IDENTITY CARD NO. : 3505543
NAME : GEORGE S. OGUTU
CONTACT : P. O. BOX 11873-00400, NAIROBI.
CELL PHONE : 0722 736 054
OCCUPATION : CIVIL SERVANT
EMPLOYER : GOVERNMENT OF KENYA, MINISTRY OF ROADS
DISTRICT : SIAYA
LOCATION : USONGA
SUB-LOCATION : USONGA
VILLAGE : NYANDORERA
RESIDENCE : RONGAI
STATES:
I am the above mentioned male adult Kenyan of the above given address, aged 52years. I am employed by the Government of Kenya, Ministry of Roads as a Technologist based in Nairobi’s Industrial Area. I am the owner and Policy Holder of Motor Vehicle Registration Number KAA 572R Nissan Sunny Saloon. I had insured the said Vehicle with M/S Gate-way Insurance Company ** policy Number 010/070/1/140134/2008/11.

The cover which was on display as on 1st September, 2012 was valued from 14th November, 2009 to expire on 13th November, 2012. I wish to state as follows:-

I do recall that on the 1st day of September, 2012, I gave my vehicle to Keziah Ogutu who is my young sister. She was to use the vehicle to go to her office. At about 8.00 am, she called me and informed me that she had been involved in an accident along Mombasa Road at Bellevue while driving to her office. She further told me that a Pedestrian ran on the road when she collided with the vehicle. She told me that the Pedestrian sustained injuries. I then rushed to the scene and found the Police at the scene. The victim had already been removed from the scene and taken to hospital by an ambulance.

After Police *** measurements, my vehicle was driven to Industrial Area Police Station where my sister recorded her statement and my vehicle inspected and then released. I informed my brokers of the accident.

That is all I can state.

R.O.C
NAME : GEORGE S. OGUTU
DATE : 5/7/2012
TIME : 1.30 P.M.
SIGNED : ___________________

IDENTITY CARD NO. : 1907208
NAME : KEZIAH ACHIENG OGUTU
CONTACT : P. O. BOX 56819 - 00200, NAIROBI.
CELL PHONE : 0722 386 001
OCCUPATION : AIR TRAFFIC CONTROL OFFICER
EMPLOYER : KENYA CIVIL AVIATION AUTHORITY
DISTRICT : SIAYA
LOCATION : USONGA
SUB-LOCATION : USONGA
VILLAGE : NYANDORERA
RESIDENCE : ONGATA - RONGAI

STATES:
I am the above named female adult Kenyan of the above given address, aged 51 years. I am a holder of Kenyan Driving License Serial No. 990818 c of c No. J496624 (GRE-191). I do renew my License annually and the renewal License receipt No. A0764979 which was on display as on 1st September, 2010 commenced on 9th January, 2009 to expire on 8th January, 2012. My License authorizes me to Classes “E” only. The same was first issued to me in the year 1995. I wish to state as follows:-

I recall well that on the 1st day of September 2010 at about 7.30 a.m., I was driving my brother’s Motor Vehicle Registration No. KAA 572R Nissan Sunny Saloon along Mombasa Road from the General direction of Nyayo Stadium towards that of Airport. I was alone in the vehicle and was driving from my residence to my place of work. Motor Traffic flow was moderate while that of human was light. The weather condition was dry with clear visibility. I was driving at a speed of 50Kilometres per hour keeping to the right inner lane of the dual carriage way.

On passing road junction to South “B” (Kapiti Road), I noticed pedestrians who were crossing the road from the left side to the right. They then stopped at the middle lane to allow the traffic on the middle lane to pass. This forced me also to slow down.

Suddenly as I was passing, one of the pedestrians dashed on my lane and collided with my vehicle. The impact was with my vehicle’s front body panel. On impact, he fell on the right hand reserve lane having gone over the bonnet. As a result, he sustained injuries. I managed to stop the vehicle about 10 metres from the impact point. The victim was picked by Red Cross ambulance which rushed him to hospital. Police from Industrial Police Station came to the scene where they took scene details. I drove the vehicle to Industrial Area Police Station
That is all I can state.
R.O.C
NAME : GEORGE S. OGUTU
DATE : 5/7/2012
TIME : 1.30 P.M.
SIGNED : ___________________
CREDIT RISK
Most financial institutions devote considerable resources to the measurement and management of credit risk. Regulators have for many years required banks to keep capital to reflect the credit risks they are bearing. This capital is in addition to the capital, described in Business Snapshot 20.1, that is required for market risk.

