CDS

Transcript CDS

Credit Swaps

Credit Default Swaps

Generic Credit Default Swap: Definition

 In a standard

credit default swap

(CDS), a counterparty buys protection against default by a particular company or economic entity from a counterparty (seller).  The company or entity is known as the

reference entity

and a default by that entity is known as a

credit event

.  The

buyer

of the CDS makes periodic payments or a

premium

to the

seller

until the end of the life of the CDS or until the credit event occurs. 2

Generic Credit Default Swap: Definition

 Depending on the contract, if the credit event occurs, the buyer has  The right to sell a particular bond (or loan) issued by the company for its par value (physical delivery) Or  Receive a cash settlement based on the difference between the defaulted bond’s par value and its market price (recovery value) 3

Generic Credit Default Swap: Definition



Example:

Suppose two parties enter into a 5-year CDS with a NP of $200,000,000.  The buyer agrees to pay 95 bp annually for protection against default by the reference entity.  If the reference entity does not default, the buyer does not receive a payoff and ends up paying $1,900,000 each year for 5 years.  If a credit event does occur, the buyer will receive the default payment and pay a final accrual payment on the unpaid premium.

Generic Credit Default Swap: Definition



Example:

 Note: If the event occurs half way through the year, then the buyer pays the seller $950,000.  If the swap contract calls for physical delivery, the buyer will sell $200 million par value of the defaulted bonds for $200,000,000.  If there is a cash settlement, then an agent will poll dealers to determine a mid-market value. If the recovery value were $30 per $100 face value, then the buyer would receive $140,000,000 minus the $950,000 accrued interest payment.

CDS Terms

In the standard CDS, payments are usually made in arrears either on a quarter, semiannual, or annual basis. 2.

The par value of the bond or debt is the notional principal used for determining the payments of the buyer. 3.

 In many CDS contracts, a number of bonds or credits can be delivered in the case of a default. A company like Motorola, for example, might have 10 bonds with similar maturities, coupons, and embedded option and protection features that a buyer of a CDS could select in the event of a default. 6

CDS Terms

In the event of a default, the payoff from the CDS is equal to the face value of the bond (or NP) minus the value of the bond just after the default.   The value of the bond just after the default expressed as a proportion of the bond’s face value is known as the

recovery rate

(RR). CDS Payoff = (1 − RR)NP – Accrued Payment If that value on the $200,000,000 CDS were $30 per $100 face value, then the recovery rate would be 30% and the payoff to the CDS buyer would be $140,000,000 minus any accrued payment.

Payoff = (1 −.30)$200,000,000) − Accrued Payment Payoff = $140,000,000 − Accrued Payment 7

CDS Terms

The payments on a CDS are quoted as an annual percentage of the NP.  The payment is referred to as the

CDS spread

. 8

CDS Terms

 Swap bankers function as both brokers and dealers in the CDS market. As

dealers

, they will provide bid and ask quotes on a particular credit entry.  For example, a swap bank might quote a 5-year CDS on a GE credit at 270 bp bid and 280 bp offer.

 The swap bank will

buy protection

on GE for

2.7%

the underlying credit’s principal per year for 5 years of  The swap bank will sell protection on GE for

2.8%

of the principal.

CDS Uses



CDS are used primarily to manage the credit risk on debt and fixed-income investment positions.

CDS Uses



Example 1:

Consider a bond fund manager who just purchased a 5-year BBB corporate bond at a price yielding 8% and wanted to eliminate the credit risk on the bond.  To eliminate default risk, suppose the manager bought a 5-year CDS on the bond.  If the spread on the CDS were equal to 2% of the bond’s principal, then the purchase of the CDS would have the effect of making the 8% BBB bond a risk-free bond yielding approximately 6%. 11

CDS Uses



Example 1:

That is, if the bond does not default, then the bond fund manager will receive 6% from owning the bond and the CDS (8% yield on bond – 2% payment on CDS).  If the bond defaults, then the bond manager would receive 6% from the bond and CDS up to the time of the default and then would receive the face value on the bond from the CDS seller, which the manager can reinvest for the remainder of the 5-year period.  Thus, the CDS allows the manager to reduce or eliminate the credit risk on the bond. 12

CDS Uses



Example 2:

Suppose a manager holding a portfolio of 5-year U.S. Treasury notes yielding 6% expected the economy to improve and therefore was willing to assume more credit risk in return for a higher return by buying BBB corporate bonds yielding 8%.  As an alternative to selling his Treasuries and buying the corporate bonds, the manager could sell a CDS.

