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VIX derivatives: Valuation models and empirical evidence

Author

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  • Lo, Chien-Ling
  • Shih, Pai-Ta
  • Wang, Yaw-Huei
  • Yu, Min-Teh

Abstract

This study proposes an efficient approach for the pricing of VIX derivatives under the affine framework and investigates the respective value of two variance components and variance jumps in the pricing of VIX derivatives. Our numerical results show that our approach significantly reduce the computational burden. Our empirical findings provide support for the use of two-variance component models as the means of capturing the fickle term structure of VIX derivatives, and the use of variance jumps is vital when included in the long-run variance component.

Suggested Citation

  • Lo, Chien-Ling & Shih, Pai-Ta & Wang, Yaw-Huei & Yu, Min-Teh, 2019. "VIX derivatives: Valuation models and empirical evidence," Pacific-Basin Finance Journal, Elsevier, vol. 53(C), pages 1-21.
    • Handle: RePEc:eee:pacfin:v:53:y:2019:i:c:p:1-21
    DOI: 10.1016/j.pacfin.2018.09.004
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    as
    1. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    2. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    3. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    4. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    5. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    6. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    7. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    8. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    10. Grunbichler, Andreas & Longstaff, Francis A., 1996. "Valuing futures and options on volatility," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 985-1001, July.
    11. Gang Li & Chu Zhang, 2010. "On the Number of State Variables in Options Pricing," Management Science, INFORMS, vol. 56(11), pages 2058-2075, November.
    12. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    13. Duan, Jin-Chuan & Yeh, Chung-Ying, 2010. "Jump and volatility risk premiums implied by VIX," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2232-2244, November.
    14. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    15. Cheng, Jun & Ibraimi, Meriton & Leippold, Markus & Zhang, Jin E., 2012. "A remark on Lin and Chang's paper ‘Consistent modeling of S&P 500 and VIX derivatives’," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 708-715.
    16. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    17. Song‐Ping Zhu & Guang‐Hua Lian, 2012. "An analytical formula for VIX futures and its applications," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(2), pages 166-190, February.
    18. Qiang Liu, 2010. "Optimal approximations of nonlinear payoffs in static replication," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(11), pages 1082-1099, November.
    19. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    20. Bruno Feunou & Roméo Tédongap, 2012. "A Stochastic Volatility Model With Conditional Skewness," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 576-591, July.
    21. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    22. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    23. G. William Schwert, 2011. "Stock Volatility during the Recent Financial Crisis," European Financial Management, European Financial Management Association, vol. 17(5), pages 789-805, November.
    24. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    25. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    26. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    27. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    28. Zhiguang Wang & Robert T. Daigler, 2011. "The performance of VIX option pricing models: Empirical evidence beyond simulation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(3), pages 251-281, March.
    29. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    30. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. Cheng, Hung-Wen & Chang, Li-Han & Lo, Chien-Ling & Tsai, Jeffrey Tzuhao, 2023. "Empirical performance of component GARCH models in pricing VIX term structure and VIX futures," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 122-142.
    2. Zhao, Yang & Yu, Min-Teh, 2019. "Measuring the liquidity impact on catastrophe bond spreads," Pacific-Basin Finance Journal, Elsevier, vol. 56(C), pages 197-210.
    3. Lin, Chung-Gee & Chang, Chia-Chang, 2020. "Approximate analytic solution for Asian options with stochastic volatility," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    4. Hong, Hui & Bian, Zhicun & Chen, Naiwei, 2020. "Leverage effect on stochastic volatility for option pricing in Hong Kong: A simulation and empirical study," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    5. Daniel Guterding, 2020. "Inventory effects on the price dynamics of VSTOXX futures quantified via machine learning," Papers 2002.08207, arXiv.org.
    6. Lo, Chien-Ling & Chang, Carolyn W. & Lee, Jin-Ping & Yu, Min-Teh, 2021. "Pricing catastrophe swaps with default risk and stochastic interest rates," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    7. Guhathakurta, Kousik & Dash, Saumya Ranjan & Maitra, Debasish, 2020. "Period specific volatility spillover based connectedness between oil and other commodity prices and their portfolio implications," Energy Economics, Elsevier, vol. 85(C).
    8. Bo Jing & Shenghong Li & Yong Ma, 2020. "Pricing VIX options with volatility clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 928-944, June.
    9. Kao, Yu-Sheng & Chuang, Hwei-Lin & Ku, Yu-Cheng, 2020. "The empirical linkages among market returns, return volatility, and trading volume: Evidence from the S&P 500 VIX Futures," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    10. Xingguo Luo & Jin E. Zhang & Wenjun Zhang, 2019. "Instantaneous squared VIX and VIX derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1193-1213, October.

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    More about this item

    Keywords

    VIX derivatives; Variance components; Variance jump; Affine model;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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