Credit risk arises from the possibility that borrowers and counterparties in derivatives transactions may default. This chapter discusses a number of different approaches to estimating the probability that a company will default and explains the key difference between risk-neutral and real-world probabilities of default. It examines the nature of the credit risk in over-the-counter derivatives transactions and discuss the clauses of derivatives dealers write into their contracts to reduce credit risk. It also covers default correlation, Gaussian copula models, and the estimation of credit value at risk.

Chapter 23 will discuss credit derivatives and show how ideas introduced in this chapter can be used to value these instruments.

CREDIT RATINGS
Rating agencies, such as Moody’s S & P, and Fitch, are in the business of providing ratings describing the creditworthiness of corporate bonds. The best rating assigned by Moody’s is Aaa. Bonds with this rating are considered to have almost no chance of defaulting. The next best rating is Aa. Following that comes A, Baa, Ba, B, Caa, Ca, C. Only bonds with ratings of Baa or above are considered to be investment grade. The S & P ratings corresponding to Moody’s Aaa, Aa, A, Baa, Ba, B, Caa, Ca and C are AAA, AA, A, BBB, BB, B, CCC, CC and C, respectively. Fitch’s rating categories are similar to those of S & P. To create finer rating measures, Moody’s divides its Aa rating category into Aa1, Aa2 and Aa3, it’s a category into A1, A2 and A3, and so on. Similarly, S & P divides its AA rating category into AA+, AA, and AA-, its aA rating category into A+, A, and A- and so on. Moody’s Aaa category and S & P’s AAA category are not subdivided, nor usually are the two lowest rating categories.

DEFAULT INTENSITIES
We can calculate the probability of a bond rated Caa or below defaulting during the third year as 39.717 – 30.494 = 9.223%. We will refer to this as the unconditional default probability. It is the probability of default during the third year as seen at time 0. The probability that the bond will survive until the end of year 2 is 100 – 30.494 – 69.506%. The probability that it will default during the third year conditional on no earlier default is therefore 0.09223/ 0.69506, or 13.27%. Conditional default probabilities are referred to as default intensities or hazard rates.
The 13.27% we have just calculated is for a 1 year time period. Suppose instead that we consider a short time period of length t. The default intensity (t) at time t is then defined so that (t) is the probability of default between time t and t + t conditional on no earlier default. If V(t) is the cumulative probability of the company surviving to time t (i.e., no default by time t), the conditional probability of default between time t.

Table 22.1 Average cumulative default rates (%), 1970-2006, Source: Moody’s.
Term (Years): 1 2 3 4 5 7 10 15 20
Aaa 0.000 0.000 0.000 0.026 0.099 0.251 0.521 0.992 1.191
Aa 0.008 0.019 0.042 0.106 0.177 0.343 0.522 1.111 1.929
A 0.021 0.095 0.220 0.344 0.472 0.759 1.287 2.364 4.238
Baa 0.181 0.506 0.930 1.434 1.938 2.959 4.637 8.244 11.362
Ba 1.205 3.219 5.568 7.958 10.215 14.005 19.118 28.380 35.093
B 5.236 11.296 17.043 22.054 26.794 34.771 43.343 52.175 54.421
Caa – C 19.476 30.494 39.717 46.904 52.622 59.938 69.178 70.870 70.870

RECOVERY RATES
When a company goes bankrupt, those that are owed money by the company file claims against the assets of the company. Sometimes there is a reorganization in which these creditors agree to a partial payment of their claims. In other cases the assets are sold by the liquidator and the proceeds are used to meet the claims as far as possible. Some claims typically have priority over other claims and are met more fully.
The recovery rate for a bond is normally defines as the bond’s market value immediately after a default, as a percent of its face value. Table 22.2 providwes historical data on average recovery rates for different categories of bonds in the United States. It shows that senior secured debt holders had an average recovery rate of 54.44 cents per dollar of face values while junior subordinated debt holders had an average recovery rate of only 24.47 cents per dollar of face value.

Table 22.2 Recovery rates on corporate bonds as a percentage of face value, 1982 – 2006. Source: Moody’s.
Class Average Recovery Rate (%)
Senior Secured 54.44
Senior Unsecured 38.39
Senior Subordinated 32.85
Subordinated 31.61
Junior Subordinated 24.47

Recovery rates are significantly negatively correlated with default rates. Moody’s looked at average recovery rates and average default rates each year between 1982 and 2006. It found that the following relationship provides a good fit to the data.
Recovery rate – 59.1 – 8.356 x Default Rate
Where the recovery rate is the average recovery rate on senior unsecured bonds in a year measured as a percentage and the default rate is the corporate default rate in the year measured as percentage.
This relationship means that a bad year for the default rate is usually doubly bad because it is accompanied by a low recovery rate. For example, when the average default rate in a year is only 0.1%, the expected recovery rate is relatively high at 58.3%. When the default rate is relatively high at 3%, the expected recovery rate is only 34.0%.