CDS Uses



Example 2:

If he were to sell a 5-year CDS on the above 5-year BBB bond to a swap bank for the 2% spread, then the manager would be adding 2% to the 6% yield on his Treasuries to obtain an effective yield of 8%.  Thus with the CDS, the manager would be able to obtain an expected yield equivalent to the BBB bond yield and would also be assuming the same credit risk associated with that bond. 14

CDS Uses



Example 3:

Consider a commercial bank with a large loan to a corporation.  Prior to the introduction of CDS, the bank would typically have to hold on to the loan once it was created.  During this period, its only strategy for minimizing its loan portfolio’s exposure to credit risk was to create a diversified loan portfolio. 15

CDS Uses



Example 3:

With CDS, such a bank can now buy credit protection for the loan.  In general, CDSs allow banks and other financial institutions to more actively manage the credit risk on their loan portfolio, buying CDSs on some loans and selling CDSs on other.  Today, commercial banks are largest purchasers of CDS and insurance companies are the largest sellers.

The Equilibrium CDS Spread



In equilibrium, the payment or spread on a CDS should be approximately equal to the credit spread on the CDS’s underlying bond or credit.

The Equilibrium CDS Spread



Example:

If the only risk on a 5-year BBB corporate bond yielding 8% were credit risk and the risk-free rate on 5-year investment were 6%, then the bond would be trading in the market with a 2% credit spread. 19

The Equilibrium CDS Spread



Example:

If the spread on 5-year CDS on a BBB quality bond were 2%, then an investor could obtain a 5-year risk-free investment yielding 6% by either  Buying a 5-year Treasury or  Buying the 5-year BBB corporate yielding 8% and purchasing the CDS on the underlying credit at a 2% spread 20

The Equilibrium CDS Spread



Example:

If the spread on a CDS is not equal to the credit spread on the underlying bond, then an arbitrage opportunity would exist by taking positions in the bond, risk-free security, and the CDS.

The Equilibrium CDS Spread



CDS Spread = 1% < Credit Spread = 2%

Suppose a swap bank were offering the above CDS for 1% instead of 2%.  In this case, an the CDS.

investor

looking for a 5-year risk-free investment would find it advantageous to create the synthetic risk-free investment with the BBB bond and  That is, the investor could earn 1% more than the yield on the Treasury by creating a

synthetic treasury by

and Buying the 5-year BBB corporate yielding 8% 2.

Purchasing the CDS on the underlying credit at a 1% 22

The Equilibrium CDS Spread



CDS Spread = 1% < Credit Spread = 2%

If the swap bank were offering the above CDS for 1% instead of 2%, then an

arbitrager

could realized a free lunch equivalent to a 5-year cash flow of 1% of the par value of bond by 1.

Shorting the Treasury at 6% (or borrowing at 6%) 2.

Using the proceeds to buy the BBB corporate 3.

Buying the CDS 23

The Equilibrium CDS Spread



CDS Spread = 1% < Credit Spread = 2%

These actions by investors and arbitrageurs, in turn, would have the impact of pushing the spread on the CDS towards 2%—the underlying bond’s credit spread.

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

If the swap bank were offering the

CDS at a 3% spread

, then an

investor

looking for a 5-year risk free investment would obviously prefer a 6% Treasury yielding 6% to a synthetic risk-free investment formed with the 5-year BBB corporate yielding 8% and a CDS on the credit requiring a payment of 3%. 25

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

If the swap bank were offering the

CDS

at a 3% spread, then a more

aggressive investor

looking to invest in the higher yielding 5-year BBB bonds, though, could earn 1% more than the 8% on the BBB bond by creating a

synthetic 5-year BBB

bond by 1.

