Digital Default Swap Example for Free

Digital Default Swap (DDS) and Credit Recovery Swaps (CRS) belong to the family of credit derivatives and are advanced cousins of the plain vanilla Credit Default Swap (CDS). 1-DIGITAL DEFAULT SWAP (DDS):

1.1) Nature:

A Digital CDS, also called a Digital Default Swap (DDS), is a simplified version of a regular CDS. DDS is simply a CDS with fixed rate of recovery. Recovery rates on regular CDS depend on where the deliverable obligations trade following a Credit Event. But DDS has a predetermined recovery rate (and hence payout) in case of a Credit Event occurring. The recovery rate in a DDS can be fixed at any level. So Digital default swaps (DDS) differ from the plain-vanilla CDS by contractually pre-defining the value of the protection payment to be made in case of default. The protection payment is determined by the "contractual recovery" rate, which is set to a level at the outset of the contract. If it was set at zero, then a protection buyer would get a payment equal to the full notional in case of default. If it was set at 50%, then the protection buyer would get a payment equal to half of the notional. In this note we assume that the DDS is set at 0% recovery unless otherwise stated. A 0% DDS should fundamentally always trade at a higher spread than a regular CDS, except in the extreme case where the expected recovery rate on the company is 0% (leading to identical expected payoffs for the CDS and the DDS in case of default). Intuitively this makes sense as the expected loss on a DDS is relatively higher. It is important to note that the default probability on a CDS and DDS contract is identical, and that the increased expected loss on a DDS is due entirely to different payouts following a Credit Event. This can be explained by the following example. Suppose a long protection position in a CDS is trading with an expected recovery rate of 40% compared to a long protection DDS position. In case the reference entity experiences a Credit Event and the recovery rate turns out to be 40% the buyer of CDS protection will make (1-R) = (1-40%) = 60% of the notional, whereas the buyer of DDS protection will make (1-R) = (1-0%) = 100% (and vice versa for sellers of protection in CDS /DDS). So clearly the expected loss in case of a DDS is higher and hence merits a spread higher than the regular CDS.

1.2) Structure:

The following example would be used to explain the structure of a DDS and how it differs from a CDS. By comparing positions and expected payouts in DDS and CDS we can establish some simple, but essential, relationships between CDS, DDS, and implied recovery rates. Consider the following positions:

a) Long CDS protection

- Notional: $ 20m - Fees: 50bp - Payout following Credit Event: $20m x (1-R) (Here R is the recovery rate)

b) Long DDS protection

- Notional: $10m - Fees: 100bp - Payout following Credit Event: $10m The market must expect equal payoffs following a Credit Event as the annual dollar amounts of the fee legs are identical on both positions ($100,000). $20m x (1-R implied) = $10m =>R implied = 50% In a similar way, we can deduce some more generic relationships. Again, consider the following positions:

c) Long CDS protection

- Notional = 1 - Fee leg = SCDS - Payout following Credit Event = 1-R

d) Long DDS protection

- Notional = SCDS / SDDS - Fee leg = SDDS x SCDS / SDDS = SCDS - Payout following Credit Event = SCDS / SDDS As before, the fee leg in position (c) and (d) are identical - hence: (1): (1-Rimplied) = SCDS / SDDS (2): Rimplied = 1- SCDS / SDDS The above relationship is extremely useful in that it tells us that we can deduce the market implied recovery rate from CDS and DDS spreads. If for example CDS and DDS spreads on company ABC are 100bp and 200bp respectively, the market implied recovery rate on company ABC is: Rimplied = 1- (100 / 200) = 50% So by looking at the spreads of CDS and DDS trading on the market we can calculate the recovery rate implied by the market in CDS.

1.3) Application of DDS:

DDS and Capital Efficiency

In a regular CDS, Financial Institutions are required by Regulatory Authorities to allocate capital based on how large the potential loss is on their positions. This means that for an instrument where the typical recovery rate is around 40%, a FI would still face 100% capital charge as this is the maximum potential loss on the position. The maximum potential loss on a 0% DDS is likewise 100% and the FI could therefore, for the same capital requirement, increase its credit exposure by roughly 67% using DDS. It is important to note that the two positions have the same default probability, and that the additional exposure entirely is due to the fixed 0% recovery rate. So the current capital allocation requirements on CDS make DDS an instrument of choice for FIs. DDS gives them a capital efficient way of extending their exposure to credit risk.