ESTIMATING DEFAULT PROBABILITIES FROM BOND PRICES
The probability of default for a company can be estimated from the prices of bonds it has issued. The usual assumption is that the only reason a corporate bond sells for less than a similar risk-free bond is the possibility of default.
Consider first an appropriate calculation. Suppose that a bond yields 200 basis points more than a similar risk-free bond and that the expected recovery rate in the event of a default is 40%. The holder of a corporate bond must be expecting to lose 200 basis points (or 2% per year) from defaults. Given the recovery rate of 40%, this leads to an estimate of the probability of a default per year conditional on no earlier default of 0.02/ (1-0.4), or 3.33%. In general, λ = s

l – R

where λ is the average default intensity (hazard rate) per year, s is the spread of the corporate bond yield over the risk-free rate, and R is the expected recovery rate.

CREDIT RISK IN DERIVATIVES TRANSACTIONS
The credit exposure on a derivatives transaction is more complicated than that on a loan. This is because the claim that will be made in the event of a default is more uncertain. Consider a financial institution that has one derivatives contract outstanding with a counterparty. Three possible situations can be distinguished:
1. Contract is always a liability to the financial institution
2. Contract is always an asset to the financial institution
3. Contract can become either an asset or a liability to the financial institution
An example of a derivatives contract in the first category is a short option position; an example in the second category is a long option position; an example in the third category is a forward contract.

Derivatives in the first category have no credit risk to the financial institution. If the counterparty goes bankrupt, there will be no loss. The derivative is one of the counterparty’s assets. It is likely to be retained, closed out, or sold to a third party. The result is no loss (or gain) to the financial institution.

Derivatives in the second category always have credit risk to the financial institution.
If the counterparty goes bankrupt, a loss is likely to be experienced. The derivative is one of the counterparty's liabilities. The financial institution has to make a claim against the assets of the counterparty and may receive some percentage of the value of the derivative. (Typically, a claim arising from a derivatives transaction is unsecured and junior.)
Derivatives in the third category may or may not have credit risk. If the counterparty defaults when the value of the derivative is positive to the financial institution, a claim will be made against the assets of the counterparty and a loss is likely to be experienced If the counterparty defaults When the value is negative to the financial institution, no loss is made because the derivative is retained, closed out, or sold to a third party.

CREDIT RISK MITIGATION
In many instances the analysis we just have presented overstates the credit risk in a derivatives transaction. This is because there are a number of clauses that derivatives dealers include in their contracts to mitigate credit risk.
Netting
A clause that has become standard in over-the-counter derivatives contracts is known as netting. This states that, if a company defaults on one contract it has with a counter-party, it must default on all outstanding contracts with the counterparty.

Netting has been successfully tested in the courts in most jurisdictions. It can substantially reduce credit risk for a financial institution. Consider, for example, a financial institution that has three contracts outstanding with a particular counterparty. The contracts are worth +$10 million, +$30 million, and -$25 million to the financial institution. Suppose the counterparty runs into financial difficulties and defaults on its outstanding obligations. To the counterparty the three contracts have values of -$10 million, -$30 million, and +$25 million, respectively. Without netting, the counterparty would default on the first two contracts and retain the third for a loss to the financial institution of $40 million. With netting, it is compelled to default on all three contracts for a loss to the financial institution of $15 million.

Suppose a financial institution has a portfolio of N derivatives contracts with a particular counterparty. Suppose that the no-default value of the ith contract is Vi and the amount recovered in the event of default is the recovery rate times this no default value. Without netting, the financial institution loses
N
(1 - R) ∑ max (Vi, 0) i=l where R is the recovery rate. With netting, it loses.

N (I - R) max ∑Vi, 0

Without netting, its loss is the payoff from a portfolio of call options on the contracts where each option has a strike price of zero. With netting, it is the payoff from a single option on the portfolio of contracts with a strike price of zero. The value of an option on a portfolio is never greater than, and is often considerably less than, the value of the corresponding portfolio of options.

The analysis presented in the previous section can be extended so that equation (22.5) gives the present value of the expected loss from all contracts with a counterparty when netting agreements are in place. This is achieved by redefining Vi in the equation as the present value of a derivative that pays off the exposure at time ti on the portfolio of all contracts with a counterparty.

A challenging task for a financial institution when considering whether it should enter into a new derivatives contract with a counterparty is to calculate the incremental effect on expected credit losses. This can be done by using equation (22.5) in the way just described to calculate expected default costs with and without the contract. It is interesting to note that, because of netting, the incremental effect of a new contract on expected default losses can be negative. This happens when the value of the new contract is negatively correlated with the value of existing contracts.

