee:dyncon:v:34:y:2010:i:11:p:2232-2244

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Model-free volatility Stochastic volatility Jump Options VIX Constant elasticity of variance;

    References

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    Cited by:
    1. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    2. Hilal, Sawsan & Poon, Ser-Huang & Tawn, Jonathan, 2011. "Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2374-2387, September.
    3. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2417-2445.
    4. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX," Working Papers in Economics 11/11, University of Canterbury, Department of Economics and Finance.
    5. Worapree Maneesoonthorn & Gael M. Martin & Catherine S. Forbes & Simone Grose, 2010. "Probabilistic Forecasts of Volatility and its Risk Premia," Monash Econometrics and Business Statistics Working Papers 22/10, Monash University, Department of Econometrics and Business Statistics.
    6. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
    7. Kaeck, Andreas & Alexander, Carol, 2013. "Continuous-time VIX dynamics: On the role of stochastic volatility of volatility," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 46-56.
    8. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    10. Chourdakis, Kyriakos & Dotsis, George, 2011. "Maximum likelihood estimation of non-affine volatility processes," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 533-545, June.
    11. Lee, Bong Soo & Ryu, Doojin, 2013. "Stock returns and implied volatility: A new VAR approach," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 7(3), pages 1-20.
    12. Li, Junye, 2012. "Option-implied volatility factors and the cross-section of market risk premia," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 249-260.

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