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Accounting in Context

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Module name: Accounting in Context Course title: ELEMENT CW2 (LJ)

Credit Risk Management Name of Supervisor: Anthony John Bray

Student: Dieu Linh Cao. ID number: 12028548.
Word count: 4,467 words. Date: 06/03/2013
Executive summary

Every day when reading the financial newspapers or news on TV, I notice that the bad debt still has been the big problem of many economics. Bad debt increases which influences to the bank first, and then to the all of the economy. So, I want to do the research about the Credit Risk Management because in my opinion, this is the way to reduce bad debt effectively.
In this report, I have researched about 3 models in Credit Risk Management: CreditMetrics, KMV, and Credit Risk Plus. In each model, I explain and analysis the case study from other document sources. Besides, I also compare and contrast the features or the use of them. In addition, critical thinking is applied in this report, when I have found the other idea, from opponent opinion to agreement. Because of the limitation of knowledge and timing, my report still has had many mistakes. Therefore, if I could do this topic again, may be in the dissertation of the master course, I will make it better, with my experience from AIC subject.

Table of Contents

Executive summary 2 Declaration 4 Content 5 1. CreditMetrics: 7 2. Portfolio Manager of KMV: 11 3. Credit Risk+: 14 Appendix 18 References 20

Declaration

I declare that this research report is my own original work, and that all sources that I have consulted have been duly acknowledged. I further declare that this work has not previously been submitted by me for a degree at the University of the West of England or any other institutions.

Signature:

Date:

Content

Lending money is one of the main operations of each Bank and causes the most credit risk as well. “Credit risk is the distribution of financial losses due to unexpected changes in the credit quality of counterparty in a financial agreement” (Morgan, 1997). By mobilizing money as saving account, the Bank uses this money for individual customer, or business to borrow and make profit. But recently, with the inflation, the credit risk increases a lot which causes the bad debt in many countries, as well as the regression of world economy. Credit risk arises from default or failure loans which are expected to be paid, between the Bank and other individual or organizations. According to Andrew Fight (Credit Risk Management, 2004), each bank has to consider the repayment ability of the company, by the reference credits and trades, the financial condition as well as the potential future of the company…Risk cannot be ignored in business, therefore, instead of hiding, it is better for the bank if it could predict and had strategy to avoid heavy loss. So, the expected and unexpected losses are planned and presented in figure:

