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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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
2
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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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
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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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A co nst i tuent of Symb iosis International Universi ty
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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
Ph : 020-22932640
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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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A co nst i tuent of Symb iosis International Universi ty
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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
Ph : 020-22932640
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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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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
Ph : 020-22932640
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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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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
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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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Symbiosis International (Deemed University),
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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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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
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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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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
Ph : 020-22932640
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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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Symbiosis International (Deemed University),
Symbiosis Infotech Campus, Plot-15,Rajiv Gandhi Infotech Campus, MIDC, Hinjewadi, Pune 411057
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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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Ph : 020-22932640
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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/