Purchasing the 5-year Treasury at 6% 2.

Selling the CDS at 3% 26

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

If the swap bank were offering the

CDS

at a 3% spread, then a

bond portfolio manager

holding 5-year BBB bonds yielding 8% could pick up an additional 1% yield with the same credit risk exposure by 1.

Selling the BBB bonds Selling the CDS at 3% Using the proceeds from the bond sale to buy the 5-year Treasuries yielding 6% 27

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

If the swap bank were offering

he CDS at a 3% spread, then an

arbitrager

could realized a free lunch equivalent to a 5-year cash flow of 1% of the par value on the bond by 1.

Shorting the BBB bond 2.

Selling the CDS Using proceeds from bond sale to purchase 5 year Treasuries 28

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

With these positions, the bond position.

arbitrageur

would receive for each of the next 5 years 6% from her Treasury investment and 3% from her CDS, but only pay 8% on her short BBB  Furthermore, her holdings of Treasury securities would enable her to cover her obligation on the CDS if there was a default.  That is, in the event of a default she would be able to pay the CDS holder from the net proceed from selling her Treasuries and closing her short BBB bond by buying back the corporate bonds at their defaulted recovery price. 29

The Equilibrium CDS Spread



CDS Spread = 3% > Credit Spread = 2%

Collectively, the actions of the investors, bond portfolio managers, and arbitrageur would have the effect of pushing the spread on CDS from 3% to 2%. 30

The Equilibrium CDS Spread

 In equilibrium, arbitrageurs and investors should ensure that the spreads on CDS are approximately equal to spreads on the underlying bond or credit.  This spread can be defined as the equilibrium spread and is referred to as the

arbitrage-free spread

and the

Z-spread

CDS Spread and the Expected Default Loss



The arbitrage-free spread, Z, on a bond or CDS can also be thought of as the bond investor’s or CDS buyer’s

expected loss from the principal from default

.

CDS Spread and the Expected Default Loss

 Consider a

portfolio

of 5-year BBB bonds trading at a 2% credit spread.  The 2% premium that investors receive from the bond portfolio represents their compensation for an implied expected loss of 2% per year of the principal from the defaulted bonds. 33

CDS Spread and the Expected Default Loss

 If the spread were 2% and bond investors believed that the expected loss from default on such bonds would be only 1% per year of the principal, then the bond investors would want more BBB bonds, driving the price up and the yield down until the premium reflected a 1% spread.  If the spread were 2% and bond investors believed the default loss on a portfolio of BBB bond would be 3% per year, then the demand and price for such bonds would decrease, increasing the yield to reflect a credit spread of 3%. 34

CDS Spread and the Expected Default Loss

 Thus, in an efficient market, the credit spread on bonds and the equilibrium spreads on CDS represent the market’s implied expectation of the expected loss per year from the principal from default.  In the case of a CDS, the equilibrium spread can therefore be defined as the

implied probability of default of principal on the contract.

CDS Valuation

 The total value of a CDS’s payments is equal to the sum of the

present values of the periodic CDS spread

(Z) times the NP over the life of the CDS, discounted at the risk-free rate (R):

PV ( CDS Payments )

 t M   1

Z NP ( 1



R )

t 37

CDS Valuation

 In terms of the above example, the present value of the payment on the 5-year CDS with an equilibrium spread of 2% and a NP of $1 would be $0.084247: PV ( CDS Payments )  t 5   1 (.

02 )($ 1 ) ( 1 .

06 ) t  $ 0 .

084247 38

CDS Valuation

 The buyer (seller) of this 5-year CDS would therefore be willing to make (receive) payments over five years that have a present value of $0.084247.

CDS Valuation

 Because the spread can also be viewed as an expected loss of principal, the present value of the payments is also equal to the expected default protection the buyer (seller) receives (pays).  The value of the CDS protection, in turn, is equal to the

present value of the expected payout in the case of default.

CDS Valuation

 The present value of the expected payout in the case of default: PV ( Expected Payout )  t M   1 p t NP ( 1  RR ) ( 1  R ) t where: • • • p t = probability of default in period t conditional on no earlier default.

