credit risk 1.1~1.2 指導教授 : 戴天時學生 : 施嘉紋. introduction to credit risk...

Credit risk1.1~1.2

指導教授 : 戴天時學生 : 施嘉紋

Introduction to Credit Risk• Default risk a probability that a counterparty in a financial contract will

not fulfill a contractual commitment her/his obligations stated in the contract.

• Credit risk the risk associated with any kind of credit-linked events. • Spread risk another components of credit risk

Introduction to Credit Risk• Reference (credit) risk assume both parties of a contract to be default- free It’s a party of the contract’s risk which is associated with the

third party(the reference entity of a given contract).• Credit derivatives developed financial instruments that allow market participants

to isolate and trade the reference risk. main:transfer the reference risk between the counterparties. • seller of reference risk buyer of an insurance against the reference risk.• buyer of reference risk bear the reference risk.

Introduction to Credit Risk• Counterparty (credit) risk 1.over-the counter derivatives is unlike the exchange-trade contracts, they are not backed by the guarantee of a clearinghouse or an exchange. 2.It emerges in a clear way in such contracts as vulnerable

claims and defaultable swaps. • vulnerable claims and defaultabnle swaps need to

quantify the default risk of both parties . • unilateral(one-sided) / bilateral(two-sided) risk the default risk takes into account one or two parties.

1.1 Corporate Bonds• Corporate Bonds 1.debt instruments issued by corporate 2.a part of the capital structure of the firm(just like the

equity). 3.make specified payments to the bondholder 4.corporate may default which the bondholders will not

receive the promised payment in full, they will suffer a financial loss.

• the occurrence of default, possibly caused by the firm’s bankruptcy , is meaningful during the the time period between the bond’s inception and its maturity.

• A corporate bond is an example of a defaultable claim

1.1 Corporate Bonds• 符號介紹 Face value=L, maturity=T D(t,T):the arbitrage price at time t of a T- maturity defaultable bond B(t,T):the arbitrage price at time t of a T- maturity default-free bond with face value=1 D(T,T)=L B(T,T)=1• Discount bond the bond pays no coupons• the defaultable term structure the term structure of interest rates implied by the yields

on the default prone corporate bonds or on the default prone sovereign bonds

1.1 Corporate Bonds• The default-free bond pays surely both the coupons and the face value to the

bondholders predetermined dates.• 1.The default bond: risky bonds 2.The default-free bond: risk –free bonds or Treasury

bonds. they exposed to the market (interest rate)risk 3. adjective default-free refers to presumed absence of the credit risk in bonds of highest credit quality.• the mathematical techniques presented in this are

applicable to the valuation of general corporate liabilities, such as corporate bonds. But corporate loans is another one.

1.1.1 Recovery Rules

• The specific recovery rules will typically include clauses such as priority payments upon default based on the debt’s seniority(seniority rules or priority structure)

• Recovery schemes(or recovery covenants or recovery rules)

determine the timing and the amount of recovery payments that is paid to creditors if the default occurs before the bond’s maturity.


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2. recovery payment determined at T and determined by recovery claim termed defaultable claims with recovery at maturity

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1.1.2 Safety Covenants• Bankruptcy firm’s bondholder take control over the firm and the

firm undergoes a reorganization. • For the sake of simplicity, this particular aspect is not

taken into account the bargaining process.• Exogenous bankruptcy bankruptcy is specified in form of some protective covenants. • Endogenous bankruptcy cover the situations when bankruptcy is declared by the firm’s stockholder if the firm’s value falls below certain pre-specified level. (max. equity,min debt)

1.1.2 Safety Covenants

• Deal with a corporate debt with the structural approach to credit risk in order to specify the default event.

• Safety Covenant is modeled as a barrier process(also called threshold process),usually denoted as υ in what follows.

• Default event: firm value process V falls below barrier process υ prior or at the maturity T.

• Propose of safety covenants: describe any mechanism which triggers default event before the maturity of the debt

1.1.3 Credit Spread

• Credit spread measures the excess return on a corporate bond over the return on a equivalent Treasury bond ,i.e., a bond which is assumed to be free of the credit risk. • Express: difference between respective yields to maturity

or difference between respective instantaneous forward rates.

• The determination of the credit spreads is in fact the ultimate goal of most credit risk models.

1.1.3 Credit Spread

• Distressed securities high level of credit spreads yielded by some

corporate securities, should they not default. Or encompasses publicly held and traded debt

or equity securities of firms that have defaulted or have filed for protection under the bankruptcy code.

1.1.4 Credit Ratings• A firm’s credit ratings is a measure of the firm’s

propensity to default.• Typically identified with elements of a finite set, also

referred to as the set of credit classes or credit grades.• Moody’s Investment Service, Standard &Poor’s

Corporation, Fitch IBCA, Duff &Phelps.• Internal ratings: based on internally developed methodologies.• official credit ratings: primarily reflect the likelihood of default• The improvement of the firm’s credit quality typically

does not result in an immediate upgrade(or downgrade)of its ratings.

1.1.5 Corporate Coupon Bonds

• Discrete time coupon payment 1.payments are only prior to the default time 2.the coupon bond may be considered as a portfolio composed of the defaultable coupons and defaultable face value .


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1.1.6 Fixed and Floating Rate Notes• Fixed-coupon bond contract stipulates coupon payments are fixed• Fixed-coupon bond risk-free bond defaultable bond• If trade at par, the coupon rate of a corporate bond would

be greater than a risk-free bond to compensate an investor for the default risk.

