IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v181y2025ics0378426625001840.html

Cyber insurance valuation with endogenous cyber loss

Author

Listed:
  • Chen, Chang-Chih
  • Chang, Chia-Chien
  • Rui, Ying
  • Yu, Min-Teh

Abstract

This research proposes a novel firm-based model for pricing cyber insurance. Our model considers two types of cyber risk: virus attacks and data breaches. Virus attacks deliver adverse shocks to the firm’s productivity, while data breaches cause premium customer departures that worsen the prospect of the firm’s product demand. We derive the endogenous structural form of cyber losses in firms and utilize it to solve the formula for cyber insurance premiums. Our quantitative results show that the consensus prediction about a strictly positive premium-risk nexus is no longer valid. Asymmetries in the sub-premium’s sensitivity to cyber risks from different sources and the premium customer loss rates jointly shape the complexity of the relation between cyber insurance premiums and cyber risks. Improvements in the product demand conditions enhance firms’ incentives to hedge cyber losses and push premiums higher. Lastly, we discuss the influence of product price competition on premiums.

Suggested Citation

  • Chen, Chang-Chih & Chang, Chia-Chien & Rui, Ying & Yu, Min-Teh, 2025. "Cyber insurance valuation with endogenous cyber loss," Journal of Banking & Finance, Elsevier, vol. 181(C).
  • Handle: RePEc:eee:jbfina:v:181:y:2025:i:c:s0378426625001840
    DOI: 10.1016/j.jbankfin.2025.107564
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426625001840
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jbankfin.2025.107564?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Eling, Martin & Jung, Kwangmin, 2018. "Copula approaches for modeling cross-sectional dependence of data breach losses," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 167-180.
    2. Philipp Doerrenberg & Andreas Peichl & Sebastian Siegloch, 2017. "The Elasticity of Taxable Income in the Presence of Deduction Possibilities," NBER Chapters, in: Personal Income Taxation and Household Behavior (TAPES), National Bureau of Economic Research, Inc.
    3. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    4. Martin Eling & Werner Schnell, 2016. "What do we know about cyber risk and cyber risk insurance?," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 17(5), pages 474-491, November.
    5. Baione, Fabio & Levantesi, Susanna, 2014. "A health insurance pricing model based on prevalence rates: Application to critical illness insurance," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 174-184.
    6. Goldstein, Robert & Ju, Nengjiu & Leland, Hayne, 2001. "An EBIT-Based Model of Dynamic Capital Structure," The Journal of Business, University of Chicago Press, vol. 74(4), pages 483-512, October.
    7. Martin Eling & Werner Schnell, 2020. "Capital Requirements for Cyber Risk and Cyber Risk Insurance: An Analysis of Solvency II, the U.S. Risk-Based Capital Standards, and the Swiss Solvency Test," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(3), pages 370-392, July.
    8. Young, Virginia R., 2008. "Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 691-703, April.
    9. Shang-Yin Yang & Chou-Wen Wang & Hong-Chih Huang, 2016. "The Valuation of Lifetime Health Insurance Policies with Limited Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 777-800, September.
    10. Low, Wen-Shinn & Lee, Jeng-Da & Cheng, Soo-May, 2013. "The link between customer satisfaction and price sensitivity: An investigation of retailing industry in Taiwan," Journal of Retailing and Consumer Services, Elsevier, vol. 20(1), pages 1-10.
    11. Jianjun Miao, 2005. "Optimal Capital Structure and Industry Dynamics," Journal of Finance, American Finance Association, vol. 60(6), pages 2621-2659, December.
    12. Andjelka Kelic & Zachary A. Collier & Christopher Brown & Walter E. Beyeler & Alexander V. Outkin & Vanessa N. Vargas & Mark A. Ehlen & Christopher Judson & Ali Zaidi & Billy Leung & Igor Linkov, 2013. "Decision framework for evaluating the macroeconomic risks and policy impacts of cyber attacks," Environment Systems and Decisions, Springer, vol. 33(4), pages 544-560, December.
    13. Chia-Chien Chang & Chou-Wen Wang & Chih-Yuan Yang, 2012. "The Effects of Macroeconomic Factors on Pricing Mortgage Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 867-895, September.
    14. Wang, Shaun S., 2019. "Integrated framework for information security investment and cyber insurance," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    15. Ricardo J. Caballero & Eduardo M. R. A. Engel, 1999. "Explaining Investment Dynamics in U.S. Manufacturing: A Generalized (S,s) Approach," Econometrica, Econometric Society, vol. 67(4), pages 783-826, July.
    16. 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.
    17. Chia‐Chien Chang & Shih‐Kuei Lin & Min‐Teh Yu, 2011. "Valuation of Catastrophe Equity Puts With Markov‐Modulated Poisson Processes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 447-473, June.
    18. Kamiya, Shinichi & Kang, Jun-Koo & Kim, Jungmin & Milidonis, Andreas & Stulz, René M., 2021. "Risk management, firm reputation, and the impact of successful cyberattacks on target firms," Journal of Financial Economics, Elsevier, vol. 139(3), pages 719-749.
    19. Gurumurthy Kalyanaram & Russell S. Winer, 1995. "Empirical Generalizations from Reference Price Research," Marketing Science, INFORMS, vol. 14(3_supplem), pages 161-169.