Source: Skewed loss distribution (Credit Measurement, 2002)
The EL is estimated by the mean of distribution, around this point with “+ σ or – σ” which is confidence interval and the bank could predict and control the situation. While the UL bases on the percentile cutoff of extreme losses, which is call the Value at Risk (VAR), and estimates UL is very difficult. However, the loss distribution is not normal totally, and it could be positive or negative skewed. The loss will be considered in a fixed period of time (horizon) and the loss market value (vertical). It will be negative loss if the market value increases in the period of time.
The causes might be the fault from Bank (improper in considering the Credit Evaluation of a business) and from the business (the change in market makes loss suddenly). Each loan is an investment and the business is required to prove the abilities, and qualities in operation to pay back the loan. Default risk is defined as the traditional risk, when the borrowers could not pay back the loan or the bank could not collect the amount of loan. Even measuring carefully each investment, the loss can still happen because of the changing in market suddenly. For example, the American people usually borrow money from bank to buy houses with the proven document that they could pay back the loan in the future base on the average wage monthly, so each person is the individual customer of the Bank. However, the economic crisis happens and many people are unemployed (unemployment rate was about 10% in the ended of 2009, and now is 7.8% in the early of 2013) (Tradingeconomics. com, 2013). People are unemployed means they could not pay back the loan for the Bank, and even the Bank could takes the house as the Collateral Security but the value could not be equal to the loan, and also takes time for liquidation. However, the fault may come from the Bank in considering the project of the investment when it lacks the ability to analysis its potentiality because of the lack of knowledge of the bank staffs, or hiring the weakness of project purposefully by the borrowers. In addition, the fault comes from the Bank when the mortgage is inequity with the amount of loan, so the Bank gets loss easily if the loan could not be collected. It seems to happen recently, when the economic goes down and people do not want to invest in any areas. Therefore, it is difficult for the Bank in attracting customers to borrow money, so the requirements as well as borrowing conditions are decreased significant and loss the security of the loan. The vague in contract and the payment schedules can cause trouble for both of the banks and borrowers which is usually affected by the personal interests. The Bank may receive less money than it has, or the borrowers can expand the period of time to pay back the loan…Therefore, as the traditional approach to credit risk, it suggests the consideration in the five “Cs” (Credit risk measurement, 2002):
- Character: the reputation of the firm, the repayment history.
- Capital: determines the equity contribution and its ratio to debt.
- Capacity: estimates the period of time to repay debt. It could be based on the financial situation or the profit from future.
- Collateral: mentions the mortgage as the security from the firms. The Bank has to require the value of equity mortgage is equal to the amount of loan.
- Cycle: considers the picture of economics, like the cycle of inflation or deflation, especially the development of the industry.
So, basing the 5 elements to analysis before making decision, the models are created and innovated as well to manage the credit risk in the banking industry.
1. CreditMetrics:
CreditMetrics was published by J.P. Morgan (1997), with the main aim is to estimate the portfolio risk due to credit events, which means the Bank will consider customers under the frameworks given, to predict the risk. This model is developed bases on the Internal Rating at Bank, which the determination is divided into levels, from AAA (minimal risk) to D (loss) (Appendix 1).
This model idea is calculating how much will be loss if the loan becomes bad debt, or the current market value, actually. Therefore, the main process of this model includes: collecting the historic date to put the value at risk of the firm in one level, and then calculating the change of credit year to year. It could be upgrade or downgrade level, and up to collecting time, the debt will be defined to be loss or not, as well as the loss distribution graph is normal or skew.
Firstly, the Bank needs the matrix of Calculating volatility of value due to credit quality changes, and the information should be come from the statistic of credit rating, like Standard & Poor’s, or Moody’s...According to Dimitris Chorafas (Managing Credit Risk, volume 1, 2000), each company analyses to following particular criteria: when S&P bases on industry risk, management and corporate strategy, Capitalisation, Investment policy and result, the Moody’s considers the investment risk, profitability, competitive situation, but both of them are interested with the value of the loan. Each customer will have the probability of recovery rate uncertainty, and it is estimated by the correlation of changing equity of customers. The probability was summarized as the following table (1996):

The Transition Probabilities (Source: Standard & Poor’s CreditWeek, 1996)
Because the changing of equity cannot be seen exactly, so the model suggests using bond as equity to evaluate. Therefore, the correlation of credit risk is equal to the correlation of recovery rate uncertainty of customers at the same time. The transition matrix is update regularly, so it is different number in different time (appendix 2): | |
For example, this following table shows the data from Standard & Poor, about the transition matrix, with today rating on the left and the horizon is rating at risk. Firstly, the Bank will calculate the transition matrix that comes from historical rating data, and BBB can up or down bases on the rate of A or BB. According to Morgan (Technical Document, 1997), with the five-year 100 million dollar with 6% loan at the end of the first year, the measurement will be:
P = 6 + 61+r1+s1 + 61+r2+s22 + 61+r3+s33 + 1061+r4+s44
When: “r” is risk-free rate and “s” is the fixed credit spread. The risk free rate is estimated to forward to zero rates, because the risk can be avoided in the business. Morgan also gives the Credit Spread to illustrate the model (Technical Document, 1992): Category | Year 1 | Year 2 | Year 3 | Year 4 | AAA | 3.60 | 4.17 | 4.73 | 5.12 | AA | 3.65 | 4.22 | 4.78 | 5.17 | A | 3.72 | 4.32 | 4.93 | 5.32 | BBB | 4.10 | 4.67 | 5.25 | 5.63 | BB | 5.55 | 6.02 | 6,78 | 7.27 | B | 6.05 | 7.02 | 8.03 | 8.52 | CCC | 15.05 | 15.02 | 14.03 | 13.52 |