RR = recovery rate (as a proportion of the face value) on the bond at the time of default.

NP = notional principal equal to the par value of the bond.

CDS Valuation

 Note that the probability of default, p t , is defined as a

conditional probability of no prior defaults

.  Thus the conditional probability of default in Year 4 is based on the probability that the bond will survive until Year 4.  In contrast, an

unconditional probability

is the likelihood that the bond will default at a given time as seen from the present. 42

CDS Valuation

 As noted in Chapter 5, conditional default probabilities are referred to as

default intensities

.  Over a period of time, these probabilities will change, increasing or decreasing depending on the quality of the credit.

CDS Valuation

 Instead of defining a CDS’s expected payout in terms periodic probability density, p t , the CDS’s expected payout can alternatively by defined by the

average conditional

PV ( Expected Payout )  t M   1 p NP ( 1  RR ) ( 1  R ) t PV ( Expected Payout )  p NP ( 1  RR ) t M   1 ( 1  1 R ) t 44

CDS Valuation

 Given the equilibrium spread of .02 in our example and assuming a recovery rate of 30% if the underlying bond defaults, the implied probability density for our illustrative CDS would be .02857.  This implied probability is obtained by solving for payout equal to present value of the payments of $.084247.

 The implied probability is obtained by solving the present value of the expected payout equal to present value of the payments:

CDS Valuation

PV ( Expected Payout ) t M   1 p NP ( 1  RR ) ( 1  R ) t  t M   1 Z NP ( 1  R ) t p  ( 1  Z RR )  PV ( Payments ) p  .

02 ( 1  .

30 )  .

02857 PV ( Expected Payout )  PV ( Expected Payout ) PV ( Expected Payout ) t M   1 p NP ( 1  RR ) ( 1  R ) t   t 5   1 (.

02857 ) ($ 1 )( 1  .

30 ) ( 1 .

06 ) t $ 0 .

084247 46

CDS Valuation

 Note that if there were no recovery (RR = 0), then the implied probability would be equal to the spread Z, which as noted can be thought of as the probability of default of principal.  The probability density implied by the market is referred to as the

risk-neutral probability

because it is based on an equilibrium spread that is arbitrage free. 47

Alternative CDS Valuation

Alternative CDS Valuation Approach

 Suppose in the illustrative example, the

estimated

default intensity, sometimes referred to as the

real world probability

, on the 5-year BBB bond were .02 and not the implied probability of .02857. 49

Alternative CDS Valuation Approach

 In this case, the present value of the CDS expected payout would be $0.058973 instead of $0.084247: PV ( Expected Payout )  t 5   1 (.

02 ) ($ 1 )( 1  .

30 ) ( 1 .

06 ) t  $ 0 .

058973 50

Alternative CDS Valuation Approach

 Given the spread on the CDS is at 2% and the present value of the payments are $0.084247, buyers of the CDS would have to pay more on the CDS than the value they receive on the expected payoff ($0.058973).  If the real world probability density of .02 is accurate, then buyers of the CDS would eventually push the CDS spread down until it is equal to the value of the protection. 51

Alternative CDS Valuation Approach

 For the payment on the CDS to match the expected protection, the spread would have to equal .014.  This implied spread is found by solving for the Z that equates the present value of the payments to the present value of the expected payout given the real world probability of .02 and the estimated recovery rate of RR = .30. 52

 The spread, Z, that equates the present value of the payments to the present value of the expected payout given the real world probability is .014.

Alternative CDS Valuation Approach

PV ( Payments )  PV ( Expected Payout ) Z t M   1  Z ( 1  p NP R ) t ( 1   RR ) t M   1 p NP ( 1  RR ) ( 1  R ) t Z  (.

02 )( 1  .

30 )  .

014 PV ( Payments )  t M   1 Z NP ( 1  R ) t PV ( Payments )  t 5   1 (.

014 ) ($ 1 ) ( 1 .

06 ) t PV ( Payments )  $ 0 .

