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Instantaneous squared VIX and VIX derivatives

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  • Xingguo Luo
  • Jin E. Zhang
  • Wenjun Zhang

Abstract

In this paper, we propose a parsimonious and efficient model to price derivatives written on VIXs with different horizons. Our model is built on Luo and Zhang's (2012, J Futures Markets, 32, 1092–1123) concept of the instantaneous squared VIX (ISVIX) that is the sum of instantaneous diffusive and jump variances of the SPX return. Modeling the ISVIX as a mean‐reverting jump‐diffusion process with a stochastic long‐term mean, we obtain analytical formulas for VIX options and futures. Estimation with VIX term structure and calibration with VIX options data show that our model performs well in matching both time series and cross‐sectional VIX derivatives market prices.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:10:p:1193-1213
    DOI: 10.1002/fut.22037
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    1. Claudio Albanese & Harry Lo & Aleksandar Mijatovic, 2009. "Spectral methods for volatility derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 663-692.
    2. Yueh‐Neng Lin, 2007. "Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(12), pages 1175-1217, December.
    3. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    4. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    5. Grunbichler, Andreas & Longstaff, Francis A., 1996. "Valuing futures and options on volatility," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 985-1001, July.
    6. Rama Cont & Thomas Kokholm, 2013. "A Consistent Pricing Model For Index Options And Volatility Derivatives," Post-Print hal-00801536, HAL.
    7. Xingguo Luo & Jin E. Zhang, 2012. "The Term Structure of VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(12), pages 1092-1123, December.
    8. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    9. 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.
    10. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    11. Andrew Papanicolaou & Ronnie Sircar, 2014. "A regime-switching Heston model for VIX and S&P 500 implied volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1811-1827, October.
    12. 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.
    13. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    14. 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.
    15. Jacinto Marabel Romo, 2017. "Pricing volatility options under stochastic skew with application to the VIX index," The European Journal of Finance, Taylor & Francis Journals, vol. 23(4), pages 353-374, March.
    16. San‐Lin Chung & Wei‐Che Tsai & Yaw‐Huei Wang & Pei‐Shih Weng, 2011. "The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(12), pages 1170-1201, December.
    17. Yingzi Zhu & Jin E. Zhang, 2007. "Variance Term Structure And Vix Futures Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 111-127.
    18. Lin, Yueh-Neng & Chang, Chien-Hung, 2010. "Consistent modeling of S&P 500 and VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2302-2319, November.
    19. 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.
    20. Peter Carr & Dilip B. Madan, 2014. "Joint modeling of VIX and SPX options at a single and common maturity with risk management applications," IISE Transactions, Taylor & Francis Journals, vol. 46(11), pages 1125-1131, November.
    21. Jin E. Zhang & Yuqin Huang, 2010. "The CBOE S&P 500 three‐month variance futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(1), pages 48-70, January.
    22. 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.
    23. 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.
    24. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    25. 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.
    26. Zhuo Huang & Chen Tong & Tianyi Wang, 2019. "VIX term structure and VIX futures pricing with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 72-93, January.
    27. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    28. 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.
    29. Bujar Huskaj & Marcus Nossman, 2013. "A Term Structure Model for VIX Futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(5), pages 421-442, May.
    30. Jin E. Zhang & Jinghong Shu & Menachem Brenner, 2010. "The new market for volatility trading," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(9), pages 809-833, September.
    31. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    32. 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.
    33. Tianyi Wang & Yiwen Shen & Yueting Jiang & Zhuo Huang, 2017. "Pricing the CBOE VIX Futures with the Heston–Nandi GARCH Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(7), pages 641-659, July.
    34. Lin, Yueh-Neng, 2013. "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4432-4446.
    35. Brice Dupoyet & Robert T. Daigler & Zhiyao Chen, 2011. "A simplified pricing model for volatility futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(4), pages 307-339, April.
    36. Guang-Hua Lian & Song-Ping Zhu, 2013. "Pricing VIX options with stochastic volatility and random jumps," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 71-88, May.
    37. Zhongjin Lu & Yingzi Zhu, 2010. "Volatility components: The term structure dynamics of VIX futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(3), pages 230-256, March.
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    Cited by:

    1. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    2. Chen Tong & Zhuo Huang & Tianyi Wang, 2022. "Do VIX futures contribute to the valuation of VIX options?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(9), pages 1644-1664, September.
    3. Chen Tong & Zhuo Huang, 2021. "Pricing VIX options with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1180-1200, August.
    4. Venter, Pierre J & Maré, Eben, 2022. "Price discovery in the volatility index option market: A univariate GARCH approach," Finance Research Letters, Elsevier, vol. 44(C).
    5. Hongkai Cao & Alexandru Badescu & Zhenyu Cui & Sarath Kumar Jayaraman, 2020. "Valuation of VIX and target volatility options with affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(12), pages 1880-1917, December.
    6. Chen, Xiaoyi & Feng, JianFen & Wang, Tianyi, 2023. "Pricing VIX futures: A framework with random level shifts," Finance Research Letters, Elsevier, vol. 52(C).
    7. Jing, Bo & Li, Shenghong & Ma, Yong, 2021. "Consistent pricing of VIX options with the Hawkes jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    8. Qiang Liu & Yuhan Jiao & Shuxin Guo, 2022. "GARCH pricing and hedging of VIX options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 1039-1066, June.
    9. Fangsheng Yin & Yang Bian & Tianyi Wang, 2021. "A short cut: Directly pricing VIX futures with discrete‐time long memory model and asymmetric jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 458-477, April.

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