Financial Engineering – IC302
Autumn Term 2020/1
Seminar 4: Credit Derivatives Answers
1. Use the credit default swap confirmation at the end of this exercise to answer the following questions.
(a) Which institution is buying credit protection and which is selling protection?
Barclays Bank plc is selling protection, Deutsche Bank AG is buying protection
(b) Which entity’s credit risk is being transferred?
Sandridge Energy Inc
(c) Suppose that on the trade date the par spread for the reference entity is 90 basis points. Given that the CDS has a fixed coupon of 100 bp, which counterparty would be required to make an upfront payment?
The protection seller receives 100 basis points per annum while the par spread is 10 basis points lower. The par spread is set at a level that ensures that the transaction is an equitable exchange of cash flows; transacting at 100 basis points makes this deal off market. As a result, the protection seller (Barclays) should make an upfront payment to the protection buyer (Deutsche).
(d) According to the confirmation, which of the following constitutes a credit event?
Bankruptcy
Obligation Acceleration / default Failure to pay
Repudiation / moratorium Restructuring
Bankruptcy and failure to pay are credit events in this CDS.
(e) Suppose a credit event is declared and as a result of the auction the deliverable obligations are valued at 38.00. How much would the protection buyer receive on this transaction?
Since the notional amount was $10,000,000 the protection buyer should receive $10m x (1 – 0.38) = $6,200,000 .
2. The calculations required by the questions in this exercise may be performed using the Excel workbook CDS-Simplified Pricing.
In the course notes, we described the pricing and revaluation of a five-year CDS under the following assumptions:
• Annual premium payments
• Fixed coupon 100 basis points per year
• Recovery rate 40%
• Risk-free interest rate 1% per year
• Conditional default probability 0.016393 per year
We showed that, under these assumptions, the risky PV01 of the CDS would be approximately 4.621. The intermediate values leading to this result are shown below:
(a) Suppose that we were to repeat the risky PV01 calculation performed above for a 5-year CDS on a reference entity with constant conditional default probability of 2% per year. Other things remaining equal, what effect will this increase in the conditional default probability have on the risky PV01? What explanation can you offer for this result?
Increasing the conditional default probability to 2% per year but leaving the other parameters in the example unchanged will reduce the risky PV01 to about 4.572, as shown below:
The conditional default probability in the example was about 1.64% per year. A higher conditional default probability of 2% per year would make the survival probabilities to each future date slightly smaller. This in turn will reduce the risky PV01.
(b) The constant conditional default probability of 1.6393% per year in our original example was consistent with a par spread of 100 bp per year and resulted in a risky PV01 of approximately 4.621. Suppose instead that the par spread on the reference entity were 75 bp per year. Will this result in a risky PV01 greater than, less than, or equal to 4.621? What explanation can you offer for this result?
[Hint: You can calculate the risky PV01 that is consistent with a breakeven spread of 75 bp per year by using Goal Seek in Excel to set the spread (cell K12) equal to 75 by choosing an appropriate value for the conditional default probability (cell B6).]
A lower spread would be associated with lower conditional default probability and higher survival probabilities; this should result in a higher risky PV01.
Leaving the other parameters in the example unchanged, a par spread of 76 bp per year is associated with a risky PV01 of about 4.678. Other things remaining equal, a lower spread will result in a higher risky PV01, because it increases the survival probabilities to each future date. The intermediate values leading to this result are shown below:
(c) With a par spread of 75 bp and a fixed coupon of 100 bp as in part (b) of the question, the CDS will require an upfront payment in order to be fairly valued. How large is this payment and which party will make it? What explanation can you offer for this result?
According to the spreadsheet model, the protection seller must make an upfront payment of $116,944 to the protection buyer, as shown in the screen capture in part (c). With a fixed coupon of 100 bp and a par spread of 75 bp, the buyer is overpaying for protection by 25 bp per year. The upfront payment is the risky present value of this amount.
