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Sound Deposit Insurance Pricing Using a Machine Learning Approach

Author

Listed:
  • Hirbod Assa

    (Mathematical Sciences Building, University of Liverpool, Liverpool L69 7ZL, UK)

  • Mostafa Pouralizadeh

    (Department of Statistics, Faculty of Mathematical Science and Computer, Allameh Tabataba’i University, Tehran 1489684511, Iran)

  • Abdolrahim Badamchizadeh

    (Department of Statistics, Faculty of Mathematical Science and Computer, Allameh Tabataba’i University, Tehran 1489684511, Iran)

Abstract

While the main conceptual issue related to deposit insurances is the moral hazard risk, the main technical issue is inaccurate calibration of the implied volatility. This issue can raise the risk of generating an arbitrage. In this paper, first, we discuss that by imposing the no-moral-hazard risk, the removal of arbitrage is equivalent to removing the static arbitrage. Then, we propose a simple quadratic model to parameterize implied volatility and remove the static arbitrage. The process of removing the static risk is as follows: Using a machine learning approach with a regularized cost function, we update the parameters in such a way that butterfly arbitrage is ruled out and also implementing a calibration method, we make some conditions on the parameters of each time slice to rule out calendar spread arbitrage. Therefore, eliminating the effects of both butterfly and calendar spread arbitrage make the implied volatility surface free of static arbitrage.

Suggested Citation

  • Hirbod Assa & Mostafa Pouralizadeh & Abdolrahim Badamchizadeh, 2019. "Sound Deposit Insurance Pricing Using a Machine Learning Approach," Risks, MDPI, vol. 7(2), pages 1-18, April.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:45-:d:224369
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    References listed on IDEAS

    as
    1. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    4. Martin le Roux, 2007. "A Long-Term Model of the Dynamics of the S&P500 Implied Volatility Surface," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 61-75.
    5. Liu, Li & Zhang, Tao, 2015. "Economic policy uncertainty and stock market volatility," Finance Research Letters, Elsevier, vol. 15(C), pages 99-105.
    6. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    7. Bo Zhao & Stewart Hodges, 2013. "Parametric modeling of implied smile functions: a generalized SVI model," Review of Derivatives Research, Springer, vol. 16(1), pages 53-77, April.
    8. Hirbod Assa, 2015. "Risk management under a prudential policy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(2), pages 217-230, October.
    9. Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725, September.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Merton, Robert C., 1977. "An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory," Journal of Banking & Finance, Elsevier, vol. 1(1), pages 3-11, June.
    12. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
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    Cited by:

    1. Vali Asimit & Ioannis Kyriakou & Jens Perch Nielsen, 2020. "Special Issue “Machine Learning in Insurance”," Risks, MDPI, vol. 8(2), pages 1-2, May.

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