Journal article
Sharp asymptotics for large portfolio losses under extreme risks
European journal of operational research, Vol.276(2), pp.710-722
07/16/2019
DOI: 10.1016/j.ejor.2019.01.025
Abstract
•We conduct an asymptotic study of losses from defaults of a large portfolio.•The latent variables are modeled by a mixture combining multi-level risks.•Obligor-specific variables constitute a continuum to underlie different risk types.•The portfolio effect is taken into account.•We conclude that large losses are due to either common shock or systematic risk. 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.
Details
- Title: Subtitle
- Sharp asymptotics for large portfolio losses under extreme risks
- Creators
- Qihe Tang - School of Risk and Actuarial Studies, UNSW Sydney, Sydney, NSW 2052 AustraliaZhaofeng Tang - Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USAYang Yang - Department of Statistics, Nanjing Audit University, Nanjing, Jiangsu 211815, China
- Resource Type
- Journal article
- Publication Details
- European journal of operational research, Vol.276(2), pp.710-722
- DOI
- 10.1016/j.ejor.2019.01.025
- ISSN
- 0377-2217
- eISSN
- 1872-6860
- Publisher
- Elsevier B.V
- Grant note
- DOI: 10.13039/501100008982, name: National Science Foundation, award: CMMI-1435864; DOI: 10.13039/100008139, name: Society of Actuaries, award: 2018–2021; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 71471090, 71671166; DOI: 10.13039/501100004608, name: Natural Science Foundation of Jiangsu Province of China, award: BK20161578
- Language
- English
- Date published
- 07/16/2019
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985925402771
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