    20. Maochao Xu & Lei Hua, 2019. "Cybersecurity Insurance: Modeling and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(2), pages 220-249, April.
    21. 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.
    22. Carina Neisser, 2021. "The Elasticity of Taxable Income: A Meta-Regression Analysis [The top 1% in international and historical perspective]," The Economic Journal, Royal Economic Society, vol. 131(640), pages 3365-3391.
    23. Lee, Jin-Ping & Yu, Min-Teh, 2007. "Valuation of catastrophe reinsurance with catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 264-278, September.
    24. Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    25. 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.
    26. Chang-Chih Chen & Chia-Chien Chang, 2019. "How Big are the Ambiguity-Based Premiums on Mortgage Insurances?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(1), pages 133-157, January.
    27. Chen, Jie & Su, Xunhua & Tian, Xuan & Xu, Bin, 2022. "Does customer-base structure influence managerial risk-taking incentives?," Journal of Financial Economics, Elsevier, vol. 143(1), pages 462-483.
    28. Braun, Alexander & Eling, Martin & Jaenicke, Christoph, 2023. "Cyber insurance-linked securities," ASTIN Bulletin, Cambridge University Press, vol. 53(3), pages 684-705, September.
    29. Cao, Xiyang & Ni, Jian & Wang, Fei & Xu, Yue, 2023. "Does customer concentration affect corporate risk-taking? Evidence from China," Finance Research Letters, Elsevier, vol. 58(PA).
    30. Chuang, Hwei-Lin & Yu, Min-Teh, 2010. "Pricing Unemployment Insurance – An Unemployment-Duration-Adjusted Approach," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 519-545, November.
    31. Fischer, Tom, 2007. "A law of large numbers approach to valuation in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 35-57, January.
    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. 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.
    2. 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.
    3. Da, Gaofeng & Xu, Maochao & Zhao, Peng, 2021. "Multivariate dependence among cyber risks based on L-hop propagation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 525-546.
    4. 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.
    5. 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.
    6. Gabriela Zeller & Matthias Scherer, 2023. "Risk mitigation services in cyber insurance: optimal contract design and price structure," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 502-547, April.
    7. 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).
    8. Zängerle, Daniel & Schiereck, Dirk, 2025. "Modelling and predicting enterprise-level cyber risks in the context of sparse data availability," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 156328, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    9. Martin Eling & Michael McShane & Trung Nguyen, 2021. "Cyber risk management: History and future research directions," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 24(1), pages 93-125, March.
    10. Yin-Yee Leong & Yen-Chih Chen, 2020. "Cyber risk cost and management in IoT devices-linked health insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(4), pages 737-759, October.
    11. Frank Cremer & Barry Sheehan & Michael Fortmann & Arash N. Kia & Martin Mullins & Finbarr Murphy & Stefan Materne, 2022. "Cyber risk and cybersecurity: a systematic review of data availability," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(3), pages 698-736, July.
    12. Yin-Yee Leong & Yen-Chih Chen, 0. "Cyber risk cost and management in IoT devices-linked health insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 0, pages 1-23.
    13. Na Ren & Xin Zhang, 2024. "A novel k-generation propagation model for cyber risk and its application to cyber insurance," Papers 2408.14151, arXiv.org.
    14. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Trück & Jiwook Jang, 2023. "Cyber loss model risk translates to premium mispricing and risk sensitivity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 372-433, April.
    15. Zhang, Xiaoyu & Xu, Maochao & Su, Jianxi & Zhao, Peng, 2023. "Structural models for fog computing based internet of things architectures with insurance and risk management applications," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1273-1291.
    16. Dacorogna, Michel & Debbabi, Nehla & Kratz, Marie, 2023. "Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data," European Journal of Operational Research, Elsevier, vol. 311(2), pages 708-729.
    17. Ulrik Franke, 2020. "IT service outage cost: case study and implications for cyber insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(4), pages 760-784, October.
    18. Farkas, Sébastien & Lopez, Olivier & Thomas, Maud, 2021. "Cyber claim analysis using Generalized Pareto regression trees with applications to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 92-105.
    19. Ulrik Franke, 0. "IT service outage cost: case study and implications for cyber insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 0, pages 1-25.
    20. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang, 2022. "Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity," Papers 2202.10588, arXiv.org, revised Mar 2023.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:jbfina:v:181:y:2025:i:c:s0378426625001840. 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/jbf .

    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.