• The corresponding discrepancy is referred as fixed-rate credit spread over Treasury for a given corporate bond

• Credit spread reflects the credit quality of the issuer. • Financial market requires a higher risk premium for a lower

quality debt, so the cost of capital for a debtor of lower credit quality is higher.

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• Callable FRN has the right to redeem the note before maturity.• Putable FRN has the right to force an early redeemption• The changes in credit quality determine

whether option exercise is advantageous.

1.1.7 Bank Loans and Sovereign Debt

• Syndicated bank loans (SBLs) primarily large , high grade commercial loans secondary trading paralleled by the emergence of bank loan ratings substitutes or complements of corporate bonds• Sovereign Debt(Brady bonds) issued by several developed countries denominated in U.S. dollars contain various forms of credit guarantees and protections,

so it is hard to isolate the country-specific credit spread that is embedded in yields on Brady bonds.

1.1.8 Cross Default

• Basically corresponds to provision in loan agreements or bond indentures, which trigger an event of default if the counterparty(borrower or issue) defaults on another obligation.

• A provision of a loan or swap agreement stating that any default on another loan or swap will be considered a default on the issue with cross- default provision.

• Protect a creditor or counterparty from actions favoring another creditor

1.1.9 Default Correlations

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1.1.9 Default Correlations

• The default correlation between the two defaultable claims is defined as the correlation coefficient between the random variable X and Y

• Default correlation are an important building block of credit risk measurement and management methodologies for credit-risk sensitive portfolio.

1.2 Vulnerable Claims• Trade over-the-counter between default-prone

parties; each side of the contract is thus exposed to the counterparty risk of the other party.

• the underlying (reference) assets are assumed to be insensitive to the credit risk.

• Credit derivatives allow secluded trading in the reference risk handle or transfer the reference credit risk also a Vulnerable claim

1.2.1 Vulnerable Claims with Unilateral Default Risk

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1.2.2 Vulnerable Claims with biilateral Default Risk

• Contracts in which both counterparties are susceptible to default risk.

• default swaps insurance against reference risk• defaultable swaps 1.swap agreements between two default-prone entities 2.alternative settlement rules in case of default may largely influence the valuation of defaultable swap 3.need to specify the debt’s seniority 4.assume swaps are subordinated to debt in bankruptcy

1.2.2 Vulnerable Claims with biilateral Default Risk

• If the party in default due to receive a swap payment, two alternative settlement rules can be examined:

(1) the swap payment is received option-like features total value of a swap contract depends on the

value of the embedded option (2) the swap payment is withheld become valueless in case of default

1.2.3 Defaultable Interest Rate Contracts

• (default-free) spot interest rate agreement (or a credit agreement) notional amount=L nominal interest rate =κ accrual period=[T,U] refer to T as the reset date; U as the settlement date• An interest rate agreement can be described as a financial

contract between receiver and payer ,which is subject to the following covenants:

-at time T the receiver passes the notional amount L to the payer - he receives from the payer the accrued amount L(1+ κ(U-T)) at

time U Assumption: the payer (of the fixed rate κ) is certain to deliver the

promised payment to the receiver at time U

• Default-free features 1.the actual timing of the payment is not essential 見 P.14 例子 2.the covenants of the interest rate agreement described above invoke exchange of principal payments. It is equivalent to a loan subject to a fixed interest rate κ, where the receiver is the lending party, and the payer is the borrowing party. Such agreement gives rise to (default-

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• Defaultable interest rate agreement (or, a defaultable credit agreement) payer party is prone to default • assumption: none of parties has gone bankruptcy before the date T• Convenants -at time T the receiver passes the notional amount L - if the payer doesn’t default in the time interval (T,U] then at the

settlement date U he pays to the receiver the accrued amount L(1+ κ(U-T))

- if the payer defaults in (T,U] then he pays the receiver at time U the reduced amount δ L(1+ κ(U-T)), δ is recovery rate

• we deal here with a loan in which the debtor may default on his • obligation to repay the debt.

1.2.3 Defaultable Interest Rate Contracts• The basic type of a spot default-free interest rate swap

is the fixed-for-floating swap for the accrual period [T,U], settled in arrears, with the spot default-free LIBOR rate L(T) being the reference floating rate.

• One party is the payer of the fixed rate κand the other is the payer of the floating rate L(T); the parties agree to exchange at the settlement date U the nominal payments based on the nominal amount L.

• If L=1 the net cash flow at the contract’s settlement date U to one of one of the parties ,to the payer of the fixed rate κ says ,is equal to (L(T)- κ)(U-T)

1.2.3 Defaultable Interest Rate Contracts• The value of the fixed rate κ ,which makes this

cash flow have a value zero at the inception T, is called the (default-free) spot swap rate.

• In the default-free environment the spot swap rate and the spot LIBOR rate coincide

• In the default-free environment, the loan agreements and the interest rate swaps are equivalent

Example- the receiver passes at settlement date U to the payer the

full floating amount due: L(T)(U-T)- if the payer doesn’t default in the time period (T,U] ,the

receiver collects at the settlement date U the full fixed amount due:κ(U-T)

- if the payer defaults in (T,U] ,the receiver gets at the time U the reduced amount due:δκ(U-T)

- κ: defaultable spot swap rate ,which makes the above contract valueless at the inception time T. It differs from the defaultable spot LIBOR rate.

in the presence of a counterparty risk, the loan and the swap contract are not equivalent to each other.

credit risk 1.1~1.2 指導教授 : 戴天時 學 生 : 施嘉紋. introduction to credit risk...

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credit risk 1.1~1.2 指導教授 : 戴天時學生 : 施嘉紋. introduction to credit risk...