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Market-based estimation of stochastic volatility models

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  • Aït-Sahalia, Yacine
  • Amengual, Dante
  • Manresa, Elena

Abstract

We propose a method for estimating stochastic volatility models by adapting the HJM approach to the case of volatility derivatives. We characterize restrictions that observed variance swap dynamics have to satisfy to prevent arbitrage opportunities. When the drift of variance swap rates are affine under the pricing measure, we obtain closed form expressions for those restrictions and formulas for forward variance curves. Using data on the S&P500 index and variance swap rates on different time to maturities, we find that linear mean-reverting one factor models provide inaccurate representation of the dynamics of the variance swap rates while two-factor models significantly outperform the former both in and out of sample.

Suggested Citation

  • Aït-Sahalia, Yacine & Amengual, Dante & Manresa, Elena, 2015. "Market-based estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 187(2), pages 418-435.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:2:p:418-435
    DOI: 10.1016/j.jeconom.2015.02.028
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    Cited by:

    1. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    2. Agarwal, Vikas & Arisoy, Y. Eser & Naik, Narayan Y., 2017. "Volatility of aggregate volatility and hedge fund returns," Journal of Financial Economics, Elsevier, vol. 125(3), pages 491-510.
    3. Oh, Dong Hwan & Park, Yang-Ho, 2023. "GARCH option pricing with volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 146(C).
    4. 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.
    5. Muneer Shaik & S. Maheswaran, 2019. "Robust Volatility Estimation with and Without the Drift Parameter," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 57-91, March.
    6. Mohammed Bouasabah & Oshamah Ibrahim Khalaf, 2023. "A Technical Indicator for a Short-term Trading Decision in the NASDAQ Market," Advances in Decision Sciences, Asia University, Taiwan, vol. 27(3), pages 1-13, September.
    7. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    8. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    10. Yang-Ho Park, 2015. "The Effects of Asymmetric Volatility and Jumps on the Pricing of VIX Derivatives," Finance and Economics Discussion Series 2015-71, Board of Governors of the Federal Reserve System (U.S.).
    11. Park, Yang-Ho, 2020. "Variance disparity and market frictions," Journal of Econometrics, Elsevier, vol. 214(2), pages 326-348.

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    More about this item

    Keywords

    HJM approach; Variance swaps; Maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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