Source: Technical Document, J.P.Morgan (1997).
Therefore, the bank can determine how much the value of the loan in each year. From the formulation, the value of the loan in the year 1 in this example will be: Rating | Probability (%) | New loan value ($) | Probability weighted value ($) | Deviation | Probability weighted difference squared | AAA | 0.02 | 109.37 | 0.02 | 2.28 | 0.0010 | AA | 0.33 | 109.19 | 0.36 | 2.10 | 0.0146 | A | 5.95 | 108.66 | 6.47 | 1.57 | 0.1474 | BBB | 86.93 | 107.55 | 93.49 | 0.46 | 0.1853 | BB | 5.30 | 102.02 | 5.41 | (5.06) | 1.3592 | B | 1.17 | 98.10 | 1.15 | (8.99) | 0.9446 | CCC | 0.12 | 83.64 | 1.10 | (23.45) | 0.6598 | Default | 0.18 | 51.13 | 0.09 | (55.96) | 5.6358 | | | | Mean = 107.09 | | Variance = 8.9477 |

Value at risk Calculations (Source: Credit Management, 2002)
Thus, the standard deviation = 8.9477 = 2.99.
So, we could calculate the possible loan value at the end of each year, but it is better if the unexpected risk was shown. * With the normal distribution, it takes 5% value at risk which is $4.93, and 1% is $6.97. So the unexpected loss is $6.97. * With the actual distribution, it takes 6.77% (the total probability from level BB to Default) value at risk is $5.07, and 1.47% (the total from B to Default) is $8.99.
Applying the model in emerging markets, 2 authorities were Nisso Bucay and Dan Rosen who tested the portfolio with 197 trade bonds in 29 countries. Using the process above, they considered the statistic of the distribution: the mean of loss distribution identify the expected loss, maximum loss, and standard deviation.

Source: Credit Risk of an International Bond Portfolio (2000)
After that, they concluded from the application: * It could determine the correlation of parties who had the effect to the portfolio loss. * It shown the possibility of credit risk, may be default or unexpected based on the historical information. * The change of Risk-free rate could make the change in the mark-to-market value and caused loss. * Risk could be reduced in expanding business within country, not sovereigns.
The application also compares the results between using transition matrix of Standard and Poor’s, KMV and Moody’s. The result from Moody’s matrix is determined to be similar with the real situation of firms, and more comparative but the result from KMV is different and it will be explained in the next part.
The other thing which is developed from the model is considering the sovereign risk, not only the default risk. It may be suitable with the business environment nowadays, when the globalization becomes popular. The authors want to test whether the model works within sovereign business. The result is shown in the following table, so it is nearly same but with the bond investment, they realized that it was not enough to attract within country, and the other countries are better. Therefore, in the conclusion, they suggest sovereigns as the way to reduce risk, base on the result from CreditMetrics.

