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Sharp asymptotics for large portfolio losses under extreme risks

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  • Tang, Qihe
  • Tang, Zhaofeng
  • Yang, Yang

Abstract

We study the asymptotic behavior of the loss from defaults of a large portfolio. Inspired by the work of Bassamboo, Juneja and Zeevi (2008), we consider a static structural model in which latent variables governing individual defaults follow a mixture structure incorporating idiosyncratic risk, systematic risk, and common shock. In our setting, the portfolio effect, namely the decrease in overall risk due to the portfolio size increase, is taken into account by assuming that the individual default thresholds are proportional to a positive deterministic function diverging to infinity. Furthermore, the obligor-specific variables form a sequence of independent and identically distributed vectors, which still allows heterogeneity of the portfolio though. We derive sharp asymptotics for the tail probability of the portfolio loss as the portfolio size becomes large under the assumption, among others, that either the common shock variable or the systematic risk factor has a regularly varying tail. Our main finding is that the occurrence of large losses can be attributed to either the common shock variable or the systematic risk factor, whichever has a heavier tail.

Suggested Citation

  • Tang, Qihe & Tang, Zhaofeng & Yang, Yang, 2019. "Sharp asymptotics for large portfolio losses under extreme risks," European Journal of Operational Research, Elsevier, vol. 276(2), pages 710-722.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:2:p:710-722
    DOI: 10.1016/j.ejor.2019.01.025
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