**!UNDER CONSTRUCTION!**

## Author

Jin Zhang^{1}

## Keywords

Credit Risk, Asset Corellation

## Review Status

*Unreviewed*

# 1 Introduction

Credit risk (i.e. liquidity risk, transparency risk, market risk, recovery risk, and so on) has become a major concern over the last few years. The probability of default, which occurs when debtors are unable to meet the obligations associated with a loan, may affect payoffs associated with financial contracts. Therefore, credit risk management is currently an important issue. Credit derivative products (that is collateralized obligation (CDO) and credit default swaps (CDS), and so on) have been developed, in recent decade, to help bank and non-bank institutions efficiently diversify credit exposure.

The aim of this project is primarily to focus on the issue of credit correlation risk. In recent decades, the importance of risk management is recognized by the financial institutions and the companies. They believe that the use of risk management is vital for their survival in the market and this can be characterized as an undeniable fact if we take into account the turmoil of August 2007.

# 2. Methodology

In the project, we consider a homogeneous portfolio with independent defaults and secondly when we have a homogeneous portfolio with dependent defaults driven by a single factor. In order to implement the models for these two cases, the concepts of the VaR and ES will be briefly explained.

# 2.1 Value at Risk (VaR)

VaR is recognized as the most useful tool for risk measure. It plays a vital role in risk management as it measures the percentage of certainty of not losing a certain amount of money in a certain period of time. In other words, during a concrete horizon and a given portfolio, VaR gives the amount of the worst expected losses in case that the market conditions are normal while the time period and the confidence level are known. Hence, the risk measurement can be successful only if the two significant parameters (time interval and confidence level) are chosen after deep consideration.

# 2.2 Expected Shortfall(ES)

ES is a risk measure that gives the mean of expected losses beyond the level of VaR. There are different points of view when the ES measure is compared with the VaR measure. Some of the researchers think the ES as an alternative way of measuring the risk while some others believe that ES is a ‘remedy for the deficiencies of VaR which in general is not a coherent risk measure’ (Acerbi, Tasche, 2002, p.1). In addition to this, ES gains popularity not only because of its sub-additivity property as this property is one more deficiency for the VaR, but because of its conservativeness as well. Our portfolio which is comprised of bank loans is subject to the risk of default. Hence, it is of high significance to estimate efficiently the average excess loss given the time interval. As a result, the combination of VaR and the ES is in our case the best way to meet our goals.

# 3. Results

# 4. Conclusions

In this project, we study two important classes of portfolio credit risk methods: the factor model and Monte-Carlo method to study default correlation which is an important issue in credit risk management. Particularly we employ two important concepts which are Value at Risk and Expected Short fall to exam the impact of default correlation on probability of default. Though employing two different methods’ experiments, we find that default probabilities of low default events happened turns higher with the increasing default correlation.

In the experiments, we use one factor model to study Value at Risk, Expected Short fall and default probabilities for a homogenous pool; since there is the one factor model is hard to use to compute Value at Risk, Expected Short fall and default probabilities for multiple-homogenous pool, Monte-Carlo method is used in this case. The validity of Mote-Carlo method in computing Value at Risk and Expected Short fall is verified through comparing the results from one factor model and Mote-Carlo’s.

In the future works, the Mote-Carlo method could be extended further to pricing CDO. The idea is similar with the one in computing Value at Risk and Expected Short fall. We need to simulate default event scenarios and generate future values for different default layers in CDO, after that, the price of CDO today is given by taking the average value of the discounted prices from different scenarios.