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Variance Risk Premia

Author

Listed:
  • Peter Carr

    (New York University & Bloomberg)

  • Liuren Wu

    (Zicklin School of Business, Baruch College)

Abstract

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.

Suggested Citation

  • Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0409015
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    Cited by:

    1. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    2. Corradi, Valentina & Distaso, Walter & Mele, Antonio, 2008. "Macroeconomic determinants of stock market returns, volatility and volatility risk-premia," LSE Research Online Documents on Economics 24436, London School of Economics and Political Science, LSE Library.
    3. Mo, Henry & Wu, Liuren, 2007. "International capital asset pricing: Evidence from options," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 465-498, September.
    4. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    5. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    6. Lieven Baele, 2010. "The Determinants of Stock and Bond Return Comovements," The Review of Financial Studies, Society for Financial Studies, vol. 23(6), pages 2374-2428, June.
    7. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
    8. Gurdip Bakshi & Dilip Madan, 2006. "A Theory of Volatility Spreads," Management Science, INFORMS, vol. 52(12), pages 1945-1956, December.
    9. Richard Holowczak & Yusif Simaan & Liuren Wu, 2006. "Price discovery in the U.S. stock and stock options markets: A portfolio approach," Review of Derivatives Research, Springer, vol. 9(1), pages 37-65, January.
    10. Doran, James S. & Ronn, Ehud I., 2008. "Computing the market price of volatility risk in the energy commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2541-2552, December.
    11. Wu, Liuren, 2018. "Estimating risk-return relations with analysts price targets," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 183-197.
    12. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    13. Torben G. Andersen & Oleg Bondarenko, 2007. "Construction and Interpretation of Model-Free Implied Volatility," CREATES Research Papers 2007-24, Department of Economics and Business Economics, Aarhus University.
    14. Fousseni Chabi-Yo, 2006. "Conditioning Information and Variance Bounds on Pricing Kernels with Higher-Order Moments: Theory and Evidence," Staff Working Papers 06-38, Bank of Canada.
    15. Lieven Baele & Geert Bekaert & Koen Inghelbrecht, 2007. "The determinants of stock and bond return comovements," Working Paper Research 119, National Bank of Belgium.
    16. Hao Wang & Hao Zhou & Yi Zhou, 2011. "Credit default swap spreads and variance risk premia," Finance and Economics Discussion Series 2011-02, Board of Governors of the Federal Reserve System (U.S.).
    17. Cameron, Ken & Schnusenberg, Oliver, 2009. "Oil prices, SUVs, and Iraq: An investigation of automobile manufacturer oil price sensitivity," Energy Economics, Elsevier, vol. 31(3), pages 375-381, May.
    18. Ziegler, Alexandre & Schürhoff, Norman, 2011. "Variance risk, financial intermediation, and the cross-section of expected option returns," CEPR Discussion Papers 8268, C.E.P.R. Discussion Papers.
    19. André Schöne, 2010. "Zum Informationsgehalt der Volatilitätsindizes VDAX und VDAX-New der Deutsche Börse AG," Schmalenbach Journal of Business Research, Springer, vol. 62(6), pages 625-661, September.

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    More about this item

    Keywords

    Stochastic volatility; variance risk premia; variance swap; volatility swap; option pricing; expectation hypothesis;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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