Introduction to Credit Risk

Credit Course and Rating Agencies

Emre Tezmen

MYRA Training

18 Şubat 2010

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

What do We Aim With This Presantation?

Provide an understanding of the basic principles of credit risk

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

What do We Aim With This Presantation?

Provide an understanding of the basic principles of credit risk

Learn how to model default events, default probabilities, andbond prices

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

What do We Aim With This Presantation?

Provide an understanding of the basic principles of credit risk

Learn how to model default events, default probabilities, andbond prices

Learn how to calibrate and apply these models in practice

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

What do We Aim With This Presantation?

Provide an understanding of the basic principles of credit risk

Learn how to model default events, default probabilities, andbond prices

Learn how to calibrate and apply these models in practice

Provide an understanding of the structure and rationale ofpopulare derivate products for credit risk insurance

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

What do We Aim With This Presantation?

Provide an understanding of the basic principles of credit risk

Learn how to model default events, default probabilities, andbond prices

Learn how to calibrate and apply these models in practice

Provide an understanding of the structure and rationale ofpopulare derivate products for credit risk insurance

Learn how to analyze the risk and value of these transactions

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

- Mis-pricing of instruments

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

- Mis-pricing of instruments- Mis-understanding of involved risks

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

- Mis-pricing of instruments- Mis-understanding of involved risks- Fraud (’rough trader‘)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

- Mis-pricing of instruments- Mis-understanding of involved risks- Fraud (’rough trader‘)- Systems failure

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks

In classical parlance, we can outline financial risks as:

Market risk: possibility of unexpected changes in market pricesand rates

Operational risk: possibility of mistake or breakdown intrading/risk management operation

- Mis-pricing of instruments- Mis-understanding of involved risks- Fraud (’rough trader‘)- Systems failure- Legal exposure due to inappropriate services

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks II

Or we can define financial risk in a more eloborate way:

Liquidity risk: possibility of increased costs/inability to adjustposition(s)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks II

Or we can define financial risk in a more eloborate way:

Liquidity risk: possibility of increased costs/inability to adjustposition(s)

- Bid-ask spreads widen dramatically over a short period of time

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks II

Or we can define financial risk in a more eloborate way:

Liquidity risk: possibility of increased costs/inability to adjustposition(s)

- Bid-ask spreads widen dramatically over a short period of time- Access to credit deteriorates

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks II

Or we can define financial risk in a more eloborate way:

Liquidity risk: possibility of increased costs/inability to adjustposition(s)

- Bid-ask spreads widen dramatically over a short period of time- Access to credit deteriorates

Credit risk: possibility of losses due to unexpected changes inthe credit quality of a counterparty or issuer

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Financial Risks II

Or we can define financial risk in a more eloborate way:

Liquidity risk: possibility of increased costs/inability to adjustposition(s)

- Bid-ask spreads widen dramatically over a short period of time- Access to credit deteriorates

Credit risk: possibility of losses due to unexpected changes inthe credit quality of a counterparty or issuer

Systemic risk: market-wide liquidity breakdowns ordomino-style correlated defaults

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Market vs.Credit Risk

Basically, credit risk is part of market risk. But there are illiquidcontracts for which market prices are not available, for exampleloans. Other differences may be stated as:

Market Risk Credit Risk

Time horizon short (days) long (years)Portfolio static dynamicHedging standardized often customizedInformation market related contract specificData abound sparse

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Some Sources of Credit Risk

Exposure to the credit risk of an underlying, for example

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Some Sources of Credit Risk

Exposure to the credit risk of an underlying, for example

- Bank loan

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Some Sources of Credit Risk

Exposure to the credit risk of an underlying, for example

- Bank loan- Corporate or sovereign bond

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Some Sources of Credit Risk

Exposure to the credit risk of an underlying, for example

- Bank loan- Corporate or sovereign bond

Exposure to the credit risk of the (OTC) counterparty:vulnerable claims

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Some Sources of Credit Risk

Exposure to the credit risk of an underlying, for example

- Bank loan- Corporate or sovereign bond

Exposure to the credit risk of the (OTC) counterparty:vulnerable claims

Combinations of both, for example with options on corporatebonds

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Components of Credit Risk

Default

- Not receiving ALL you were promised- Probability of Default

Recovery

- How much do you receive?- Fraction of the owed amount recoverd by the lender- Usually expressed as a % of owed notional- Loss Given Default= 1 - Recovery Rate

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect Markets

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefits

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?Increase average interest rates (take a ’lemon’s premium’ )

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?Increase average interest rates (take a ’lemon’s premium’ )

- Adverse selection: Bad risks remain at the bank

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?Increase average interest rates (take a ’lemon’s premium’ )