058973 53

Comparison of Valuation Approach



We now have two alternative methods for pricing a CDS.

Comparison of Valuation Approach

We can value the CDS swap given the credit spread in the market and then determine the present value of the payments;  In terms of our example, we would use the market spread of 2% and value the swap at $0.084247 with the implied probability density (or risk-neutral probability) being .02857.  See Slide 46.

Comparison of Valuation Approach

We can value the swap given estimated probabilities of default and then determine the present value of the expected payout.

 In terms of our example, we would use the estimated real world probability of .02 and value the CDS at $0.058973 with the implied credit spread being .014.  See Slide 53.

Comparison of Valuation Approach



What valuation method should be used?

Comparison of Valuation Approach

 Some scholars argue for the use of valuing swaps with risk-neutral probabilities or

underlying bonds equivalently pricing swaps in terms of credit spreads on the

because it reflects an arbitrage free price.  Thus, in our example they would price the 5-year CDS equal to the 2% spread with a total value of $0.084247. 58

Comparison of Valuation Approach

 If one can estimate real-world probabilities on bonds and CDS that are more accurate than the probabilities implied by current credit spread, then eventually the bond and CDS market will price such claims so that the credit spread reflects the real world probability.  If this is the case, then in our example one should price the 5-year CDS at $0.058973 given the estimated probability density of .02.  The argument for

pricing CDS using real world probabilities

depends on the ability of practitioners to estimated default probabilities.

Estimating Default Rates and Valuing CDS Based on Estimated Default Intensities  There are several approaches for estimating conditional probabilities.  The simplest and most direct one is to estimate the probabilities based on historical default rates.

Estimating Probability Intensities from Historical Default Rates

 1.

The next slide shows three different probabilities for corporate bonds with quality ratings of Aaa, Baa, B, and Caa: Cumulative default rates Unconditional probability rates Conditional probability rates (probability intensities) 61

Cumulative Default Rates, Probability Intensities, and CDS Values and Spreads t M   1 p t NP ( 1  RR ) ( 1  R ) t Z  t M   1 t M   1 p t ( ( 1 1   RR R ) t ) 1 ( 1  R ) t 62

Estimating Probability Intensities from Historical Default Rates

 The probabilities shown in the table are the average historical cumulative default rates from 1970-2006 as complied by Moody’s.  The unconditional probability of a bond defaulting during year t is equal to the difference in the cumulative probability in year t minus the cumulative probability of default in year t −1.  Example: The probability of a Caa bond default during year 4 is equal to 7.18% (= 46.9%% − 39.72%). 63

Estimating Probability Intensities from Historical Default Rates

 As previously noted, the conditional probability is the probability of default in a given year conditional on no prior defaults.  This probability is equal to unconditional probability of default in time t as a proportion of the bond’s probability of survival at the beginning of the period.  The probability of survival is equal to 100 minus the cumulative probability.  Example: The probability that a Caa bond will survive until the end of year three is 39.72% (100 minus its cumulative probability 39.72%), and the probability that the Caa bond will default during year 4 conditional on no prior defaults is 11.91% (= 7.18%/60.28%). 64

Valuing CDS Based on Estimated Historical Default Intensities  Using the conditional probabilities generated from the historical cumulative default rates, the values and spreads for four CDS with quality ratings of Aaa, Baa, B, and Caa are shown in Slide 62.  Each swap is assumed to have a maturity of five years, annual payments, NP of $100, and recovery rate of 30%.  The values are obtained by determining the present values of the expected payoff, with the discount rate assumed to be 6% and with the possible defaults assumed to occur at the end each year (implying there are no accrued payments).  The spreads on the CDS are the spreads that equate the present value of the payments to the present value of the expected payoff. 65

Valuing CDS Based on Estimated Historical Default Intensities 

Example:

The present value of the expected payoff for the CDS with a B quality rating is 17.78: PV ( Expected Payoff )  t M   1 p t NP ( 1  RR ) ( 1  R ) t PV ( Expected Payoff PV ( Expected Payoff ) )  ($ 100 )( 1  .

3 )   .

0524 ( 1 .

