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Arithmetic variance swaps

Author

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  • Stamatis Leontsinis
  • Carol Alexander
Abstract
Biases in standard variance swap rates (VSRs) can induce substantial deviations below market rates. Defining realized variance as the sum of squared price (not log-price) changes yields an ‘arithmetic’ variance swap with no such biases. Its fair value has advantages over the standard VSR: no discrete monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair value for the arithmetic variance swap and compare it with the standard VSR by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher moment arithmetic swap.

Suggested Citation

  • Stamatis Leontsinis & Carol Alexander, 2017. "Arithmetic variance swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 551-569, April.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:4:p:551-569
    DOI: 10.1080/14697688.2016.1212167
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    References listed on IDEAS

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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Peter Friz & Jim Gatheral, 2005. "Valuation of volatility derivatives as an inverse problem," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 531-542.
    3. Anthony Neuberger, 2012. "Realized Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 25(11), pages 3423-3455.
    4. 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 621-651, October.
    5. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    6. Andreas Kaeck & Carol Alexander, 2013. "Stochastic Volatility Jump†Diffusions for European Equity Index Dynamics," European Financial Management, European Financial Management Association, vol. 19(3), pages 470-496, June.
    7. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    8. repec:bla:jfinan:v:59:y:2004:i:1:p:407-446 is not listed on IDEAS
    9. Konstantinidi, Eirini & Skiadopoulos, George, 2016. "How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 62-75.
    10. Alexandros Kostakis & Nikolaos Panigirtzoglou & George Skiadopoulos, 2011. "Market Timing with Option-Implied Distributions: A Forward-Looking Approach," Management Science, INFORMS, vol. 57(7), pages 1231-1249, July.
    11. Neumann, Michael & Skiadopoulos, George, 2013. "Predictable Dynamics in Higher-Order Risk-Neutral Moments: Evidence from the S&P 500 Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(3), pages 947-977, June.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    14. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.
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    3. Ana‐Maria Fuertes & Zhenya Liu & Weiqing Tang, 2022. "Risk‐neutral skewness and commodity futures pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 751-785, April.

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