- Adverse selection: Bad risks remain at the bank

- Moral hazard: Incentive for borrower to gamble, particularly

for large loan sizes

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?Increase average interest rates (take a ’lemon’s premium’ )

- Adverse selection: Bad risks remain at the bank

- Moral hazard: Incentive for borrower to gamble, particularly

for large loan sizes

Reduce exposure, but this may lead to credit rationing andreduces potential profits

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Why Measure & Manage Credit Risk

♣ Perfect vs. Imperfect MarketsIn perfect capital markets, adding/subtracting financial risk hasno impact on the market value of a firm (Modigliani-Miller)In imperfect capital markets, measuring and managingfinancial risk has significant benefitsDue to informational asymmetries, credit markets are imperfect

♣ Bank’s response to credit market imperfections?Increase average interest rates (take a ’lemon’s premium’ )

- Adverse selection: Bad risks remain at the bank

- Moral hazard: Incentive for borrower to gamble, particularly

for large loan sizes

Reduce exposure, but this may lead to credit rationing andreduces potential profits

♣ In practice, banks would set both interest rates and exposurelimits according to the measured credit risk of the borrower.

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

Restructuring

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to pay

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiation

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcy

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcyIn case of the last three events we also speak of a ’default’.

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcyIn case of the last three events we also speak of a ’default’.

♣ Credit Ratings provide information about corporate defaultprobabilities i.e. credit worthiness of bonds. Ratings are issuedby private rating agencies:

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcyIn case of the last three events we also speak of a ’default’.

♣ Credit Ratings provide information about corporate defaultprobabilities i.e. credit worthiness of bonds. Ratings are issuedby private rating agencies:

S&P: classes AAA, AA; A, BBB, BB, B, CCC; with AAA thebest

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcyIn case of the last three events we also speak of a ’default’.

♣ Credit Ratings provide information about corporate defaultprobabilities i.e. credit worthiness of bonds. Ratings are issuedby private rating agencies:

S&P: classes AAA, AA; A, BBB, BB, B, CCC; with AAA thebestMoody’s: classes Aaa, Aa, A, Baa, Ba, B, Caa, with Aaa thebest

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Credit Ratings

♣ Credit Event may be said to lead a change the credit quality ofan issuer and classified as:

RestructuringFailure to payRepudiationBankruptcyIn case of the last three events we also speak of a ’default’.

♣ Credit Ratings provide information about corporate defaultprobabilities i.e. credit worthiness of bonds. Ratings are issuedby private rating agencies:

S&P: classes AAA, AA; A, BBB, BB, B, CCC; with AAA thebestMoody’s: classes Aaa, Aa, A, Baa, Ba, B, Caa, with Aaa thebestBonds with ratings of BBB/Baa and above are considered’investment grade‘; below are considered non-investment grade

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Moody’s Average Cumulative Default Probabilities

1970-2003

Years 1 2 3 4 5 7 10 15 20

Aaa 0,00 0,00 0,00 0,04 0,12 0,29 0,62 1,21 1,55Aa 0,02 0,03 0,06 0,15 0,24 0,43 0,68 1,51 2,70A 0,02 0,09 0,23 0,38 0,54 0,91 1,59 2,94 5,24

Baa 0,20 0,57 1,03 1,62 2,16 3,24 5,10 9,12 12,59Ba 1,26 3,48 6,00 8,59 11,17 15,44 21,01 30,88 38,56B 6,21 13,76 20,65 26,66 31,99 40,79 50,02 59,21 60,73

Caa 23,65 37,20 48,02 55,56 60,83 69,36 77,91 80,23 80,23

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

S&P’s Average Cumulative Default Probabilities 2001

Years 1 2 3 4 5 10

AAA 0,00 0,00 0,07 0,15 0,24 1,40AA 0,00 0,02 0,12 0,25 0,43 1,29A 0,06 0,16 0,27 0,44 0,67 2,17

BBB 0,18 0,44 0,72 1,27 1,78 4,34BB 1,06 3,48 6,12 8,68 10,97 17,73B 5,20 11,00 15,95 19,40 21,88 29,02

CCC 19,79 26,92 31,63 35,97 40,15 45,10

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Bond yield y(t,T ) satisifes BT

t = e−y(t,T )(T−t)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Bond yield y(t,T ) satisifes BT

t = e−y(t,T )(T−t)

BTt price at time t of a defaultable zero-coupon bond paying 1

at T

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Bond yield y(t,T ) satisifes BT

t = e−y(t,T )(T−t)

BTt price at time t of a defaultable zero-coupon bond paying 1

at T

Bond yield y(t,T ) satisfies BTt = e−y(t,T )(T−t)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Bond yield y(t,T ) satisifes BT

t = e−y(t,T )(T−t)

BTt price at time t of a defaultable zero-coupon bond paying 1

at T

Bond yield y(t,T ) satisfies BTt = e−y(t,T )(T−t)

