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LLN-type approximations for large portfolio losses

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  • Liu, Jing

Abstract

We are concerned with the loss from defaults of a large portfolio of defaultable obligors. A static structural model is constructed, in which for each obligor i its default is driven by a latent variable Ui and its loss given default (LGD) is driven by another latent variable Vi through a general loss settlement function G. In this way, the default indicator 1Ui>a, with a denoting a default threshold, and the LGD G(Vi) are not necessarily comonotonic, hence essentially different from the ones used in some recent works. It is further assumed that the two latent variables Ui andVi are correlated in the way that they share a common systematic risk factor but each has its own idiosyncratic risk factor. We employ the law of large numbers (LLN) to derive the exact limit distribution of the portfolio loss as the portfolio size becomes large. As applications, we also derive exact approximations for the TVaR and moments of the portfolio loss.

Suggested Citation

  • Liu, Jing, 2018. "LLN-type approximations for large portfolio losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 71-77.
    • Handle: RePEc:eee:insuma:v:81:y:2018:i:c:p:71-77
    DOI: 10.1016/j.insmatheco.2018.05.003
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    References listed on IDEAS

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    More about this item

    Keywords

    Portfolio loss; Default; Law of large numbers; Systematic risk; Loss given default; Inverse;
    All these keywords.

    JEL classification:

    • 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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