06 )  .

06395 ( 1 .

06 ) 2  .

0647125 ( 1 .

06 ) 3  .

0603905  ( 1 .

06 ) 4 .

0608082 ( 1 .

06 ) 5    17 .

78 66

Valuing CDS Based on Estimated Historical Default Intensities 

Example:

The spread on the B quality CDS that equates the present value of its payments to the expected payoff of $17.78 is .0422: t M   1 Z NP ( 1  R ) t Z t 5   1 $ 100 ( 1 .

06 ) t Z  $ 17 .

78 t 5   1 $ 100 ( 1 .

06 ) t  t M   1 p t NP ( 1  RR ) ( 1  R ) t  $ 17 .

78  $ 17 .

78 $ 421 .

2364  .

0422 67

Valuing CDS Based on Estimated Historical Default Intensities 

Example:

As shown in Slide 62, the present values of the expected payoffs on the Caa quality CDS is $41.43 and its spread is 0.0983.  As expected, the CDS values and spreads are greater, the greater the default risk.

Estimating Expected Default Rates: Implied Default Rates  The above default rates are based on historical frequencies.  Past frequencies are often not the best predictors of futures probabilities.  If the market is efficient such that the prices of bonds reflect the market’s expectation of future economic conditions, then the implied probabilities based on CDS’s risk spread would represent an expected future default probability. 69

Estimating Expected Default Rates: Implied Default Rates  We previously calculated the average implied probability by solving for the probability that equated the present value of the expected payoff to the present value of the payments based on the current bond’s credit spread.

 Using this methodology, one could estimate the implied conditional probabilities for each year for a given quality rating using the CDS spread on 1-year to m-year swaps.  This would result in a set of implied default probabilities that could be used to determine the spread on any swap. 70

Estimating Expected Default Rates: Implied Default Rates   The table shows the spreads (Z) and the implied probability densities given an assume recovery rate of 30% on 5 B-rated CDS with maturities ranging from 1 to 5 years: The implied probability densities are equal to Z(1 −RR).

Maturity t

1 2 3 4 5

Spread

0.0400

0.0425

0.0450

0.0475

0.0500

Implied Probabilty

0.0571

0.0607

0.0643

0.0679

0.0714

Estimating Expected Default Rates: Implied Default Rates  Given the implied probabilities, the value of a 5-year CDS based on its expected payoff would be $18.83 and its spread would be .0447: PV ( Expected Payoff )  t M   1 p t NP ( 1  RR ) ( 1  R ) t PV ( Expected Payoff ) PV ( Expected Payoff )  ($ 100 )( 1  .

3 )   .

0571 ( 1 .

06 )  .

0607 ( 1 .

06 ) 2  $ 18 .

33  .

0643 ( 1 .

06 ) 3  .

0679 ( 1 .

06 ) 4  .

0714 ( 1 .

06 ) 5   t M   1 Z NP ( 1  R ) t Z t 5   1 $ 100 ( 1 .

06 ) t  t M   1 p t NP ( 1  RR ) ( 1  R ) t  $ 18 .

83 Z  $ 18 .

83 t 5   1 $ 100 ( 1 .

06 ) t  $ 18 .

83 $ 421 .

2364  .

0447 72



Summary of the Two Valuation Approaches

Pricing CDS in Terms Credit Spreads

Many scholars argue for valuing CDS in terms credit spreads on the underlying bonds because it result in an arbitrage-free price.  Pricing CDS in terms of bond credits spreads also implies that the default probability for determining the expected payout by the seller is a probability implied by the credit spread of bonds traded in the market and not a real-world estimated probability. 73

Summary of the Two Valuation Approaches



Pricing CDS Based on Estimates of the Conditional Probability

The alternative to pricing CDS in terms of bond credit spreads is to determine the spread that will equate the present value of the payments to the present value of the expected payout based on estimates of the conditional probability.  Default probabilities can be estimated using historical cumulative default rates and implied default rates. 74

Summary of the Two Valuation Approaches



Note:

There are a number of other more advanced estimating techniques that practitioners can use to determine default probabilities

.

