An investor with a long or short position in an existing credit-default swap can monetise a change in the default swap premium, and realize profit and loss, in three ways:
* Agreeing an unwind payment with the original default swap counterparty in termination of the transaction.
The investor receives or pays the current mark-to-market value of the existing default swap from or to the current default swap counterparty. One of the benefits of 'tearing up' an existing trade is that all future cashflow streams are cancelled and ongoing legal risk (i.e. possible disputes over deliverable obligations) is removed. This method also has potentially advantageous capital treatment.
* Assignment to another counterparty. A less common method for unwinding credit-default swaps is to assign the existing swap to a third party and receive or pay the current mark-to-market value from or to the third party. This depends on there being an attractive market price for the existing default swap (made more unlikely if the existing swap has an irregular amount of time outstanding). It will also be subject to the protection buyer agreeing to take on the counterparty risk of the protection seller. Again this may reduce legal or capital risk for the investor who has closed their position.
* Entering into an offsetting transaction. The final alternative is to enter into an offsetting long or short protection position with another counterparty. Offsetting transactions are not as popular with end investors as they require the signing of further documentation and added legal risk. Nonetheless, unwinding with another counterparty may be the most desirable option for holders of illiquid positions where better unwind terms may be available away from the original counterparty.
Offsetting transactions are used extensively by dealers when unwinding positions for themselves and clients. This is because dealers will need to replace terminated default swaps to remain hedged. For this reason, valuing offsetting transactions is essential to the understanding of swap unwind pricing methodology. Unwind payments will therefore reflect the risk that the dealer assumes in having to source an additional default swap to remain hedged.
Conceptualizing Default Swap Mark-To-Market Values
Intuitively, the mark-to-market value of a default swap should equate to the cost of entering into an offsetting transaction. For an investor who has sold protection, the offsetting trade constitutes buying protection on the same reference entity, and with essentially the same terms as the original trade. The main variations in the contracts will be a) pricing, reflecting market movements and b) contract term, so that the new contract expires on the same date as the existing contract.
Conceptualizing the mark-to-market value requires an analysis of the resultant flows that would arise if the two offsetting transactions were put in place. For simplicity, if we assume that the payment dates of the two trades perfectly match, then the investor is effectively long, or short, an annuity payment (the aggregate of the premiums) until the maturity of the original default swap. The mark-to-market is then derived by discounting the annuity.
Chart 1 shows how the mark-to-market value can be thought of for an investor who has sold five year protection at 150bps and wishes to mark-to-market the position after one year. In this case, we assume the current market premium to buy four year protection on the same reference entity is 100bps. Thinking in terms of two offsetting trades, the investor can be considered long a four year 50bps annuity. Discounting this annuity would then give the investor the mark-to-market value of his original default swap position.
The above methodology is incomplete, as the annuity stream is not risk free. Credit events during the remaining life of the parallel contracts would put an end to both sets of payments. Following a credit event, both legs of the long and short protection positions would net out and terminate, leaving the investor flat. Since the annuity may cease prior to its maturity, the carry earned by the investor may fall short of the expected carry. The following chart shows the case where a credit event terminates the annuity prior to its maturity.
Survival Probabilities As Weighting Factors
To factor this risk into the value of the annuity, each cash flow in the annuity stream must be weighted by the probability of there being no credit event before that cash flow date. We term these weighting factors the survival probabilities of the credit-default swap. The expected value of the annuity, and hence our mark-to-market on the existing default swap position can now be defined as:
MTM = ...[Annuity ($) * Survival Probability
* Risk-Free Discount Factor]
summed over each cash flow in the annuity. The risk-free discount factors can be derived from current market swap rates.
The introduction of survival probabilities (between 0 and 1) has the effect of reducing the absolute mark-to-market value. This will mean a smaller gain from the unwind of a profitable default swap position but also a smaller loss from the unwind of an unprofitable default swap position. The survival probabilities of credit-default swaps are clearly not known but can be calculated from a model of default and recovery. The normal approach is to calculate them from market data, particularly credit risk premiums and also an assumption about the recovery rate of deliverable obligations in the default swap contract.
Determining Recovery Rates
We define the recovery rate of a defaultable obligation as the percentage of par claim of the obligation recovered by investors following default. Recovery rates depend not only on the actual recovery rate post default but also the time taken for the recovery rate to be realized. The recovery at the date of default involves discounting the recovery rate on the day it is recovered to the date of default.
Empirical studies by rating agencies have looked at recovery rates of defaulted bond issuers over time.
| Recovery Rates And Their Dispersion For U.S. Corporate Issues, 1988-2001 | ||
| Class of Debt | Recovery | Standard |
| Rate (%) | Deviation (%) | |
| Bank Debt | 84.9 | 26.1 |
| Senior Secured Bond | 69.3 | 31.1 |
| Senior Unsecured Bond | 52.8 | 35.4 |
| Senior Subordinated | 36.1 | 32.6 |
| Subordinated | 32.2 | 35.3 |
| Junior Subordinated | 19.2 | 30.2 |
| Source: Standard & Poor's |
The recovery rate is a function of the seniority of the obligation.
The data exhibits a considerable amount of dispersion around the mean for each class of debt.
The overall recovery rate distribution is asymmetrical and skewed with a long right tail and does not appear to be a normal distribution.
One would also expect average recovery values to change over time (e.g. in relation to movements in the average default rate). For instance, it is reasonable to expect current recovery rates to be lower than the long-run average, given the present state of the world's economy.
This week's Learning Curve was written by Barnaby Martin (left) and Chris Francisin credit derivatives research at Merrill Lynchin London.
