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Cross-sectional Dependence in Idiosyncratic Volatility

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  • Ilze Kalnina
  • Kokouvi Tewou

Abstract

This paper introduces an econometric framework for analyzing cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Naive estimators of these measures are biased due to the use of the error-laden estimates of idiosyncratic volatilities. We provide bias-corrected estimators and the relevant asymptotic theory. Next, we introduce an idiosyncratic volatility factor model, in which we decompose the variation in idiosyncratic volatilities into two parts: the variation related to the systematic factors such as the market volatility, and the residual variation. Again, naive estimators of the decomposition are biased, and we provide bias-corrected estimators. We also provide the asymptotic theory that allows us to test whether the residual (non-systematic) components of the idiosyncratic volatilities exhibit cross-sectional dependence. We apply our methodology to the S&P 100 index constituents, and document strong cross-sectional dependence in their idiosyncratic volatilities. We consider two different sets of idiosyncratic volatility factors, and find that neither can fully account for the cross-sectional dependence in idiosyncratic volatilities. For each model, we map out the network of dependencies in residual (non-systematic) idiosyncratic volatilities across all stocks.

Suggested Citation

  • Ilze Kalnina & Kokouvi Tewou, 2024. "Cross-sectional Dependence in Idiosyncratic Volatility," Papers 2408.13437, arXiv.org.
  • Handle: RePEc:arx:papers:2408.13437
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    References listed on IDEAS

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    1. Li, Jia & Patton, Andrew J., 2018. "Asymptotic inference about predictive accuracy using high frequency data," Journal of Econometrics, Elsevier, vol. 203(2), pages 223-240.
    2. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    3. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
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