3. Suppose that you sell protection on a 4-6% tranche of a 100-name equally weighted CDS index.
(a) If the recovery rate on each entity is 50%, what is the maximum number of defaults that can occur before you suffer any losses?
Each entity in the index makes up one percent of the portfolio notional. With a recovery rate of 50%, each default will wipe out 0.5% of the portfolio. You will therefore suffer no loss from the first eight defaults, since 8 x 0.5% = 4%. At this point, the total losses will have reached the attachment point of your tranche.
(b) For the same parameters as in the previous question, how many defaults will it take to exhaust your tranche (i.e. for you to suffer a complete loss)?
We saw in the answer to part (a) that, with a recovery rate of 50%, the attachment point of your tranche will be reached after 8 defaults. Each subsequent default will wipe out 0.5% of the portfolio, which is 25% of your tranche (since the width of your tranche is 2%). Your tranche will be exhausted after 12 defaults.
(c) Suppose that we create a 4-5% tranche on the portfolio described in the previous questions. How would you expect the spread on this tranche to compare with the spread on the 4-6% tranche described earlier?
The 4-5% tranche will trade at a higher spread than the 4-6% tranche. Both tranches have the same attachment point or subordination, but the 4-5% tranche would be exhausted after only ten defaults. It should therefore trade at a higher spread than the 4-6% tranche.
(d) Suppose that we wanted to create a tranche with 1% width that had similar credit risk (in terms of expected losses) to the 4-6% tranche described earlier in this question. Would this tranche need to have attachment point higher or lower than 4%? Explain your answer.
Higher than 4%. To have the same credit exposure (in terms of expected losses) as the wider 4-6% tranche, the new tranche will need a higher attachment point. This will give it a larger initial cushion against credit losses than the 4-6% tranche.
Credit Default Swap Confirmation
The purpose of this agreement is to confirm the conditions of the credit derivative transaction entered into between Barclays Bank plc (“Party A”) and Deutsche Bank AG (“Party B”) on the trade date specified below.
The terms of the transaction to which this confirmation relates are as follows:
General Terms
Trade date
Effective date
Scheduled Termination date Floating rate payer
Fixed rate payer
Calculation agent Calculation agent City Business Days
Business day convention
Reference Entity Reference Obligation Maturity
Original issue amount Reference price
Fixed payments
Fixed rate payer calculation amount Fixed rate payer payment dates
Par spread
Fixed coupon
Fixed rate day count fraction Initial upfront adjustment
Floating Payment
Floating rate payer calculation amount
Friday 18th September 2018 Monday 21st September 2018 Sunday 20th December 2023 Barclays Bank plc (the “seller”) Deutsche Bank AG (“the “buyer”) Seller
London
London and New York and solely for the purposes of physical settlement, if applicable a day in any other jurisdiction in which banks must be open in order to effect the settlement of any deliverable obligation being delivered in the portfolio.
Following
Sandridge Energy Inc 5.00% senior note 1st October 2025 $650,000,000
100%
$ 10,000,000
20th December 2018 and then June 20 and December in each year thereafter. 90 bps
100 basis points p.a.
Actual / 360
$42,060
$10,000,000 minus auction recovery amount
Credit events
The following credit events shall apply to this transaction:
1. Bankruptcy
2. Failure to pay
Grace period extension: Payment requirement:
Obligations
Obligation category Obligation characteristics Excluded obligations
Settlement terms
Settlement method
Deliverable Obligations
Deliverable Obligation Category Deliverable obligation characteristics
Not applicable
USD1, 000,000 or its equivalent in the relevant obligation currency as of the occurrence of the relevant failure to pay
Borrowed money None
None
Auction with option to physically settle Exclude accrued interest
Bond or Loan
Bond or loan
Not subordinated
Specified currency: standard specified currencies
Transferable
Assignable loan
Consent required loan
Not contingent
Maximum maturity of 30 years
Not bearer
None
Excluded deliverable obligations