 Of particular note is Gaussian Copula Model.

The Value of an Off-Market CDS Swap

 Similar to a generic par value interest rate swap, the swap rate on a new CDS is generally set so that there is not an initial exchange of money.  Over time and as economic conditions change the credit spreads on new CDS, the value of an existing CDS will change. 77

The Value of an Off-Market CDS Swap



Example:

Suppose one year after a bond fund manager bought our illustrative 5-year CDS on BBB bond at the 2% spread, the economy became weaker and credit spreads on 4-year BBB bonds and new CDS on such bonds were 50 bp greater at 2.5%.

 Assume for this discussion that CDS spreads are determine by bond credit spreads in the market. 78

The Value of an Off-Market CDS Swap



Example:

Suppose the bond fund manager sold her 2% CDS to a swap bank who hedged the CDS by selling a new 2.5% CDS on the 4-year BBB bond.  With a buyer’s position on the assumed 2% CDS and seller’s position on the 2.5% CDS, the swap bank, in turn, would gain 0.5% of the NP for the next four years. 79

The Value of an Off-Market CDS Swap



Example:

Given a discount rate of 6%, the present value of this gain would be $1.73 per $100 NP. The swap banks would therefore pay the bond manager a maximum of $1.73 for assuming the swap.

• •

Offsetting Swap Positions

Buyer of 2% CDS Swap Seller of 2.5% CDS Swap • • Pay 2% of NP Receive 2.5% Receive 0.5% per year • • Receive Default Protection Pay Default Protection SV  t 4   1 ( Current SV  Spread  Exisitng ( 1  R ) t t 4   1 0 .

005 ($ 100 ) ( 1 .

06 ) t  $ 1 .

73 Spread )( NP ) 80

The Value of an Off-Market CDS Swap

 With four years left on the current swap, the increase in credit spread in the market has increased the value of the buyer’s position on the CDS swap by $1.73 from $6.93 to 8.66: Exisitng CDS : PV ( CDS Payments )  t 4   1 (.

02 )($ 100 ) ( 1 .

06 ) t  $ 6 .

93 Current Change PV ( CDS Payments )  t 4   1 (.

025 )($ 100 ) ( 1 .

06 ) t in Value  $ 1 .

73  $ 8 .

66 81

The Value of an Off-Market CDS Swap

 The increase in value on the buyer’s position of the exiting swap reflects the fact that with poorer economic conditions, the 2% swap payments now provide greater default protection (i.e., the present value of the expect payout is greater). 82

The Value of an Off-Market CDS Swap



For the initial seller, an increase in credit spreads causes a decrease in the value on seller’s positions.

The Value of an Off-Market CDS Swap



Example

Suppose that an insurance company was the one who sold the 5-year CDS on the BBB bond at the 2% spread to the bond portfolio manager (via a swap bank) and that one year later the credit spread on new 4-year CDS on BBB bonds was again at 2.5%. 84

The Value of an Off-Market CDS Swap



Example:

If the insurance company were to sell its seller’s position to a swap bank, the swap bank could hedge the assumed position by taking a buyer’s position on a new 4-year, 2.5% CDS on the BBB bond.  With the offsetting positions, the swap bank would lose 0.5% of the NP for the next four years. 85

The Value of an Off-Market CDS Swap



Example:

Given a discount rate of 6%, the present value of this loss would be $1.73 per $100 NP. The swap banks would therefore charge the insurance company at least $1.73 for assuming the seller’s position on the swap:

Offsetting Swap Positions

• Seller of 2% CDS Swap • Buyer of 2.5% CDS Swap • • Receive 2% of NP Pay 2.5% Pay 0.5% per year • Pay Default Protection • Receive Default Protection SV SV   t 4   1 ( Current Spread  Exisitng ( 1  R ) t t 4   1  0 .

005 ($ 100 ) ( 1 .

06 ) t   $ 1 .

73 Spread )( NP ) 86

The Value of an Off-Market CDS Swap



Example

For the insurance company, the increase in the credit spread has decreased the value of their seller’s position on the CDS swap by $1.73.  That is, for the increase in credit risk, the seller should be receiving $8.66 instead of $6.93.

