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Dynamics of implied volatility surfaces from random matrix theory

Author

Listed:
  • Kim, Min Jae
  • Lee, Sun Young
  • Hwang, Dong Il
  • Kim, Soo Yong
  • Ko, In Kyu

Abstract

We analyze the dynamics of the implied volatility surface of KOSPI 200 futures options from random matrix theory. To extract the informative data, we use random matrix criteria. Implied volatility data have a colossal eigenvalue, and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction. We discern the marketwide knowledge of the implied volatility surface movement such as the level, skew, and smile effect. These dynamics has the ergodic property and long range autocorrelation. We also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics, and confirm the existence of leverage effect even in the short time interval.

Suggested Citation

  • Kim, Min Jae & Lee, Sun Young & Hwang, Dong Il & Kim, Soo Yong & Ko, In Kyu, 2010. "Dynamics of implied volatility surfaces from random matrix theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2762-2769.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:14:p:2762-2769
    DOI: 10.1016/j.physa.2010.02.042
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    Citations

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    Cited by:

    1. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    2. Bernales, Alejandro & Guidolin, Massimo, 2014. "Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 326-342.
    3. Connor J.A. Stuart & Sebastian A. Gehricke & Jin E. Zhang & Xinfeng Ruan, 2021. "Implied volatility smirk in the Australian dollar market," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 61(3), pages 4573-4599, September.
    4. Guidolin, Massimo & Wang, Kai, 2023. "The empirical performance of option implied volatility surface-driven optimal portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    5. Bernales, Alejandro & Guidolin, Massimo, 2015. "Learning to smile: Can rational learning explain predictable dynamics in the implied volatility surface?," Journal of Financial Markets, Elsevier, vol. 26(C), pages 1-37.
    6. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    7. Choi, Jungjun & Yang, Xiye, 2022. "Asymptotic properties of correlation-based principal component analysis," Journal of Econometrics, Elsevier, vol. 229(1), pages 1-18.

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