research report on credit risk models_print

8/10/2019 Research Report on Credit Risk Models_PRINT

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SymbiosisCentre for Management and

Human Resource Development (SCMHRD)

A co nst i tuent of Symb iosis International Universi ty

Accredited by NAAC with A Grade

SymbiosisCenter for Management and Human Resource Development (SCMHRD)

Symbiosis International (Deemed University),

Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057

Ph : 020-22932640

1

Ex-MBA 2010-2013

Semester -V (Minor Project)

Credit Risk Models

Project Guide: Prof. Manish Sinha

Submitted by

Abhishek Verma (2010G43)

Ex-MBA2010-13


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Contents

Credit ratings 3

Using external credit ratings 4

Benefits of credit risk models 4

Models used by Bank 5

VaR (Value at Risk) 5

Merton Model 8

KMV Model 10

Greek letters: 15

Bibliography 16


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Credit ratings:

The international rating agencies: Standard and Poors(S&P) and Moodysprovide markets with

the most credible and objective measure of creditworthiness for companies, financial

instruments and sovereign nations.

Significant resources and sophisticated programs are used to analyze and manage risk. Some

companies run a credit risk department whose job is to assess the financial health of their

customers, and extend credit (or not) accordingly. They may use in house programs to advice on

avoiding, reducing and transferring risk. They also use third party provided intelligence.

Companies like Standard & Poor's, Moody's, Fitch Ratings, and Dun and Bradstreet provide such

information for a fee.

Most lenders employ their own models (credit scorecards) to rank potential and existing

customers according to risk, and then apply appropriate strategies. With products such as

unsecured personal loans or mortgages, lenders charge a higher price for higher risk customers

and vice versa. With revolving products such as credit cards and overdrafts, risk is controlled

through the setting of credit limits. Some products also require security, most commonly in theform of property.

Credit score models are used by banks or financial institutions grant credit to its clients. For

corporate and commercial borrowers, these models generally have qualitative and quantitative

sections outlining various aspects of the risk including, but not limited to, operating experience,

management expertise, asset quality, and leverage and liquidity ratios, respectively. Once this

information has been fully reviewed by credit officers and credit committees, the lender

provides the funds subject to the terms and conditions presented within the contract.

In the past credit risk has been shown to be particularly damaging for very large investmentprojects, the so-called megaprojects. This is because such projects are prone to end up in what

has been called the "debt trap," i.e., a situation where due to cost overruns, schedule delays,

etc.the costs of servicing debt becomes larger than the revenues available to pay interest on

and bring down the debt.


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Using External Credit Ratings:

Utilising international rating agency information from Moodys and S&P is a key element of a

sound credit management methodology. Investment grade ratings provide the standard for

acceptable counterparty risk and contractual risk accepted with customers defined by rating

agencies as being below investment grade should typically return a higher level of reward.

However, producers must bear in mind that it is the customer that pays for a credit rating for

the primary purpose of facilitating their own borrowings and investment. Some companies pay

for ratings because they dont disclose financial information to the wider market. During theglobal financial crisis, some companies chose to discontinue their use of credit agencies when

their ratings began to drop and threatened to fall below investment grade as defined by the

major agencies. Even when ratings are available, they must be treated with caution. Credit

ratings agencies are not responsible for verifying the accuracy of the financial data supplied to

them. The recent financial crisis demonstrated that even accurate historical financial

information is not always a good indicator of credit worthiness.

Key external indicators such as share-price movement can give an immediate indication of

deteriorating financial position even when the credit rating remains good. Internal qualitative

measures such as late payments for recent shipments or erratic re-scheduling of shipments may

also give a better indication of credit risk position than the current credit rating.

Benefits of Credit Risk Models:

Banks credit exposures typically cut across geographical locations and product lines. The use of

credit risk models offers banks a framework for examining this risk in a timely manner,

centralising data on global exposures and analysing marginal and absolute contributions to risk.

These properties of models may contribute to an improvement in a banks overall ability to

identify measure and manage risk.

Credit risk models may provide estimates of credit risk (such as unexpected loss) which

reflect individual portfolio composition; hence, they may provide a better reflection of

risk.


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By design, models may be both influenced by, and be responsive to, shifts in business

lines, credit quality, market variables and the economic environment. Consequently,

modelling methodology holds out the possibility of providing a more responsive and

informative tool for risk management.

