Credit default swap

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A credit default swap (CDS) is a swap designed to transfer the credit exposure of fixed income products between parties. It is the most widely used credit derivative. It is an agreement between a protection buyer and a protection seller whereby the buyer pays a periodic fee in return for a contingent payment by the seller upon a credit event (such as a certain default) happening in the reference entity. Most CDS contracts are physically settled, where upon a credit event the protection seller must pay the par amount of the contract against the protection buyer's obligation to deliver a bond or loan of the name against which protection is being sold.

A CDS is often used like an insurance policy, or hedge for the holder of debt, though because there is no requirement to actually hold any asset or suffer a loss, a CDS is not actually insurance. The typical term of a CDS contract is five years, although being an over-the-counter derivative almost any maturity is possible.

1 Terms of a Typical CDS contract
2 Quotes of a CDS contract
3 Example
4 Speculation
5 Pricing
6 Levels and flows
7 Criticisms
8 Operational Issues in Settlement
9 See also
10 External links

[edit] Terms of a Typical CDS contract

A CDS contract is typically documented under a confirmation referencing the 2003 Credit Derivatives Definitions as published by the International Swaps and Derivatives Association. The confirmation typically specifies a reference entity, a corporation or sovereign which generally, although not always, has debt outstanding, and a reference obligation, usually an unsubordinated corporate bond or government bond. The period over which default protection extends is defined by the contract effective date and scheduled termination date.

The confirmation also specifies a calculation agent who is responsible for making determinations as to successors and substitute reference obligations, and for performing various calculation and administrative functions in connection with the transaction. By market convention, in contracts between CDS dealers and end-users, the dealer is generally the calculation agent, and in contracts between CDS dealers, the protection seller is generally the calculation agent. It is not the responsibility of the calculation agent to determine whether or not a credit event has occurred but rather a matter of fact that, pursuant to the terms of typical contracts, must be supported by publicly available information delivered along with a credit event notice. Typical CDS contracts do not provide an internal mechanism for challenging the occurrence or non-occurrence of a credit event and rather leave the matter to the courts if necessary, though actual instances of specific events being disputed are relatively rare.

CDS confirmations also specify the credit events that will trigger a credit event and give rise to payment obligations by the protection seller and delivery obligations by the protection buyer. Typical credit events include bankruptcy with respect to the reference entity and failure to pay with respect to its direct or guaranteed bond or loan debt. CDS written on North American investment grade corporate reference entities, European corporate reference entities and sovereigns generally also include 'restructuring' as a credit event, whereas trades referencing North American high yield corporate reference entities typically do not. The definition of restructuring is quite technical but is essentially intended to pick up circumstances where a reference entity, as a result of the deterioration of its credit, negotiates changes in the terms in its debt with its creditors as an alternative to formal insolvency proceedings. This practice is far more typical in jurisdictions that do not provide protective status to insolvent debtors similar to that provided by Chapter 11 of the United States Bankruptcy Code. In particular, concerns arising out of Conseco's restructuring in 2000 led to the credit event's removal from North American high yield trades.^[1]

Finally, standard CDS contracts specify deliverable obligation characteristics that limit the range of obligations that a protection buyer may deliver upon a credit event. Trading conventions for deliverable obligation characteristics vary for different markets and CDS contract types. Typical limitations include that deliverable debt be a bond or loan, that it have a maximum maturity of 30 years, that it not be subordinated, that it not be subject to transfer restrictions (other than Rule 144A), that it be of a standard currency and that it not be subject to some contingency before becoming due.

[edit] Quotes of a CDS contract

Sellers of CDS contracts will give a par quote (see par value) for a given reference entity, seniority, maturity and restructuring e.g. a seller of CDS contracts may quote the premium on a 5 year CDS contract on Ford Motor Company senior debt with modified restructuring as 100 basis points. The par premium is calculated so that the contract has zero present value on the effective date. This is because the expected value of protection payments is exactly equal and opposite to the expected value of the fee or coupon payments. The most important factor affecting the cost of protection provided by a CDS is the credit quality (often proxied by the credit rating) of the reference obligation. Lower credit ratings imply a greater risk that the reference entity will default on its payments and therefore the cost of protection will be higher.

The swap adjusted spread of a CDS should trade closely with that of the underlying cash bond. Cash bond refers to the reference entity. Misalignments in spreads may occur due to technical minutia such as specific settlement differences, shortages in a particular underlying instrument, and the existence of buyers constrained from buying exotic derivatives.

[edit] Example

A pension fund owns 10 million euro worth of a 5 year bond issued by Risky Corporation. In order to manage their risk of losing money if Risky Corporation defaults on its debt, the pension fund buys a CDS from Derivative Bank in a notional amount of 10 million euros which trades at 200 basis points. In return for this credit protection, the pension fund pays 2% of 10 million (200,000 euro) in quarterly installments of 50,000 euro to Derivative Bank. If Risky Corporation does not default on its bond payments, the pension fund makes quarterly payments to Derivative Bank for 5 years and receives its 10 millions loan back after 5 years from the Risky Corporation. Though the protection payments reduce investment returns for the pension fund, its risk of loss in a default scenario is eliminated. If Risky Corporation defaults on its debt 3 years into the CDS contract then the premium payments would stop and Derivative Bank would ensure that the pension fund is refunded for its loss of 10 million euro. Another scenario would be if Risky Corporation's credit profile improved dramatically or it is acquired by a stronger company after 3 years, the pension fund could effectively cancel or reduce its original CDS position by selling the remaining two years of credit protection in the market.

