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Observability of Market Daily Volatility

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  • Filippo Petroni
  • Maurizio Serva

Abstract

We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $\sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=\sigma(t) \omega(t)$ where the $r(t)$ are the daily returns of the market index and the $\omega(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=\sigma(t) \omega(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.

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  • Filippo Petroni & Maurizio Serva, 2015. "Observability of Market Daily Volatility," Papers 1503.08032, arXiv.org.
    • Handle: RePEc:arx:papers:1503.08032
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    References listed on IDEAS

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    Cited by:

    1. Pan, Zhiyuan & Liu, Li, 2018. "Forecasting stock return volatility: A comparison between the roles of short-term and long-term leverage effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 168-180.
    2. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    3. D’Amico, Guglielmo & Gismondi, Fulvio & Petroni, Filippo & Prattico, Flavio, 2019. "Stock market daily volatility and information measures of predictability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 22-29.
    4. Zhu, Sha & Liu, Qiuhong & Wang, Yan & Wei, Yu & Wei, Guiwu, 2019. "Which fear index matters for predicting US stock market volatilities: Text-counts or option based measurement?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).

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