Lecture 9 - Credit Derivatives - CDS(1)

Credit Derivatives - CDS

Rohit Sonika

Credit Derivatives

• Last we looked at corporate bonds, bringing the concept of credit risk into our debt market

• We saw that the credit risk was linked to the borrower’s ability to pay

• This will impact on the value of the security as we saw in our discussion of credit spreads

• Credit derivatives were created as a tool to allow us to manage this risk

• Today they are such an integral part of the market that in many cases they are more liquid than the corporate bonds they were intended to protect

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Credit Default Swaps

• Credit default swaps (CDS) are the most popular credit derivative

• Intended originally to protect against default they are now so actively traded changes in their value will protect against movements in a bond’s credit spread

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CDS Structure

• The CDS is a bilateral contract• The buyer is buying credit protection, the seller selling this• Unlike most swaps the structure involves an uneven pattern of

cashflows: the buyer makes periodic payments of a CDS premium, the seller pays nothing except in the event of a credit event

• Strictly speaking this is not quite true as CDS trades will typically need to be collateralised but this is a matter of trading practice and counterparty risk reduction rather than anything inherent in the structure

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CDS Structure

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Wal-mart CDS Spreads

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CDS Prices

• This price that we have seen on the screen is an annual value to be paid against the notional amount on the trade

• The payment is typically paid quarterly in arrears with, these days, these payments tending to be standardized around the IMM dates of March, June, September and December

• The swap is against a specific reference entity and relates directly to a nominated reference debt security

• This is used to judge whether the credit has experienced a credit event

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Credit Events

• Bankruptcy of the reference entity • Credit event upon merger• Failure to Pay (failure by the reference name to meet its payment

obligations when due)• Obligation Default • Obligation Acceleration – a debt obligation whose repayment has

become due earlier than on its scheduled maturity. Typically this is the result of an event of default on another of the issuer's obligations, which triggers a cross-default clause on the obligation in question

• Repudiation or Moratorium (for sovereign entities) • Restructuring of the issuer's debt with materially adverse consequences

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Settlement

• A credit event will trigger a settlement of the swap

• This settlement can take place in one of three forms:– Physical settlement– Cash settlement– Binary settlement

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Physical Settlement• This is how CDS were originally settled but today has been

superseded by cash settlement• In this case the buyer delivers the a nominal amount of bonds

equivalent to the notional value of the swap• The bonds to be delivered must be deliverable obligations of the

issuer, essentially the reference obligation• If not, look to create a pool of comparable issues, of comparable

seniority and preferably ranking pari passu• This was to ensure consistency of recovery rates• Against this delivery of bonds the swap seller would pay a contract

rate, typically 100• The seller then would be the one to receive the recovery value in the

event of default of the security but this payment would be received after termination of the swap

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Cash Settlement

• In this settlement procedure securities do not change hands, instead the buyer and seller exchange values

• They reference a Final Price for the Reference Obligation determined by an auction process

• The protection buyer receives a cash payment proportional to the loss severity on the reference asset (i.e. Reference Price - Recovery Value).

• Not surprisingly settlement typically does not include any unpaid accrued interest on the bond

• Then the termination payment in a cash-settled CDS is set as : Termination Payment = Notional Amount x (Reference Price – Recovery Value)

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Binary Settlement

• Some CDS contracts will have a pre-defined fixed settlement amount

• This gives the seller a level of certainty over their exposure as opposed to the uncertainty of values through the auction process

• Binary Settlement Amount = Par (100) – Pre-agreed Price

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CDS and Asset Swaps

INVESTOR

5%

FUNDING

SWAP

BOND

4.2%

$100 $100

LIBOR

LIBOR

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CDS Pricing• In the last lecture on corporate bonds we looked at a price screen for

Wal-mart bonds and discussed the Asset Swap Spread • We saw that this was the value achieved if the returns on the bond

were swapped in the IRS market• A corporate bond consists of interest rate and credit risk• If we swap the flows on a fixed rate bond into floating we remove the

interest rate risk so therefore any excess return must be the value of the credit risk of the bond

• It is this credit risk that is being bought and sold in a CDS deal and so therefore we can see that the relationship between these should be:

• CDS Premium = Par Asset Swap Spread

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CDS and Asset Swaps• In this scenario the interest rate risk is negated and the investor can achieve

the same net result by selling a CDS at a price of 80bp• This will give an identical exposure• This shows us a couple of relationships:

• Yield on asset swap = LIBOR + (Bond yield - swap rate) = L + (Y - S)