Credit yield spread S(t,T ) is then

S(t,T ) = y(t,T )− y(t,T ) = −1

T − tln

BTt

BT

t

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds

Two types of bonds: default free and defaultable

BT

t price at time t of a default free zero-coupon bond paying 1at T

Bond yield y(t,T ) satisifes BT

t = e−y(t,T )(T−t)

BTt price at time t of a defaultable zero-coupon bond paying 1

at T

Bond yield y(t,T ) satisfies BTt = e−y(t,T )(T−t)

Credit yield spread S(t,T ) is then

S(t,T ) = y(t,T )− y(t,T ) = −1

T − tln

BTt

BT

t

The term structure of credit spreads is the schedule of S(t,T )against T

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds A Numerical Example I

Being said the relation between a risky and risk free asset thequestion remains: How do we translate bond calculations into onesimple default probability expressed in %?

Years Default Recovery Default Free Default Discount PVProbability Rate VB Loss Rate Loss

1 λ 30 104,5 74,5 0,95 70,9 λ

2 λ 30 104,6 74,6 0,90 67,5 λ

3 λ 30 104,7 74,7 0,86 64,3 λ

4 λ 30 104,8 74,8 0,82 61,2 λ

5 λ 30 104,9 74,9 0,78 58,3 λ

6 λ 30 105 75 0,74 55,6 λ

Total 377,8λ

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable and Default Free Bonds A Numerical Example II

Solving for λ, Default Probability

λ =14, 6

377, 8≈ 0, 039 = 3, 9%

Where does this magical number 14,6 come from?

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Present Value of Expected Loss I

A risky bond maturing in six years pays an annual coupon of%5, and yield to maturity is %8

A risk-free bond, maturing at te same time pays an annualcoupon of %5, and yield to maturity is %5

Risky Bond Price (X )

PVX = 5e−0,08∗1 + 5e−0,08∗2 + · · ·+ 105e−0,08∗6 = 84, 76

Risk Free Bond Price (B)

PVB = 5e−0,05∗1 + 5e−0,05∗2 + · · ·+ 105e−0,05∗6 = 99, 36

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Present Value of Expected Loss II

And here comes the magic:

14, 6 = PVB − PVX = 99, 36 − 84, 76

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable Bonds Issuer and Credit Risk

A firm has a given probability of defaulting and not paying allit borrowed.

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable Bonds Issuer and Credit Risk

A firm has a given probability of defaulting and not paying allit borrowed.

So where does credit risk show up?

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable Bonds Issuer and Credit Risk

A firm has a given probability of defaulting and not paying allit borrowed.

So where does credit risk show up?

Credit risk will determine the borrowing costs of that company:

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable Bonds Issuer and Credit Risk

A firm has a given probability of defaulting and not paying allit borrowed.

So where does credit risk show up?

Credit risk will determine the borrowing costs of that company:

- The firm will have to pay higher coupon on its bonds in orderfor investors to be willing to buy them

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Defaultable Bonds Issuer and Credit Risk

A firm has a given probability of defaulting and not paying allit borrowed.

So where does credit risk show up?

Credit risk will determine the borrowing costs of that company:

- The firm will have to pay higher coupon on its bonds in orderfor investors to be willing to buy them

- Banks will require higher interests on the loan

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Default Modelling Challenges

How can we model the default event, default probabilities, andbond prices?

1 Structural approach: Economic arguments about why a firmdefaults

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Default Modelling Challenges

How can we model the default event, default probabilities, andbond prices?

1 Structural approach: Economic arguments about why a firmdefaults

1 Classic option-theoretic model of Merton (1974)

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Default Modelling Challenges

How can we model the default event, default probabilities, andbond prices?

1 Structural approach: Economic arguments about why a firmdefaults

1 Classic option-theoretic model of Merton (1974)2 First-passage model

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Default Modelling Challenges

How can we model the default event, default probabilities, andbond prices?

1 Structural approach: Economic arguments about why a firmdefaults

1 Classic option-theoretic model of Merton (1974)2 First-passage model

2 Reduced form/intensity based approach: Tractable ad-hocfinancial engineering type approach

Emre Tezmen Credit Course and Rating Agencies

Introduction to Credit Risk

Goals of The TrainingClassification of Financial RisksMeasuring Credit RiskBonds and Default Modelling Challenge

Default Modelling Challenges

How can we model the default event, default probabilities, andbond prices?

1 Structural approach: Economic arguments about why a firmdefaults

1 Classic option-theoretic model of Merton (1974)2 First-passage model

2 Reduced form/intensity based approach: Tractable ad-hocfinancial engineering type approach

3 Hyprid approach: Unifies economic and financial engineeringtype arguments

Emre Tezmen Credit Course and Rating Agencies