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Variance swaps valuation under non-affine GARCH models and their diffusion limits

Author

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  • Alexandru Badescu
  • Yuyu Chen
  • Matthew Couch
  • Zhenyu Cui

Abstract

In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based discretely sampled variance swaps. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as the pricing kernel candidate. Following standard assumptions on time-varying GARCH parameters, we show that these quantities converge respectively to fair strikes of discretely and continuously sampled variance swaps that are constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we further investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns.

Suggested Citation

  • Alexandru Badescu & Yuyu Chen & Matthew Couch & Zhenyu Cui, 2019. "Variance swaps valuation under non-affine GARCH models and their diffusion limits," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 227-246, February.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:2:p:227-246
    DOI: 10.1080/14697688.2018.1478120
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    Citations

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    Cited by:

    1. Jin, Xing & Hong, Yi, 2023. "Jump-diffusion volatility models for variance swaps: An empirical performance analysis," International Review of Financial Analysis, Elsevier, vol. 87(C).
    2. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    3. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2020. "Affine multivariate GARCH models," Journal of Banking & Finance, Elsevier, vol. 118(C).
    4. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2023. "Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing," International Review of Financial Analysis, Elsevier, vol. 87(C).
    5. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).

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