In addition, models may offer:

o The incentive to improve systems and data collection efforts;

o A more informed setting of limits and reserves;

o More accurate risk and performance-based pricing, which may contribute to a

more transparent decision-making process;

o A more consistent basis for economic capital allocation.

Models used by Banks:

VaR (Value at Risk):A value at risk calculation makes a statement of the form: We are X percent certain that we will

not lose more than V Rs in the next N days. The variable V is VaR, X % is the confidence level,

and N days is the time horizon.

The Variable V is the VaR of the Portfolio. It is the loss level over N days that has a probability of

only (100-X)% of being exceeded.

Bank regulators also use VaR in determining the capital a bank is required to keep for the risks it

is bearing. The Basel Committee published what is now known as BIS accord which calculates for

the trading book using the measure with N 10 and X = 99. It means its focus is on the revaluation

loss over a 10 day period that is expected to be exceeded only 1% of the time. The capital it

requires the bank to hold is K times this VaR measure. The multiplier K is chosen on a bank-by-

bank basis by the regulators and must be atleast 3.0.


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A recommended methodology for calculating the VaR:

Historical Simulation:

It is one of the popular ways of estimating the VaR. Most Banks in India use this methodology to

Calculate VaR. The RBI says itscomfortable with the methodology but the only mandatory thing

they have asked to follow is by reporting VaR each day so that all the relevant data arising out of

that daystrade are incorporated into the VaR computation.

It uses past data as the guide to what might happen in the future. E.g. VaR is to be calculated

for a portfolio using a 1-day time horizon, a 99% confidence level and 200 days of data.

Firstly we need to identify what market variables will affect the portfolio. It could be currency

exchange rates, stock prices, and interest rates etc; these we take as market variables. Then we

need to collect the data on these movements in the market variables over a period of 200 days.

This provides 199 alternative scenarios in what can happen between today & tomorrow.

Scenario 1 is where the percentage change in the values is all the same as they were between

day 0 and day 1, scenario 2 they are all the same between day 1 and day 2 and so on. For each

scenario the Rs change in the value of the portfolio between today and tomorrow is calculated.

This will define the probability distribution for daily changes in the value of the portfolio. TheEstimate of VaR is the loss at this first percentile point. Assuming that the last 200 days are the

good guide to what could happen during the next day, the company is 99% certain that it will

not take a loss greater than what VaR has estimated.

Two tables are shown as T1 & T2. T1 shows observation on market variables over the last 200

days. The observations are taken at the close of trading. First day as Day 0, second day as day 1

and so on. Today is day 199 and tomorrow is day 200.

T2 shows the value of market variables tomorrow if their percentage changes between today

and tomorrow are the same as they were between Day i-1 and day i for 1


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Define Vi as the value of a market variable on Day i and suppose that today is Day m. The ith

Scenario assumes that the value of the market variable tomorrow will be

Vm * (Vi /V(i-1) )

As shown in the table m = 200. For the first variable the value today, V200 is 25.85. Also V0=

20.33 and V1 = 20.78. The Value of the first market variable in the first scenario is 25.85 *

(20.78/20.33) = 26.42.

The penultimate column of table 2 shows the value of the portfolio tomorrow for each of the

200 scenarios. We suppose the value of portfolio is Rs. 23.50 Million. This leads to the change in

the value between today and tomorrow for all different scenarios. For scenario 1 the change in

value is +210,000. For scenario 2 it is -380,000.

Each day the VaR estimate is updated using the most recent 200 days of data. Consider, for

example what happens on day 201, new values for the variable becomes available and are used

to calculate a new value for our portfolio. This procedure is employed to calculate a new VaR

using data on the market variables from Day 1 to Day 200. Then Day 1 values are no longer used

then for next day day 2 to day 201 values are used to determine VaR, and so on.

