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Volatility Flocking by Cucker–Smale Mechanism in Financial Markets

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Abstract

We analyze empirical evidence of flocking stock volatilities according to the Cucker–Smale (C–S) mechanism. By using daily realized volatilities of stocks listed on Dow Jones Industrial Average from January, 2007 to December, 2009, we calibrate key parameters such as time-varying coupling strength, communication weight and stochastic noise in coupling of a benchmark C–S model in Bae et al. (Math Models Methods Appl Sci 25:1299–1335, 2015). Our numerical solutions show that the flocking mechanism explains average volatility dynamics better than a stochastic volatility model without the mechanism over the sample period. The model’s empirical implications are found from cyclicality of Volatility Flocking Index (VFI), an aggregate measure of differences between volatilities. Results from Granger causality tests after vector autoregression estimation show that VFI helps us predict the implied volatility index, and weighted average return of S&P500 Index.

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Fig. 1
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Fig. 3

Source: Authors’ calculation based on the price data provided by Thomson Reuters Eikon. (Color figure online)

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Notes

  1. Some previous studies such as Bellomo (2008), Bellomo et al. (2010a, b, 2013), Bertotti and Delitala (2008, 2010), Galam et al. (1982), Galam and Zucker (2000) and Ha et al. (2012, 2013) have applied this mechanism to collective behavior of human society.

  2. The list of firms is available in the “Appendix A”.

  3. The results are available upon request.

  4. We may compare cyclical movement of the \(VFI_t\) with some macro variables such as interest rates, term spread, credit spread, and monetary aggregates (M1, M2, and M3). VIX and the rate of return of S&P500 show a stock market’s signal in a timely manner relative to production indicators including “Building Permit” and industrial production.

  5. We find that VFI is a stationary process according to results of augmented Dickey–Fuller test. These test results are available upon request.

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Author information

Authors and Affiliations

  1. Department of Financial Engineering, Ajou University, Suwon, South Korea

    Hyeong-Ohk Bae & Jane Yoo

  2. Department of Mathematical Sciences, Research Institute of Mathematics, Seoul National University, Seoul, South Korea

    Seung-Yeal Ha

  3. Financial Engineering Center, Korea Asset Pricing, Seoul, South Korea

    Yongsik Kim

  4. Department of Mathematics, Chonnam National University, Gwangju, South Korea

    Hyuncheul Lim

Authors
  1. Hyeong-Ohk Bae
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  2. Seung-Yeal Ha
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  3. Yongsik Kim
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  4. Hyuncheul Lim
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  5. Jane Yoo
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Corresponding author

Correspondence to Jane Yoo.

Additional information

Bae (2018R1D1A1A09082848), Ha (NRF-2017R1A2B2001864), Kim (NRF-2016R1D1A1A09917026), Lim (NRF-2019R1I1A3A03059382) and Yoo (NRF-2017S1A5A8022379) were supported by National Research Foundation (NRF) of Republic of Korea. Bae and Yoo were supported by Ajou university research fund.

Appendices

Appendix A

See Table 6.

Table 6 Company name, ticker, and sector (GICs)
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Appendix B

See Table 7.

Table 7 Ridge regression results
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Bae, HO., Ha, SY., Kim, Y. et al. Volatility Flocking by Cucker–Smale Mechanism in Financial Markets. Asia-Pac Financ Markets 27, 387–414 (2020). https://doi.org/10.1007/s10690-019-09299-9

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  • DOI: https://doi.org/10.1007/s10690-019-09299-9

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