Comparing between risks of diversification within country and sovereign.
Source: Credit Risk of an International Bond Portfolio (2000)
The model could be trusted and used because it based on the historical information of the firm by the famous ranking organization. This record is observed in a long time so it could reflect the financial situation of the firm. The information is published and easy to collect as well. Besides, depending on the result of the case study, the CreditMetrics could be use in the variety business environments (because the test in 29 countries with different industries), so the model is applicable. The model gets the main purpose when calculating the value of the loan in the period of time. On the other hand, the average transition of firms in the same group is the same, which makes the argument. The Moody’s opinion objected with the idea Morgan’s idea and Crouhy (2000) against as well by the opinion that the default rate was continuous in case of rating does not. Because of the different results between using the transition matrix, KMV or Standard and Poor’s, still causes conflict for users who do not really know how to use. Besides, the models are designed to work in liquid market might provide the wrong result in illiquid market (Dimitris Chorafas, 2000). In addition, the model requires the information from rating organization so the result will be change when the criteria change, so it affects to the purpose of model. Finally, the model could be applied with the known rating firm when the information is available (Schmid, 2004) and the suggestion for the unknown rating firm is taking the financial information from the financial fundamental of the unknown to combine to the known could find the rating.
2. Portfolio Manager of KMV:
This model also considers credit quality changes due to rating migrations like CreditMetrics, but finds the recovery rate uncertainty directly which called Expected Default Frequency (EDF), by Stephen Kealhofer, John McQuown and Oldrich Vasicek. In fact, this is the expansion of Merton (1974)’s model. It means that this model focuses on the structure of equity of the customer, the insecure of the equity valuation, and the market value of equity. The Bank decides the loan for a company by characterizing the company's equity as a call option on its assets. The borrowing of the company stands for the put option to the equity owned by this company that the exercise price is equal to the value of the loan. At the time to pay back to the bank, if the market value of the equity is lower than the loan value, the company has to do the put option. The price of the put option can be calculated by the formular of Black-Scholes (1973). In another word, the company is said to be default when the value of equity is smaller than the debt, so the payoff for shareholders (according to the theory of Merton, 1997) is equal to the face value of the share minus the selling value of the firm.
Basing on the Merton theory, the Bank can evaluate the value of EDF:
1. Identifying the market value of the equity (V), as well as the insecure of the equity valuation (σ).
2. Calculating the distance between EDF to the impossible pay back of the company (DD – Distance to default).
3. Exchange DD to EDF bases on historical debt and bond.
Up to now, this model has been developed a lot, with the second generation, by the development of Longstaff and Schwartz (1995) when they said to calculate the recovery rate for the firm based on the default risk and interest rate. They combined them randomly, and relied the correlation which influence on the properties of the credit spread. And in 1999, basing on the research of Duffie and Singleton (1999), the reduced-form model has been defined.
And about the market value of equity and the insecure of the equity, they are determined by the Merton model. Assuming that each company has a private capital, so it is defined as the Call option to the equity that market price is equal to the loan at the payback time. Therefore, the value of Call option (S) and the insecure of private capital value (σs) (Greg M. Gupton, 1997):
S = f × (V, σ, LR, c, r)
(σs) = g × (V, σ, LR, c, r) * LR: the current market value of capital structure of the company. * c: the average value of interest paid recurrently of long term debt of the company. * r: interest of unrisk. * S: the value of private capital of the company (the value of share)
From this information, the Bank can calculate the V, as well as σ. Finally, the Distance to Default is presented by the formula (Greg M. Gupton, 1997):
DD = E V- DPTσ
The loss of the Bank is estimated like the CreditMetrics, with the level of the risk as the application test in the case study of CreditMetrics above when they applied both of 2 models.

Comparison between using S&P and KMV information.
Source: Credit Risk of an International Bond Portfolio (2000) Besides, the result from KMV matrix seems to be different significantly, when the distribution allocates around the mean mainly but the frequency is low. According to the criteria of them, the higher transition between credit states is, the lower default probabilities are which means the less losses base on the movement. It seems to be suitable with the US business environment, and the company in US also created the KMV matrix. Because of the big difference between the result of KMV and Standard and Poor’s in application of CreditMetrics, so they decided to compare each element in each results, like expected losses, standard deviation, (Appendix 3)…While KMV’s transition matrix defined larger probabilities to migration, and lower probabilities to default, but the larger default losses account is calculated by Standard and Poor’s.