Day Market Varibale 1 Market Variable 2 - - - Market Variable n

0 20.33 0.1132 - - - 65.37

1 20.78 0.1159 - - - 64.91

2 21.44 0.1162 - - - 65.02

- - - - - - -

- - - - - - -

199 25.75 0.1323 - - - 61.99200 25.85 0.1343 - - - 62.10

Data for VaR historical Simulation Calculation

Table 1


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Scenario

Num Market Varibale 1 Market Variable 2 - Market Variable N

Portfolio Value

(Rs Mill ion)

Change in Value

(Rs Mill ion)

1 26.42 0.1375 - 61.66 23.71 0.21

2 26.67 0.1346 - 62.21 23.12 -0.38

3 25.28 0.1368 - 61.99 22.94 -0.56

- - - - - - -

- - - - - - -

199 25.88 0.1354 - 61.87 23.63 0.13

200 25.95 0.1363 - 62.21 22.87 -0.63

Table 2

Scenarios generated for tomorrow (day 200) using data in Table 1

Merton Model:

The Model was proposed by Merton in 1974. Suppose a firm has one zero-coupon bond

outstanding and that the bond matures at time T.

V0 = Value of Company Assets Today

Vt = Value of Company Assets at time TE0= Value of companys equity today

Et = Value of companys equity at time T

D: Debt repayment due at time T

v: Volatility of assets

e: Instantaneous volatility of equity

If Vt < D (Theoretically) then the company will default at time T. The value of the equity is then

zero.

If Vt > D, the company will make the debt repayment at time T and the value of the equity atthis time is Vt-D. Mertons model give the value of the firm equity at time T as:

Et = max(Vt-D,0)

The above equation explains that the equity is a call option on the value of the assets with the

strike price equal to the repayment period on debt. The Black schools formula gives the value of

the equity today as E0 = (Equation 1)


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R= Risk free rate of return.

D1 =

and D2 =

The value of debt today is V0-E0

The risk-neutral probability that the company will default on the debt is N(-d2). To calculate this,

we require V0 and v. Neither of these 2 are directly observable. However if the company is

publicly traded we can observe E0. This means that equation (1) provides one condition that

must be satisfied by V0 and v. We can also estimate vfrom historical data.


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Using Itos Lemma : e * E0= N(d1) v * V0

This provides another equation that must be satisfied by V0 and v. Equation 1 and 2 provides a

pair of simultaneous equation that can be solved.

Itos Lemma: It is used to find the differential of a time-dependent function of a stochastic

process (continuous changing variables)

KMV Model:

The accuracy of VaR model relies upon the assumption: that the actual default rate is equal to

the historical average default rate. This assumption was challenged by KMV. This cannot be true

since default rates are continuous, while ratings are adjusted in a discrete fashion, simply

because rating agencies take time to upgrade or downgrade companies whose default risk have

changed.

Unlike VaR, KMV does not use Moodys or Standard & Poors statistical data to assign a

probability of default which only depends on the rating of the obligor. Instead, KMV derives the

actual probability of default, the Expected Default Frequency (EDF), for each obligor based on a

Merton (1974)s type model of the firm. The probability of default is thus a function of the firms

capital structure, the volatility of the asset returns and the current asset value. The EDF is firm-

specific, and can be mapped into any rating system to derive the equivalent rating of the

obligor. EDFs can be viewed as a ``cardinal ranking'' of obligors relative to default risk, instead

of the more conventional ``ordinal ranking'' proposed by rating agencies and which relies on

letters like AAA, AA, etc. Contrary to VaR, KMVs model does not make any explicit reference to

the transition probabilities which, in KMVs methodology, are already imbedded in the EDFs.

KMV best applies to publicly traded companies for which the value of equity is marketdetermined. The information contained in the firms stock price and balance sheet can then be

translated into an implied risk of default.


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The KMV model uses 3 steps to derive the actual probabilities of default:

Estimation of the market value and firmsassets volatility.

Calculation of distance to default

Scaling of the distance to default to actual probabilities of default.

Firm Value (V), Volatility of Firm Value (V).

Equity Value, E = f(V, V, K, c, r)

Volatility of equity, E = g(V, V, K, c, r)

where

- K denotes the leverage ratio

-

c is the average coupon paid on the long-term debt

- r is the risk-free rate.

- functions f , g determined by option pricing theory

Default Point, DPT: = short term debt + 0.5*long term debt

Distance-to-default: (DD) which is the distance between the expected asset value in 1 year,

E(V1), and the default point, DPT expressed in standard deviation

E (V1) = expected asset value in 1 year

The last stage consists as mapping the DD to the Expected Default Frequency (EDF), for a giventime horizon. These probabilities are called by KMV, EDFs, for Expected Default Frequencies.

