The most important building block of the credit sector is the credit default swap, which was introduced in the first chapter as an example of the swap family. These consist of the negative cash flow(1+Cot0)100that occurs in the timet3default state. In this way we should be able to recover the cash flows from the defaulted bond.
The instrument we have in Figure 16-4b is equivalent to selling protection against the default risk of the bond.
Negative Basis Trades
In such a trade, known as a negative basis trade, the investor has hedged their credit risk but earns more on their bond position than they pay out on their CDS position. During an LBO, the buyer of the company issues large amounts of debt, increasing the debt-to-equity ratio on the balance sheet. Bondholders who hear that a company is becoming an LBO target may sell before the likely LBO; bond prices can fall suddenly and interest rates can rise.
On the other hand, CDS rates may move less since an LBO will not necessarily increase the probability of default.
Measuring Credit Risk of Cash Bonds
Asset Swap
In the asset swap, bond cash flows are discounted based on the corresponding zero-coupon swap rates. A spread (called the asset swap spread) is added to (subtracted from) the cash flows of the bonds, so that the resulting bond price is equal to the market price. By definition, discounts to the zero-coupon swap curve are obtained using the corresponding forward interest rate and the equation.
It is therefore how much one must be paid extra to compensate for the difference between the market price and the theoretical price implied by the default-free exchange curve. This is the case, since if there was no default risk, the value of the bond would be P˜t0, which is greater than the market pricePt0. The˜at0 is a measure that converts this price difference into an additive spread. 11 In an asset swap, the IRS and the mortgage position are written on separate tickets.
The latter is negative if the bond is sold at a discount and positive if the bond is at a premium. Assume that the bond trades at a discount, then a prepayment of upft0plus an IRS entered into at a rate 0+ ˜at0 corresponds to the present value of the bond's coupon payments. In other words, a pair of swap rates must be increased by ˜at0 to compensate for the bond's default risk.
The Z-Spread
Real-World Complications
Restructuring
Any failure to pay interest or principal would count as the former and any type of formal bankruptcy would count as the latter. In this case, the maturity limits for the deliverable bonds or loans are slightly different. 14 The condition here is that in the event of a restructuring event, the maximum term of the bonds delivered may not exceed 30 months after the event, although there are exceptions.
It is clear that CDS contracts with restructuring will have higher CDS spreads than the contracts of the same name, without restructuring. Note the key difference: in a bankruptcy or failure to pay type of credit event, the price differences of deliverable bonds will be relatively small.
A Note on the Arbitrage Equality
CDS Analytics
Default Probability Arithmetic
The DV01’s
With this, we can write the initial value of the CDS at the initial timet0 as follows. First, if within three years the name defaults, the present value of the cash flows denoted by P VN will be D. The expected present value of the accrued premium, denoted by P VAP, if the event of default occurs, will be.
If the default occurs just before the next settlement date, theΔi will be close to theδi.15 Assuming that the expected default time is the middle of the settlement period, this yields. The expected value of the compensation for the cash payouts in case of default is given by. This is obtained by letting ct0N = 1 on the right side of the expression in equation (36).
Risky DV01 is how much the CDS value changes if one increasesct0 by .0001. In general, this will not be equal to A, although it will be close to it depending on the shape of the curve and the change in spread. The reason is the relationship between the defaultpt0 probability derived in the first chapter and the spread CDSct0,17.
Unwinding a CDS
This means that the risky DV01 is a non-linear function of thect0 and that there will be a convexity effect. Most market participants ignore this effect and consider the annuity factor A˜ to be a good approximation of DV01. However, if the CDS spreads move in a volatile environment, the two sensitivity measures will differ.
To determine the present value (PV) of these cash flows, we use risk-adjusted probabilities of default p obtained from the CDS spread at time0. Therefore, we can write down the present value of the coupon payments if no default occurs. Note that we had to use default risky discounts and the corresponding DV01 because the default will change the timing of the cash flows.
Credit Curve Strategies
The example below is a strategy that deals with changes in the curvature of the credit curve. If the synthetic CDO pipeline takes off and focuses on the 7-year maturity, the 5s-7s segment of the iTraxx may be too steep and the 7s-10s too flat.
Structured Credit Products
- Digital CDS
- Credit Options
- Forward Start CDOs
- The CMDS
- Leveraged Super Senior Notes
- EDS versus CDS
The constant distribution default (CMDS) is an important component of the structured credit sector. In essence, this is an extension of the CMS swaps to the case where the underlying risk includes default risk. The CMDS can be used to take exposure to the movements of the credit curve.
With note investors, they take on additional exposure to the market value of the tranche, and the trigger protects the bank from the investor's credit risk. In this sense, a super senior leveraged bond can be said to be a modification of the super senior tranche. For example, the market value trigger could be defined as 70% of the issue amount of $18 million.
If the market value of the note falls below this limit, let's say it becomes 12, then 12 is returned to the investors instead of the original investment of 18. The risk faced by investors lies mainly in the behavior of the market value of the CDS tranche, which depends from spreads and correlations. It is worth adding that the EDS structure is very similar to an out-of-the-money put option written on shares.
Total Return Swaps
Equivalence to Funded Positions
Again, similar to CDS, dealers can and have attempted to construct equity swap CDOs. In both cases, there is a hurdle, which is the strike price in the case of an option, so that the buyer of the option receives a cash payment. The main difference may be the EDS expiration date, which can be much longer.
Argentina, WorldCom and Enron are all interesting names that can be associated with the CDS market due to the sheer size of the respective defaults. One-year Argentine credit default swap mid-level reached 4,000bp late last week, although the highest trade with the sovereign is believed to have been a one-year deal at 2,350bp at the start of the week. Dealers who have sold protection also consulted their lawyers to plan tactics in case Argentina defaults or restructures its debt.
More than US$1 billion of credit protection in Argentina is likely to have been traded in the past few years, which could result in the largest ever default swap payout in the event of a clear default or debt restructuring. There is plenty of room for disagreement over whether or not the terms of the swaps payout have been met, depending on how the Argentine authorities handle a potential debt restructuring. For most of this year, traders used a default basis against asset swaps of around 10% of the total spread for trades in Latin American countries.
Conclusions
Derivatives market makers were cautiously quoting default swap prices at an unusually wide bid/offer spread (Argentina's two-year average rose to around 3,900bp), but mostly focused on balancing market hedges. money, which was not easy. At the end of last week traders were working from Thursday's closing price of Argentina's FRBs of 63.5, which was the equivalent of 3,060bp over Libor, then adding a 30-40%.
Suggested Reading
Except that in this particular case, instead of proceeding with this transaction, the market participant can simply sign a TRS with an appropriate counterparty. For an introduction to some market terminology and new products, the reader can consult Tavakoli (2001) or Das (2000).
Exercises
All nine of the over-hedged CDOs were high-yield bond deals that closed before 1999. With the benefit of hindsight, a balanced collateralized or custom swap would have mitigated the over-hedged CDO's risks. Plain vanilla swaps, which were economically beneficial, ended up costing money in the long run because the assumed balance of the swap was fixed at the closing date of the transaction and did not change over time, the report said.
CDOs tend to use a plain vanilla swap rather than a custom swap because they are cheaper. a) Graph the cash flows generated by a simple CDO. Imagine you have 100 euros to invest in such a position, what would be the costs and expected return. Implied future CDS levels look high as shorter-dated CDS are currently too cheap for a five-year term, BNP Paribas says.
CASE STUDY: Credit-Linked Notes