Credit Hedging Applications

As the pay out on a DDS is independent of the actual recovery rate, DDS do not serve as a good hedge for bonds and loans carrying both credit and recovery risk. CDS is the preferred instruments for hedging those risks. There are, however, other types of credit exposure, such as credit contingent profits and losses, which are independent from recovery rates. This could, for example, be credit exposure with a different level of seniority from the traditional Senior Unsecured level which CDS are normally traded on. Under such types of credit exposure the bank would probably prefer to have a fixed pay off following a Credit Event rather than having the additional exposure to recovery rates. A specific example of bank credit exposure independent of recovery rates is that of off-setting CDS positions. Imagine a bank buys CDS protection at 100bp and, following credit spread widening, sells CDS protection at 200bp in equal notional sizes. This position has a mark-to-market gain in the form of a risky stream of future cash flows - if the Reference Entity experiences a Credit Event, both CDS are triggered, resulting in zero profit on the position irrespective of the recovery rate. This is a pure credit contingent loss and could be hedged by buying DDS protection with a notional equivalent to the mark-to-market on the position (for the hedge to work perfectly, the notional would have to be changed as CDS spreads change, as rates change, and as the maturity on the CDS decreases).

Benefits for Corporate:

One of the main uses of DDS was the risk management of corporate accounts receivables, operational risks and other such exposures whose value is not naturally tied to the price of the underlying issuer's bonds or traded loans. Unlike asset managers or banks who need to hedge the losses on a corporate bond or loan portfolios and thus find the conventional floating rate CDS the most natural proxy, the corporate treasurers who need to hedge the specific dollar exposure to a trading counterparty have found the DDS to be better suited (even though often not liquid enough due to a niche nature of that market). Corporate can also benefit from the use of DDS. Consider a corporate with accounts receivables of $10m from company ABC. Accounts receivables stand differently in the creditor ranking from senior unsecured debt and may or may not be linked to senior unsecured recovery rates should company ABC default. Irrespective of this, the corporate in question may prefer a credit contingent fixed payout through a DDS rather than additional recovery rate exposure in the CDS instrument. The hedge ratio applied should naturally be adjusted to reflect the expected recovery rate on the accounts receivables. For instance, if the corporate expects to get 20% of accounts receivable back following default, it should use an 80% hedge ratio - in other words buy $8m of DDS protection on $10m accounts receivables. Many of the uses of DDS described above naturally work better on single name DDS rather than on DDS based index products such as DDS DJ TRAC-X Europe and DJ CDX.NA.IG. As we have seen on, for example, DJ TRAC-X Europe 10Y and HY, index trading can significantly increase the trading volume in the underlying single name CDS. As volumes on DDS-based indices and Recovery Swaps increase, we would likewise expect improved liquidity in the underlying single name DDS as well.

2-CREDIT RECOVERY SWAP (CRS):

2.1) Nature:

CRS is simply a plain vanilla CDS bundled with a DDS, allowing investors to isolate views on recovery rates. The instruments can be used to take views on recovery rates, hedge recovery rate independent credit exposure, and to make capital efficient investments.

2.2) Structure:

Since both CDS and DDS instruments trade in the market it is possible to create a synthetic instrument by packaging both for pure recovery rate trades. These instruments are referred to as Recovery Swaps. The payout happens only in case of a Credit Event. The Recovery Swap is based on a regular CDS and a DDS having a fixed recovery rate equal to the traded recovery rate. Recovery Swap is priced at par and has a carry of zero bp. The synthetic position is created by going long on the CDS and shorts on the DDS and the premium of both cancel each other out. So a CRS is priced at par and has zero carry. Currently CRS doesn't trade in the market as one instrument. Investors willing to take bet on Recovery Rate have to create synthetic position as explained above. But if the market for CRS deepens then we can expect standardised CRS products to come in the market where investor can directly bet on recovery rate. In case there is a Credit Event during the life of the Recovery Swap, the investor short recovery rates will make money on the trade if he is able to buy defaulted debt at a lower price than the recovery rate implied by the market at the time of trading. If, for example, the market implied recovery rate on the trade date is 50%, the company in question experiences a Credit Event and the investor buys bonds in the market at 40% of par, the investor can deliver these bonds into the contract, receive 50% of notional traded, and net make 10% times notional on the trade. Clarification on Recovery Rate- Recovery rates in the context of Recovery Swaps implies the cheapest to deliverable (CTD) type of debt the investor can get in the market following the Credit Event to meet the obligation. This is different from the long term recovery rates which in general mean the value of debt instruments after a company has finished its restructuring post bankruptcy under chapter 11.