Credit loss distribution by KMV (on the left) and CreditMetrics (on the right).
Source: Source: Credit Risk of an International Bond Portfolio (2000)
Each matrix has advantage and disadvantage, so basing on the purpose of using to choose which one is possible. Another advantage of KMV model is to calculate the asset return correlation which explained by Crouhy (2001) with 3 levels of vary factors. The first level is single composite of factor, the second is the combination of the first level and the industry, as well as country risk. And finally, the risk will be added with the global, regional risks. In addition, according to Credit Risk Measurement (Saunders and Allen, 2002), KMV is used for over 40,000 private firms and 3,400 public companies to produce the EDF scores. The KMV model is still used by the Moody’ Analytics company, which means it is useful and exact in reality. The added table in Appendix presents the cooperation credit rating between KMV model and agency, from 1997 to 2001. Even the agency rating was very stable at BBB level, the KMV level is fluctuate, because the EDF was updated every few minutes so the rate of risk also updated immediately.
While the CreditMetrics describes the distribution of value of the credit risk bases on the information of agencies, the Portfolio Manager simulates directly the distribution of the loss dependently. So, it seems to be more exact if using Portfolio Manager because the date is updated soon, and independent. The evaluation of KMV is based on the 30 years data base storage and it can give out the general view for investors. However, the disadvantage of this model is complicated in calculation. Because it does not use the information from agents, so the statistical determination and the market premium have to be collected. Besides, the asset return does not have a form of distribution, and easy to be misunderstood. Finally, the asset return is easy to be over optimistic for investors.
3. Credit Risk+:
This model considers about the default number of distribution over a period by identifying default rates and their volatilities which means the total loss distribution but does not deal with the time of the defaults. To compare with 2 models above, the Credit Risk+ does not focus and depend on the Credit quality change. It collects information from the book value only of the company to work the model and divide customers: payback or not. While CreditMetrics follows the mark-to-market model, Credit Risk + prefers Default mode (DM). According to this model, each individual loan is supposed as having a probability of default, and independence with others. The main idea of this model is to find the total loss distribution which according to the Poison distribution:

With “µ” is the mean customer without paying back, and “n” is the number of total of customers without paying back in the period of time, “e” is exponential, 2.71828. The Credit Risk+ combines the variable of discrete nature of rating transitions like the graph in Appendix.
The loss for the Bank is calculated by the recovery rate for each type of customers. To find out the credit portfolio loss distribution, the customers are divided into groups and there are some expected loss numbers for each, relies on the weighted average of the unpaid loan. The unpaid correlation between customers is calculated when CreditRisk+ assumes that the average of unpaid rate in each group change randomly, following the Gamma distributed default rates. In this model, there will be some assumptions, like the distribution of the default probabilities in the formulation and the 2 main things of uncertainty: severity of losses and Frequency of Defaults. According to Saunders and Allen (2002), assuming that the severity is £20,000 and £40,000 of each £100,000, the loss distribution for single loan portfolio is calculated and then combined into one. With the assumption about the mean default rate (m) is 3, the (n) defaults is from 0 to 8 and then applied to the formulation above, the probability of them will be: N | Probability | Cumulative Probability | 0 | 0.049787 | 0.049787 | 1 | 0.149361 | 0.199148 | 2 | 0.224042 | 0.432190 | 3 | 0.224042 | 0.647232 | 4 | 0.168031 | 0.815263 | 5 | 0.100819 | 0.916082 | 6 | 0.050409 | 0.966491 | 7 | 0.021604 | 0.988095 | 8 | 0.008102 | 0.996197 |

Source: Credit Risk of an International Bond Portfolio (2000)
And then, the loss distribution of combination will be presented as:

Loss distribution with severity rates.
Source: Credit Risk of an International Bond Portfolio (2000)
In general, the Credit Risk+ seems to be statistic model. Gundlach and Lehrbass (2004) described the model to be more intuitive and no need the cash flow information of each loan in practicing. Bessis (2002) commented about this model that there was no linear presented the relation between factors and obligors. But this model, after that, provides an additional portfolio segment linear which independence with the existing. Besides, the Credit Suisse (1997) concluded that the model understands the credit default events with experience in observation for many years so it could be good at the assumptions and classification of customers. However, Smithson (2000) was worried about the sensitivity and the limitation of the user-defined, because the wrong in assumption could affect to the whole result. In addition, Credit Suisse also gives out some other advantages of this model, like the effect result, and flexible in calculating as well as analysis. It is described in case of low data requirement, the calculation becomes easy, so it is useful in evaluating with the small firms for the bank. Crouhy (2001) gave the opposed idea, and concluded that the model did not involve some necessary of Credit risk Management, like the rating transition risk, or market risk, so it was impossible to combine with others traditional models.
Up to now, there are many models for the Bank when evaluating and making decision a loan for customers, but it is better if the Bank could combine them and use at the same time because it could consider the customer in many sides and more flexible. In the Journal of Banking and Finance in January 2000, Jose A.Loper relied on some limitations of the credit risk model in general, such as without the market price as a factor in calculating, so the result would not present for the future. On the other hand, Gordy (2000) in the same publisher, supported for these models, especially with CreditMetrics and Credit Risk+ because they could be used for a rage of plausible loan portfolio, satisfy the demand on lower quality portfolio, and both of them do not depend on the size of the loan. Saunders & Allen (2002) have a summary and comparison between credit risk models with 10 criteria. About the data requirement, the CreditMetrics uses the historical transition matrices, KMV cares the equity price, risk-free debt, and Credit Risk+ set up for itself the default rate distribution. These are the reason why the CreditMetrics model usually uses the information by financial agents, because this model requires a huge of information, when the 2 others could calculate independently. And about the Risk Classification, the CreditMetrics uses the rate to arrange the loans, but the KMV uses Empirical EDF and Credit Risk+ exposures bands. Even the Credit Suisse First Boston (CSFB) confirmed about having an exposure bands to classify, but Lopez (2000) did not satisfy, and it was said that could not be applied in reality and useful for only small companies. However, Saunders & Allen used the exposure bands to the case study with 588 obligators, but they have not given any negative comments and also compared with others. This information will be presented in Appendix. Each model requires particular information and implementation, so it is very difficult to comments which one is the best. Therefore the Bank should consider some problems: * Is the Model suitable with the customers, as well as the structure of the Bank? Or does it reflect most of the characters of the Credit risk? For example, with the huge of individual customers, we could use the Credit Risk + because the customers will be classified into group to easy managing. * Is it easy to use and apply to the Bank? Is it suitable with the skills and abilities of staff? Like the difference of result between 2 models can cause the misunderstanding of user without knowledge. * Is it easy to collect the required information to set up the Model? With the big companies, it is better to use the data from agencies and CreditMetrics model. * How to evaluate the reliability of the result from the Model?
The economic crisis is happening now, with the companies, including Banks, go bankrupt increases. Bad debt goes up, from countries to countries, and the cash flow in the world stuck. The Government and financial organizations also suggest the Bank improve the Credit risk Management system. Depending on the real situation, the Bank will choose the suitable models for itself.
Word count: 4,467

Appendix

1. The level of risk in evaluation of CreditMetrix Rating | Level of Risk | AAA | Minimal | AA | Modest | A | Average | BBB | Acceptable | BB | Acceptable with consideration | B | Management attention | CCC | Special mention | CC | Substandard | C | Doubtful | D | Loss |

