*by Xinzheng Huang and Cornelis W. Oosterlee *

The last year has seen financial institutions worldwide announce writedowns of hundreds of billions of dollars as a result of participating in the US mortgage market, in particular in subprime and other lower-rated mortgage-backed securities. Improving the practice of credit risk management by banks has thus become a top priority. Researchers Huang (Delft University of Technology) and Oosterlee (CWI) in the Netherlands focus on quantifying portfolio credit risk by advanced numerical techniques with an eye to active credit portfolio management. This work is sponsored by the Dutch Rabobank.

Credit risk is the risk of loss resulting from an obligor's inability to meet its obligations. Generally speaking, credit risk is the largest source of risk facing banking institutions. For these institutions, sound management involves measuring the credit risk at portfolio level to determine the amount of capital they need to hold as a cushion against potentially extreme losses. In practice, the portfolio risk is often measured by Value at Risk (VaR), which is simply the quantile of the distribution of portfolio loss for a given confidence level. With the Basel II accords (the recommendations on banking laws and regulations issued in 2004 by the Basel Committee on Banking Supervision), financial regulators aim to safeguard the banking institutions' solvency against such extreme losses.

From a bank's perspective, a high level of credit risk management means more than simply meeting regulatory requirements: the aim is rather to enhance the risk/return performance of credit assets. To achieve this goal, it is essential to measure how much a single obligor in a portfolio contributes to the total risk, ie the risk contributions of single exposures. Risk contribution plays an integral role in risk-sensitive loan pricing and portfolio optimization.

Extrapolation of credit risk from individual obligors to portfolio level involves specifying the dependence among obligors. Widely adopted in the industry is the Vasicek model, on which is built the Basel II internal rating-based approach. It is a Gaussian one-factor model, with default events being driven by a single common factor that is assumed to follow the Gaussian distribution, and obligors being independent conditional on the common factor. Under certain homogeneity conditions, the Vasicek one-factor model leads to very simple analytic asymptotic approximations of the loss distribution, VaR and VaR Contribution. However, these analytic approximations can significantly underestimate risks in the presence of exposure concentrations, ie when the portfolio is dominated by a few obligors.

In their research, Huang and Oosterlee showed that the saddle-point approximation with a conditional approach is an efficient tool for estimating the portfolio credit loss distribution in the Vasicek model and is well able to handle exposure concentration. The saddle-point approximation can be thought of as an improved version of the central limit theorem and usually leads to a small relative error, even for very small probabilities. Moreover, the saddle-point approximation is a flexible method which can be applied beyond the Vasicek model to more heavily tailed loss distributions which provide a better fit to current financial market data.

The single factor in the Vasicek model represents generally the state of economy. More factors are necessary if one wishes to take into account the effects of different industries and geographical regions in credit portfolio loss modelling. For example, in the current crisis the financial industry is taking the hardest hit, while back in 1997 East Asian countries suffered most. Multiple factors can be used to incorporate these details, but they generally complicate the computational process, as high-dimensional integrals need to be computed. For this, the researchers proposed efficient algorithms of adaptive integration for the calculation of the tail probability, with either a deterministic multiple integration rule or a Monte Carlo type random rule.

In the Vasicek model the loss given default (LGD) - the proportion of the exposure that will be lost if a default occurs - is assumed to be constant. However, extensive empirical evidence shows that it tends to go up in economic downturn. A heuristic justification is that the LGD is determined by the value of collateral (eg house prices in the case of mortgage loans), which is sensitive to the state of the economy. To account for this, Huang and Oosterlee proposed a new flexible framework for modelling systematic risk in LGD, in which the quantities have simple economic interpretation. The random LGD framework, combined with the fat-tailed models, further provides possibilities to replicate the spreads of the senior tranches of credit market indices (eg CDX), which have widened dramatically since the emergence of the credit crisis to a level that the industrial standard Gaussian one-factor model can not produce even with 100% correlation.

This research provides useful tools to fulfill the needs of active credit portfolio management within banks. Banks can improve their insight into credit risk and take appropriate measures to maximize their risk/return profile.

**Link:**

http://homepages.cwi.nl/~oosterle

**Please contact:**

Cornelis W. Oosterlee

CWI, The Netherlands

Tel: +31 20 592 4108

E-mail: C.W.Oosterleecwi.nl