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Measuring and Optimizing Portfolio Credit Risk: A Copula-based Approach


  • Annalisa Di Clemente
  • Claudio Romano


In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non-normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula-based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t-copula, the grouped t-copula and the Clayton n-copula (or Cook-Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps. Copyright Banca Monte dei Paschi di Siena SpA, 2004

Suggested Citation

  • Annalisa Di Clemente & Claudio Romano, 2004. "Measuring and Optimizing Portfolio Credit Risk: A Copula-based Approach," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(3), pages 325-357, November.
  • Handle: RePEc:bla:ecnote:v:33:y:2004:i:3:p:325-357

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    Cited by:

    1. Desislava Chetalova & Marcel Wollschlager & Rudi Schafer, 2015. "Dependence structure of market states," Papers 1503.09004,, revised Jul 2015.
    2. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    3. Kakouris, Iakovos & Rustem, Berç, 2014. "Robust portfolio optimization with copulas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 28-37.
    4. Maldonado, Diego & Pazmiño, Mariela, 2008. "Nuevas Herramientas para la Administración del Riesgo Crediticio: El caso de una Cartera Crediticia Ecuatoriana
      [New Management Tool for Credit Risk analysis: An aplication for Financial Institutio
      ," MPRA Paper 17163, University Library of Munich, Germany, revised 30 Dec 2008.
    5. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2137-0 is not listed on IDEAS
    6. Nguyen, Tristan & Molinari, Robert Danilo, 2009. "Quantifizierung von Abhängigkeitsstrukturen zwischen Risiken in Versicherungsunternehmen," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 5(2), pages 28-52.

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