2. This table will show the transition rate in 2009 (source: Standardandpoors.com) One-year transition matrix | Rating | AAA | AA | A | BBB | BB | B | CCC/C | D | NR | AAA | 86.80 | 8.03 | 0.54 | 0.00 | 0.14 | 0.00 | 0.00 | 0.00 | 4.49 | AA | 0.30 | 86.10 | 9.36 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 3.87 | A | 0.04 | 2.66 | 86.86 | 4.26 | 0.35 | 0.07 | 0.00 | 0.06 | 5.70 | BBB | 0.00 | 0.39 | 5.07 | 82.87 | 3.08 | 0.69 | 0.03 | 0.24 | 7.63 | BB | 0.00 | 0.22 | 0.14 | 7.79 | 74.12 | 4.90 | 1.01 | 0.87 | 10.96 | B | 0.00 | 0.00 | 0.11 | 0.34 | 9.73 | 74.16 | 2.80 | 3.02 | 9.84 | CCC/C | 0.00 | 0.00 | 0.00 | 0.00 | 2.01 | 20.13 | 47.65 | 11.41 | 18.79 |

Global Bank Transition Rates For Multiple Time Horizons (%)
(Source: standardandpoors.com, 2013)

3. Comparison of result from Case study:

Source: Credit Risk of an International Bond Portfolio (2000)
4. Summary and compare between 3 Models. | Model | | CreditMetrics | KMV | Credit Risk | The Credit Risk elements are considered | Including the portfolio of credit quality change and the portfolio of unpaid loan. | The portfolio of unpaid loan, but be flexible to consider the change of credit quality | The portfolio of unpaid loan. | The portfolio of credit quality changes | It is evaluated base of the credit rating at the beginning. | Based on the change of equity value and EDF each month. | Not mention | The Correlation between unpaid loans | Estimated bases on the correlation, between the share price and another factor in model. | Estimated bases on the correlation, between the share price and another factor in model. | Included into the instability of recovery rate uncertainty of each customer group. | The expected loss | Calculated randomly by Beta distribution. | Calculated randomly by Beta distribution. | Set up already before. | The approach | Monte Carlo | Monte Carlo | Monte Carlo |
References

* Books: * Chorafas, (2000) Managing Credit Risk. England: Euromoney Books. * Fight, (2004) Credit Risk Management. England: Elsevier. * Lando, (2004) Credit Risk Modeling: Theory and Applications. England: Princeton University Press. * Saunders, and Allen, (2002) Credit Risk Management. 2nd ed. New York, Usa: John Wiley & Sons, Inc., New York. * Shimko, (2004) Credit Risk Models and Management. 2nd ed. England: London Risk. * Silverman, D., (2005) Doing Qualitative Research, 2nd ed. London: Sage Publications. * Website: * Bucay, and Rosen, (2003) Credit Risk of an International Bond Portfolio: A Case Study. Financial Risks [online]. [Accessed 02 March 2013]. * Gordy, (2000) A comparative anatomy of credit risk models. Journal of Banking & Finance [online]. 24 (1-2), pp. 119-149. [Accessed 28 Feb 2013]. * Gordy, (2012) Granularity adjustment for mark-to-market credit risk models. Journal of Banking & Finance [online]. 36 (7), pp. 1896-1910. [Accessed 01 March 2013]. * Hull, J., Nelken, I. and White, A., [2004] Merton’s Model, Credit Risk, and Volatility Skews. Journal of Credit Risk [online], 1(1), pp. 3-28. [Accessed 05 March 2013] * Kercheval, , Goldberg, and Breger, (2003) Modeling Credit Risk. Journal of Portfolio Managemen [online]. 19 (2), pp. 90-100. [Accessed 05 March 2013]. * Lopez, and Saidenberg, (2000) Evaluating credit risk models. Journal of Banking & Finance. 24 (1-2), pp. 151-165. [Accessed 04 March 2013]. * Peura, S. and Jokivuolle, E., 2004. Similation Based Stress Tests of Banks’ Regulatory Capital Adequacy. Journal of Banking and Finance [online], 28, pp. 1801-1824. [Accessed 05 March 2013] * Unknown, (1997) A Credit risk management framework. Credit Suisse First Boston. [online]. [Accessed 01 March 2013]. * Wesley, D. H., (1993) Credit Risk Management: Lessons for Success. Journal of Commercial Lending [online], 75, pp. 32-38. [Accessed 28 Feb 2013].

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