Based on historical information on a large sample of firms, which includes firms which defaulted

one can estimate, for each time horizon, the proportion of firms of a given ranking, say DD = 4,

which actually defaulted after 1 year. This proportion, say 40 bp, or 0.4%, is the EDF as shown in

Fig 1 below.


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Fig: 1

Example: Current market value of assets, V0 = 1000

Net Expected growth of assets per annum 20%

Expected asset value in 1 year V0(1.20)= 1200

Annualized asset volatility, = 100

Default Point =800


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Quantiles 10 25 50 75 90 Mean

AAA 0.02 0.02 0.02 0.02 0.10 0.04

AA 0.02 0.02 0.02 0.04 0.10 0.06

A 0.02 0.03 0.08 0.13 0.28 0.14

BBB 0.05 0.09 0.15 0.33 0.71 0.30

BB 0.12 0.22 0.62 1.30 2.53 1.09

B 0.44 0.87 2.15 3.80 7.11 3.30

CCC 1.43 2.09 4.07 12.24 18.82 7.21

Variation of EDFs within rating classes

Fig: 3 Source: KMV Corporation

KMV has constructed a transition matrix based upon default rates rather than rating classes.

They start by ranking firms into groups based on non-overlapping ranges of default probabilities

that are typical for a rating class. For instance all firms with an EDF less than 2 bp are ranked

AAA, then those with an EDF comprised between 3 and 6 bp are in the AA group, firms with an

EDF of 715 bp belong to A rating class, and so on. Then using the history of Fig 2 changes in

EDFs we can produce a transition matrix shown in Fig 4

Initial ratingAAA AA A BBB BB B CCC Default

AAA 66.26 22.22 7.37 2.45 0.86 0.67 0.14 0.02

AA 21.66 43.04 25.83 6.56 1.99 0.68 0.20 0.04

A 2.76 20.34 44.19 22.94 7.42 1.97 0.28 0.10

BBB 0.30 2.80 22.63 42.54 23.52 6.95 1.00 0.26

BB 0.08 0.24 3.69 22.93 44.41 24.53 3.41 0.71

B 0.01 0.05 0.39 3.48 20.71 53.00 20.58 2.01

CCC 0.00 0.01 0.09 0.26 1.79 17.77 69.94 10.13

KMV 1-year transition matrix based on non-overlapping EDF ranges

Rating at year-end (%)

Fig: 4 Source: KMV Corporation

According to KMV, except for AAA, the probability of staying in the same rating class is between

half and one-third of historical rates produced by the rating agencies. KMVs probabilities of

default are also lower, especially for the low grade quality. Migration probabilities are also much

higher for KMV, especially for the grade above and below the current rating class.


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Drawbacks of KMV:

Private firms EDFs can be calculated only by using somecomparability analysis based on

accounting data.

It does not distinguish among different types of long-term bonds according to their seniority,

collateral, covenants, or convertibility.

Greek letters:

Delta: Sensitivity of call price to small change in stock price.

Gamma: Sensitivity of delta to change in stock price.

Theta: Sensitivity of call price to change in the time-to-expiration.

Variance: It is a measure of how far the numbers lie from the mean (expected value).

Standard deviation, : shows how much variation exists from the average (mean, or

expected value). A low standard deviation indicates that the data points tend to be very

close to the mean; high standard deviation indicates that the data points are spread out

over a large range of values.


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Bibliography:

http://www.financerisks.com

http://ir.moodys.com

http://www.standardandpoors.com/home/en/us

Hull, J. C. (2003), Options, Futures And Other Derivatives, 7th Ed, Pearson

Education.

http://en.wikipedia.org

https://www.google.co.in/

http://www.investopedia.com/
http://www.financerisks.com/http://www.financerisks.com/http://ir.moodys.com/http://ir.moodys.com/http://www.standardandpoors.com/home/en/ushttp://www.standardandpoors.com/home/en/ushttp://en.wikipedia.org/http://en.wikipedia.org/https://www.google.co.in/https://www.google.co.in/http://www.investopedia.com/http://www.investopedia.com/http://www.investopedia.com/https://www.google.co.in/http://en.wikipedia.org/http://www.standardandpoors.com/home/en/ushttp://ir.moodys.com/http://www.financerisks.com/

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