COLLATERALIZATION
Another clause frequently used to mitigate credit risks is known as collateralization. Suppose that a company and a financial institution have entered into a number of derivatives contracts. A typical collateralization agreement specifies that the contracts be valued periodically. If the total value of the contracts to the financial institution is above a specified threshold level, the agreement requires the cumulative collateral posted by the company to equal the difference between the value of the contracts to the financial institution and the threshold level. If, after the collateral has been posted, the value of the contracts moves in favor of the company so that the difference between value of the contract to the financial institution and the threshold level is less than the total margin already posted, the company can reclaim margin. In the event of a default by the company, the financial institution can seize the collateral. If the company does not post collateral as required, the financial institution can close out the contracts.

Suppose, for example, that the threshold level for the company is $10 million and the contracts are marked to market daily for the purposes of collateralization. If on a particular day the value of the contracts to the financial institution rises from $9 million to $10.5 million, it can ask for $0.5 million of collateral. If the next day the value of the contracts rises further to $11.4 million it can ask for a further $0.9 million of collateral. If the value of the contracts falls to $10.9 million on the following day, the company can ask for $0.5 million of the collateral to be returned. Note that the threshold ($10 million in this case) can be regarded as a line of credit that the financial institution is prepared to grant to the company.

The margin must be deposited by the company with the financial institution in cash or in the form of acceptable securities such as bonds. The securities are subject to a discount known as a haircut applied to their market value for the purposes of margin calculations. Interest is normally paid on cash.

If the collateralization agreement is a two-way agreement a threshold will also be specified for the financial institution. The company can then ask the financial institution to post collateral when the value or the outstanding contracts to the company exceeds the threshold.

Collateralization agreements provide a great deal of protection against the possibility of default (just as the margin accounts discussed in Chapter 2 provide protection for people who trade futures on an exchange). However, the threshold amount is not subject to protection. Furthermore, even when the threshold is zero, the protection is not total. This is because, when a company gets into financial difficulties, it is likely to stop responding to requests to post collateral. By the time the counterparty exercises its right to close out contracts, their value may have moved further in its favor.

DOWNGRADE TRIGGERS
Another credit risk mitigation technique used by a financial institution is known as a downgrade trigger. This is a clause stating that if the credit rating of the counterparty falls below a certain level, say Baa, the financial institution has the option to close out a derivatives contract at its market value.

Downgrade triggers do not provide protection from a big jump in a company's credit rating (for example, from A to default). Also, downgrade triggers work well only if relatively little use is made of them. If a company has many downgrade triggers outstanding with its counterparties, they are liable to provide little protection to the counterparties (see Business Snapshot 22.1).

DEFAULT CORRELATION
The term default correlation is used to describe the tendency for two companies to default at about the same time. There are a number of reasons why default correlation exists. Companies in the same industry or the same geographic region tend to be affected similarly by external events and as a result may experience financial difficulties at the same time. Economic conditions generally cause average default 'rates to be higher in some years than in other years. A default by one company may cause a default by another-the credit contagion effect. Default correlation means that credit risk cannot be completely diversified away and is the major reason why risk-neutral default probabilities are greater than real-world default probabilities (see Section 22.5).

Default correlation is important in the determination of probability distributions for default losses from a portfolio of exposures to different counterparties. Two types of default correlation models that have been suggested by researchers are referred to as reduced form models and structural models.
Reduced form models assume that the default intensities for different companies follow stochastic processes and are correlated with macroeconomic variables. When the default intensity for company A is high there is a tendency for the default intensity for company B to be high. This induces a default correlation between the two companies.
Reduced form models are mathematically attractive and reflect the tendency for economic cycles to generate default correlations. Their main disadvantage is that the range of default correlations that can be achieved is limited. Even when there is a perfect correlation between the default intensities of the two companies, the probability that they will both default during the same short period of time is usually very low. This is liable to be a problem in some circumstances. For example, when two companies operate in the same industry and the same country or when the financial health of one company is for some reason heavily dependent on the financial health of another company, a relatively high default correlation may be warranted. One approach to solving this problem is by extending the model so that the default intensity exhibits large jumps.

Structural models are based on a model similar to Merton's model (see Section 22.6).
A company defaults if the value of its assets is below a certain level. Default correlation between companies A and B is introduced into the model by assuming that the stochastic process followed by the assets of company A is correlated with the stochastic process followed by the assets of company B. Structural models have the advantage over reduced form models that the correlation can be made as high as desired. Their main disadvantage is that they are liable to be computationally quite slow.