The Value of an Off-Market CDS Swap

 Alternatively stated, the poorer economic conditions reflected in the greater credit spreads have increased the probability of default on the BBB bonds and as a result has increased the present value of the seller’s expected payoff. 88

The Value of an Off-Market CDS Swap

 With the credit spread increasing from 2% to 2.5%, the implied conditional default rate on the bond has increased from .02857 to .035714, increasing the present value of the seller’s expected payout from $6.9302 to $8.66: Exisitng p  ( 1  Z RR )  .

02 ( 1  .

30 )  .

02857 Current : p  Z ( 1  RR )  .

025 ( 1  .

30 )  .

035714 PV ( Expected Exisitng Current Payout )  t M   1 p NP ( 1  RR ) ( 1  R ) t : PV ( Expected : PV ( Expected Payout )  Payout )  t 4   1 (.

02857 ) ($ 100 )( 1  .

30 ) ( 1 .

05 ) t t 4   1 (.

035714 ) ($ 100 )( 1  .

30 ) ( 1 .

05 ) t  $ 6 .

93  $ 8 .

66 89

The Value of an Off-Market CDS Swap



Summary:

To summarize, an increase in the credit spread will increase the value of the buyer’s position on an existing CDS and decrease the seller’s position.  Just the opposite occurs if economic conditions improve and credit spreads decrease.

Other Credit Derivatives

 The market for CDS has grown dramatically over the last decade. With that growth there has been an increase in the creation of other credit derivatives.  The most noteworthy of these other credit derivative are the 1.

Binary swap Credit swap basket 3.

CDS forward contracts CDS option contracts Contingent swaps 92

Binary CDS

 A

binary CDS

is identical to the generic CDS except that the payoff in the case of a default is a specified dollar amount.  Often the fixed payoff is the principal on the underlying credit. When this is the case, then the only difference between the generic and binary swap is that the generic CDS adjust the payoff by subtracting the recovery value whereas the binary CDS does not. 93

Credit Swap Basket

 In a

basket credit default swap

, there is a group of reference entities or credits instead of one and there is usually a specified payoff whenever one of the reference entities defaults.  Typically, after the relevant entry defaults, the swap is terminated.

Credit Swap Basket

 Basket CDS can vary by the type of agreement  governing the swap:

Add-up basket CDS

provides a payout when any reference credit in the basket defaults 

First-to-default CDS

provides a payout only when the first entry defaults 

Second-to-default CDS

provides a payout when the second default occurs 

Nth-to-default CDS

provides a payout when the nth credit entry defaults. 95

CDS Forward Contract

 A

CDS forward contract

is a contract to take a buyer’s position or a seller’s position on a particular CDS at a specified spread at some future date.  CDS forward contract provide a tool for locking in the credit spread on future credit position. 96

CDS Option Contract

 A

CDS option

is an option to buy or sell a particular CDS at specified swap rate at a specified future time. 

Example:

A one-year option to buy a 5-year CDS  on GE for 300 bp. At expiration, the holder of this option would exercise her right to take the buyer’s position at 300 bp if current 5-year CDSs on GM were greater than 300bp.

 In contrast, she would allow the option to expire and take the current CDS on GE if it is offered at 300 BP or less. 97

CAT Bond

 Somewhat related to credit risk is the catastrophic (CAT) risk that insurance companies face in providing protection against hurricanes, earthquakes, and other natural disasters.  Insurance companies often hedge CAT risk through reinsurance.

 Note: One CAT hedging product that insurance companies are increasingly using is the issuance of CAT bonds. 98

CAT Bond

 CAT bonds pay the buyer a higher-than-normal interest rate. In return for the additional interest, CAT bondholders agrees to provide protection for losses from a specified event up to a specified amount or when the losses exceed a specified amount.

CAT Bond



Example:

An insurance company could issue a CAT bond with a principal of $200 million against a hurricane cost exceeding $300 million.  The CAT bondholders would then lose some or all of their principal if the event occurs and the cost exceeds $300 million.

100