EXAMPLE-

The following example would be used to explain the structure of the instrument. The market implied recovery rate can be determined from the relationship between CDS and DDS spreads .Since data on the trades of both the instruments are available investor can take a view on the recovery rate if they think that the implied recovery rate is either too high or low. Let's consider the following case- 1) CDS credit derivative of under lying trading at 100bp 2) DDS credit derivative of underlying trading at 200bp Using the data we get a market implied recovery rate of: R-implied = 1- SCDS / SDDS = 1- 100/200 = 50% Let's assume the investor is of the view that the implied recovery rate in the market is relatively too high at 50% - which is tantamount to say that DDS spreads are too high as compared with the CDS spreads. To bet on this view the Investor (might be a speculator as well) requires selling protection on the DDS index at 200bp and buying protection on the CDS index at 100bp. For the carry on the trade to be zero i.e. to purely bet on the recovery rate, the notional amounts of both the leg should be same and cancel each other out. In this case, the investor needs to buy 2 units of CDS protection for every 1 unit of DDS protection sold. The combination of the above two legs is for all practical purposes equivalent to trading a Recovery Swap. The investor ends up entering in to a carry neutral trade and takes a bet on recovery rate. Let's consider the following scenarios and calculate the P/L of the position in each of the alternate scenarios.

Scenario 1- CDS spreads remain unchanged while DDS spreads tighten-

Let's say the DDS spread becomes 150 bp. The new implied recovery rate decreases to 33.3% (1-100/150). Since the initial bet was that DDS spread was too high the trade results in net gain of (50-33.3) *Notional amount.

Scenario 2- CDS spreads remain unchanged while DDS spreads further widen-

Let's say the DDS spread becomes 250 bp. The new implied recovery rate increases to 60% (1-100/250). Since the initial bet was that DDS spread was too high the trade results in net loss of (50-60) *Notional amount.

Scenario 3- CDS and DDS spreads both further widen out -

Let's say the DDS spread becomes 400 bp and the CDS spread becomes 200 bp. The new implied recovery rate remains same at 50% (1-200/400). As the implied recovery rate hasn't changed since the trade was entered in to the position expires without profit and loss. When the realised recovery rate turns out to be exactly equal to the implied recovery rate of 50% the loss on the DDS position is off-set by the gain on the CDS position resulting in a net zero P/L. The trader makes money in the scenarios when realised recovery rates are lower than the implied 50% recovery rate, which was the view at the out- set. The Underlying- The underlying instrument here can either be individual securities or a index of credit derivatives. The index credit derivatives are more liquid but are also exposed to the risk of multiple underlying and also result in high notional exposure.

2.3) Application of CRS-

Synthetic CDO investors and other structured credit market participants are the main users of CRS. They use it as a hedging instrument. The pricing and risk management of these more complex securities depends separately on the default event risk and recovery risk. But the value of plain vanilla CDS contract is driven by the combination of default risk as well as recovery risk (together called - the default loss risk). Since the Synthetic CDO investor needs to isolate the above two risk from each other they use CRS to hedge the recovery rate risk. The other side of the market is formed by speculators. Let's consider the following example to understand why a CRS can help a synthetic CDO investor. Models used to price the Synthetic CDO tranches have to assess the joint risk-neutral default probability between various underlying names in a tranche. The joint default probability is a function of individual default probabilities of each underlying and their correlation. The individual implied default probabilities are calculated by calibrating against the observed single name CDS spreads, otherwise there would be arbitrage opportunity in the market. This calibration results in a strong dependence between the assumed recovery rate and the implied default probability. The following formulae better explains the relationship. CDS Spread= Default loss risk= Default Probability (1- Recovery) So to calibrate the implied default probability to a observed CDS spread one has to assume a recovery rate. This creates an implied dependence on the recovery rate. The implied default probability calculated from the assumed recovery rate and single name CDS spread is fed in to the model along with the assumed correlation to price the CDS tranche. This explains how implicitly the pricing of the tranche is dependent upon the recovery rate. There is an explicit dependence on the recovery rate as well. As the same recovery value will be applied to calculate the loss distribution on the tranche. So, the expected value of the tranche values and standard deviation (measure of risk) depend both explicitly, and implicitly (through calibration), on the recovery rate assumptions.

3-CONCLUSION

With the advent of the recovery swaps the toolkit for separate hedging of credit risks is becoming more complete: Default loss risk (i.e. full credit risk with mark-to-market exposure): hedged by conventional (floating recovery) CDS Default event risk: hedged by digital default swaps, i.e. DDS Recovery rate risk: hedged by recovery swaps Credit risk without mark-to-market exposure: hedged by constant maturity default swaps (CMDS) Spread volatility risk: hedged by (short-term) credit default swaptions The conventional CDS still remains the linchpin of the credit derivatives market and continues to account for the majority of all traded notional, according to the most recent survey by the British Bankers Association. But the existence of the expanded toolkit also implies certain connections and (partial) substitution ability between various credit derivatives instruments. The market for DDS and CRS is not liquid as yet. When the market becomes more liquid for these instruments the arbitrage opportunities between the CDS and DDS and CRS market would start to disappear and true measure of implied volatility can be established across the three segments.

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