# Portfolio Credit Risk with Extremal Dependence

31 Pages Posted: 15 Jul 2005

See all articles by Achal Bassamboo

## Achal Bassamboo

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS)

## Sandeep Juneja

Tata Institute of Fundamental Research (TIFR)

## Assaf Zeevi

Columbia Business School - Decision Risk and Operations

Date Written: July 1, 2005

### Abstract

We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in the probability that the portfolio will incur large losses over a fixed time horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that supports {\it extremal dependence} among obligors and does not hinge solely on correlation. A particular instance within this model class is the so-called $t$-copula model that is derived from the multivariate Student $t$ distribution and hence, generalizes the normal copula model. The size of the portfolio, the heterogenous mix of obligors, and the fact that default events are rare and mutually dependent makes it quite complicated to calculate portfolio credit risk either by means of exact analysis or naive Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop multi-stage importance sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

Keywords: Portfolio, credit, asymptotics, simulation, importance sampling, rare events, risk management

JEL Classification: C15, G3

Suggested Citation

Bassamboo, Achal and Juneja, Sandeep and Zeevi, Assaf, Portfolio Credit Risk with Extremal Dependence (July 1, 2005). Available at SSRN: https://ssrn.com/abstract=756125 or http://dx.doi.org/10.2139/ssrn.756125

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