• And therefore:• CDS Premium = Yield on asset swap - Cost of funding it

= L + (Y - S) - R = (L - R) + (Y - S)

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Real Pricing

• Whilst this theory is true in practice the market rates will deviate from theoretical for a number of fundamental reasons:

– Repo cost of funding the ASW < LIBOR – Dirty Price of reference asset > 100 – Protection buyer must pay accrued premium up to the date of default – ASW spread may be negative but CDS premium >= 0– The buyer of protection on a CDS typically owns a delivery option – The protection seller in a CDS has less counterparty risk than the investor

in an ASW– Profit on ASW position may be realised with more certainty than on

equivalent CDS position

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More Exact CDS Pricing

• Another way of valuing the CDS is to consider the expected cashflows on the deal

• This is a 4 step process:1. Write down the expected premium payments contingent on the probability of

survival to each payment date2. Write down the expected payoff at future dates given the probability of default

conditional on survival until that date3. Write down the expected accrued premium due on default 4. Solve for the premium such that PV(expected payment) = PV(expected

payoff)

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Arbitrage-free Pricing

• Valuation of the fee leg:

• In case of any accruals:

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Arbitrage-free Pricing

• Valuation of the contingent claim leg:

• Now, we just equate the two:

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More Exact CDS Pricing – Step 1

• Let us assume a flat yield curve at 5% and a probability of default of 3.33

• We take the probability of survival each year, multiply by the unknown spread, s, and find the present value using the risk-free rate of interest, 5%

• This gives us an expected premium payment:

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Prob Expected DiscountSurvival Payment Factor

1 0.9667 0.9667s 0.9512 0.9196s2 0.9345 0.9345s 0.9048 0.8456s3 0.9034 0.9034s 0.8607 0.7776s4 0.8733 0.8733s 0.8187 0.7150s5 0.8442 0,8442s 0.7788 0.6575s

Total 3.9152s

Time PV

• Next we calculate the expected payoff given • Conventionally we assume default may occur halfway through the period and so

the time column becomes:

• The probability of default is contingent on survival until then and so 3.33% for year 1, then for year 2 becomes (1-0.033) * 0.033 = 3.22%, and so on, and so we find:


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0.51.52.53.54.5

Time

Prob

0.5 0.03331.5 0.03222.5 0.03113.5 0.03014.5 0.0291

Time


• From here we continue to apply this probability of default to a Recovery rate of 40%:

• And we present value usingour rate of 5%

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Prob ExpectedPayoff

0.5 0.0333 0.4 0.02001.5 0.0322 0.4 0.01932.5 0.0311 0.4 0.01873.5 0.0301 0.4 0.01804.5 0.0291 0.4 0.0174

RecoveryTime

Prob Expected DiscountDefault Payoff Factor

0.5 0.0333 0.4 0.02 0.9753 0.01951.5 0.0322 0.4 0.0193 0.9277 0.01792.5 0.0311 0.4 0.0187 0.8825 0.01653.5 0.0301 0.4 0.018 0.8395 0.01524.5 0.0291 0.4 0.0174 0.7985 0.0139

Total 0.083

Time Recovery PV


• Since we assume default occurs halfway through the period we have to assume accrual of the CDS premium

• For each period we are assuming default is at point 0.5 so we multiply this by probability of default and then present value the cashflow;

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Prob Accrual DiscountDefault Payment Factor

0.5 0.0333 0.0167s 0.9753 0.0162s1.5 0.0322 0.0161s 0.9277 0.0149s2.5 0.0311 0.0156s 0.8825 0.0137s3.5 0.0301 0.0150s 0.8395 0.0126s4.5 0.0291 0.0145s 0.7985 0.0116s

Total 0.0691s

Time PV


• Now we know the PV of all expected payments is 3.9152s + 0.0691s = 3.9843s

• Similarly the PV of the expected payoff is 0.0830• Finally we solve for the equation:• PV(expected payment) = PV(expected payoff)• This gives us a CDS spread of 208 bp

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Final Word

• We have seen how corporate bonds include the two risks of credit and interest rate and now we have seen how we can isolate the values of each and from there can create derivatives to enable us to manage this

• Credit derivatives are these tools and we have focussed on the CDS• Our approach to valuation has been very pragmatic, taking into

account these two elements and isolating the values to give us a no-arbitrage fair value

• In the real world these are very actively traded and will move away from this fair value as they start to eclipse trading in cash credit instruments

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Any questions?

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Lecture 9 - Credit Derivatives - CDS(1)