[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v106y2022icp33-45.html
   My bibliography  Save this article

Frequency and severity estimation of cyber attacks using spatial clustering analysis

Author

Listed:
  • Ma, Boyuan
  • Chu, Tingjin
  • Jin, Zhuo
Abstract
In this paper, a cluster-based method is developed to investigate the risk of cyber attacks in the continental United States. The proposed analysis considers geographical information of cyber incidents for clustering. By clustering state-based observations, the frequency and severity of cyber losses demonstrate a simplified structure: independent structure between inter-arrival time and size of cyber breaches. The independence between frequency and severity is significant in the state level instead of national level. Within clustered subcategories, the inter-arrival time is modelled by the family of Autoregressive Conditional Duration models (ACD) and log-transformed size of breach is described by an ARMA-GARCH model. Under multiple statistical tests, it is shown that the cluster-based models have better fitting and are more robust than the aggregate model, where all incidents are considered together. Finally, a numerical analysis is presented to illustrate the performance of the approach. Accordingly, the prediction of total losses are compared with other dependent models. The differences of key cyber risk features among clusters are illustrated.

Suggested Citation

  • Ma, Boyuan & Chu, Tingjin & Jin, Zhuo, 2022. "Frequency and severity estimation of cyber attacks using spatial clustering analysis," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 33-45.
    • Handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:33-45
    DOI: 10.1016/j.insmatheco.2022.04.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668722000580
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2022.04.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    2. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS
    3. Luc Bauwens & Pierre Giot, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annals of Economics and Statistics, GENES, issue 60, pages 117-149.
    4. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    5. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 104-124, January.
    6. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 16-38.
    7. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    8. Mark Camillo, 2017. "Cyber risk and the changing role of insurance," Journal of Cyber Policy, Taylor & Francis Journals, vol. 2(1), pages 53-63, January.
    9. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    10. J. A. Hartigan & M. A. Wong, 1979. "A K‐Means Clustering Algorithm," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 100-108, March.
    11. Jevtić, Petar & Lanchier, Nicolas, 2020. "Dynamic structural percolation model of loss distribution for cyber risk of small and medium-sized enterprises for tree-based LAN topology," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 209-223.
    12. Christian Biener & Martin Eling & Jan Hendrik Wirfs, 2015. "Insurability of Cyber Risk: An Empirical Analysis†," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(1), pages 131-158, January.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    15. Fahrenwaldt, Matthias A. & Weber, Stefan & Weske, Kerstin, 2018. "Pricing Of Cyber Insurance Contracts In A Network Model," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1175-1218, September.
    16. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    17. Eling, Martin & Wirfs, Jan, 2019. "What are the actual costs of cyber risk events?," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1109-1119.
    18. T. Maillart & D. Sornette, 2010. "Heavy-tailed distribution of cyber-risks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 75(3), pages 357-364, June.
    19. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    20. Chen Peng & Maochao Xu & Shouhuai Xu & Taizhong Hu, 2018. "Modeling multivariate cybersecurity risks," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(15), pages 2718-2740, November.
    21. Eling, Martin & Loperfido, Nicola, 2017. "Data breaches: Goodness of fit, pricing, and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 126-136.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    2. Stanislav Anatolyev & Dmitry Shakin, 2006. "Trade intensity in the Russian stock market:dynamics, distribution and determinants," Working Papers w0070, Center for Economic and Financial Research (CEFIR).
    3. Daniel Zängerle & Dirk Schiereck, 2023. "Modelling and predicting enterprise-level cyber risks in the context of sparse data availability," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 434-462, April.
    4. Allen, David & Lazarov, Zdravetz & McAleer, Michael & Peiris, Shelton, 2009. "Comparison of alternative ACD models via density and interval forecasts: Evidence from the Australian stock market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2535-2555.
    5. Hautsch, Nikolaus & Jeleskovic, Vahidin, 2008. "Modelling high-frequency volatility and liquidity using multiplicative error models," SFB 649 Discussion Papers 2008-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. repec:hum:wpaper:sfb649dp2008-047 is not listed on IDEAS
    7. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS
    8. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    9. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 104-124, January.
    10. Vasileios Siakoulis & Ioannis Venetis, 2015. "On inter-arrival times of bond market extreme events. An application to seven European markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(4), pages 717-741, October.
    11. Malavasi, Matteo & Peters, Gareth W. & Shevchenko, Pavel V. & Trück, Stefan & Jang, Jiwook & Sofronov, Georgy, 2022. "Cyber risk frequency, severity and insurance viability," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 90-114.
    12. repec:hum:wpaper:sfb649dp2011-022 is not listed on IDEAS
    13. Herrera, Rodrigo & Schipp, Bernhard, 2011. "Extreme value models in a conditional duration intensity framework," SFB 649 Discussion Papers 2011-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Bhatti, Chad R., 2009. "On the interday homogeneity in the intraday rate of trading," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2250-2257.
    15. Siakoulis, Vasilios, 2015. "Modeling bank default intensity in the USA using autoregressive duration models," MPRA Paper 64526, University Library of Munich, Germany.
    16. Roman Huptas, 2014. "Bayesian Estimation and Prediction for ACD Models in the Analysis of Trade Durations from the Polish Stock Market," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(4), pages 237-273, December.
    17. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    18. Pipat Wongsaart & Jiti Gao, 2011. "Nonparametric Kernel Testing in Semiparametric Autoregressive Conditional Duration Model," Monash Econometrics and Business Statistics Working Papers 18/11, Monash University, Department of Econometrics and Business Statistics.
    19. Matteo Malavasi & Gareth W. Peters & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang & Georgy Sofronov, 2021. "Cyber Risk Frequency, Severity and Insurance Viability," Papers 2111.03366, arXiv.org, revised Mar 2022.
    20. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    21. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, September.
    22. repec:wyi:journl:002120 is not listed on IDEAS
    23. Zängerle, Daniel & Schiereck, Dirk, 2022. "Modelling and predicting enterprise‑level cyber risks in the context of sparse data availability," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 136276, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    24. Katarzyna Bien-Barkowska, 2011. "Distribution Choice for the Asymmetric ACD Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 11, pages 55-72.

    More about this item

    Keywords

    Cyber risk; Breach size; Attack frequency; Time series; Spatial clustering;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:33-45. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.