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Risk Aggregation with Copula for Banking Industry

Author

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  • Toshinao Yoshiba

    (Director and Senior Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: toshinao.yoshiba@boj.or.jp))

Abstract

This paper surveys several applications of parametric copulas to market portfolios, credit portfolios, and enterprise risk management in the banking industry, focusing on how to capture stressed conditions. First, we show two simple applications for market portfolios: correlation structures for returns on three stock indices and a risk aggregation for a stock and bond portfolio. Second, we show two simple applications for credit portfolios: credit portfolio risk measurement in the banking industry and the application of copulas to CDO valuation, emphasizing the similarity to their application to market portfolios. In this way, we demonstrate the importance of capturing stressed conditions. Finally, we introduce practical applications to enterprise risk management for advanced banks and certain problems that remain open at this time.

Suggested Citation

  • Toshinao Yoshiba, 2015. "Risk Aggregation with Copula for Banking Industry," IMES Discussion Paper Series 15-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    • Handle: RePEc:ime:imedps:15-e-01
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    File URL: http://www.imes.boj.or.jp/research/papers/english/15-E-01.pdf
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    References listed on IDEAS

    as
    1. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    4. Toshinao Yoshiba, 2013. "Risk Aggregation by a Copula with a Stressed Condition," Bank of Japan Working Paper Series 13-E-12, Bank of Japan.
    5. Takashi Isogai, 2014. "Benchmarking of Unconditional VaR and ES Calculation Methods: A Comparative Simulation Analysis with Truncated Stable Distribution," Bank of Japan Working Paper Series 14-E-1, Bank of Japan.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    copula; multivariate distribution; tail dependence; risk aggregation; economic capital;
    All these keywords.

    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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