[edit] Speculation

The other use of credit default swaps, and the position usually taken by the other side of a trade, is speculation. Like investing in stock options, credit default swaps give a speculator a way to make a large profit from changes in a company's credit quality. For example, if a company has outstanding debt, and if the company has been having problems, it may be possible to buy the outstanding debt (usually bonds) at a discounted price. For example, if the company has one million dollars worth of bonds outstanding (one million dollars worth of debt), it might be possible to buy the debt for 900 thousand dollars from another party if the company has been doing badly and the other party is worried that the company won't repay (the other party would be willing to take some loss to recover some money). If the company does in fact repay the debt, you would receive one million and make a 100 thousand dollar profit. With a credit default swap, one could sell the other investor credit protection and receive, for example, one hundred thousand dollars, and keep the premium if the company does not default. In this case one would make a hundred thousand dollar profit without having invested anything.

It is also possible to buy and sell credit default swaps that are outstanding. Like the bonds themselves, the cost to purchase the swap from another party may fluctuate as the perceived credit quality of the underlying company changes. But these pricing differences are amplified compared to bonds. Therefore someone who believes that a company's credit quality would change could potentially profit much more from investing in swaps than in the underlying bonds (although encountering a greater loss potential).

[edit] Pricing

There are two competing theories usually advanced for the pricing of credit default swaps. The first, which for convenience we will refer to as the 'probability model', takes the present value of a series of cashflows weighted by their probability of non-default. This method suggests that credit default swaps should trade at a considerably lower spread than corporate bonds. Elton et al show that the effect of default plays only a very small part in the pricing of corporate bonds. By extension, the pricing of credit default swap should also depend on factors other than default, but there is not yet universal agreement on this point.

The second model, proposed by Duffie, but also by Hull and White, uses a non-arbitrage approach.

Under the probability model, a credit default swap is priced using a model that takes four inputs: the issue premium, the recovery rate, the credit curve for the reference entity and the LIBOR curve. If default events never occurred the price of a CDS would simply be the sum of the discounted premium payments. So CDS pricing models have to take into account the possibility of a default occurring some time between the effective date and maturity date of the CDS contract. For the purpose of explanation we can imagine the case of a one year CDS with effective date $t 0$ with four quarterly premium payments occurring at times $t 1$ , $t 2$ , $t 3$ , and $t 4$ . If the nominal for the CDS is $N$ and the issue premium is $c$ then the size of the quarterly premium payments is $N c / 4$ . If we assume for simplicity that defaults can only occur on one of the payment dates then there are five ways the contract could end: either it does not have any default at all, so the four premium payments are made and the contract survives until the maturity date, or a default occurs on the first, second, third or fourth payment date. To price the CDS we now need to assign probabilities to the five possible outcomes, then calculate the present value of the payoff for each outcome. The present value of the CDS is then simply the present value of the five payoffs multiplied by their probability of occurring.

This is illustrated in the following tree diagram where at each payment date either the contract has a default event, in which case it ends with a payment of $N (1 - R)$ shown in red, where $R$ is the recovery rate, or it survives without a default being triggered, in which case a premium payment of $N c / 4$ is made, shown in blue. At either side of the diagram are the cashflows up to that point in time with premium payments in blue and default payments in red. If the contract is terminated the square is shown with solid shading.

At the $i t h$ payment, the probability of surviving over the interval $t i - 1$ to $t i$ without a default payment is $p i$ and the probability of a default being triggered is $1 - p i$ . The calculation of present value, given discount factors of $δ 1$ to $δ 4$ is then

Description	Premium Payment PV	Default Payment PV	Probability
Default at time $t 1$	$0\,$	$N(1-R) \delta_1\,$	$1-p_1\,$
Default at time $t 2$	$-\frac{Nc}{4} \delta_1$	$N(1-R) \delta_2\,$	$p_1(1-p_2)\,$
Default at time $t 3$	$-\frac{Nc}{4}(\delta_1 + \delta_2)$	$N(1-R) \delta_3\,$	$p_1 p_2 (1-p_3)\,$
Default at time $t 4$	$-\frac{Nc}{4}(\delta_1 + \delta_2 + \delta_3)$	$N(1-R) \delta_4\,$	$p_1 p_2 p_3 (1-p_4)\,$
No defaults	$-\frac{Nc}{4} ( \delta_1 + \delta_2 + \delta_3 + \delta_4 )$	$0\,$	$p_1 \times p_2 \times p_3 \times p_4$

The probabilities $p 1$ , $p 2$ , $p 3$ , $p 4$ can be calculated using the credit spread curve. The probability of no default occurring over a time period from $t$ to $t + Δ t$ decays exponentially with a time-constant determined by the credit spread, or mathematically $p = e x p ( - s (t)Δ t)$ where $s (t)$ is the credit spread zero curve at time $t$ . The riskier the reference entity the greater the spread and the more rapidly the survival probability decays with time.

To get the total present value of the credit default swap we add the probability of each outcome by its present value to give

$PV\,$	$=\,$	$(1 - p_1) N(1-R) \delta_1\,$
		$+ p_1 ( 1 - p_2 ) [ N(1-R) \delta_2 - \frac{Nc}{4} \delta_1 ]$
		$+p_1 p_2 ( 1 - p_3 ) [ N(1-R) \delta_3 - \frac{Nc}{4} (\delta_1 + \delta_2) ]$
		$+p_1 p_2 p_3 (1 - p_4) [ N(1-R) \delta_4 - \frac{Nc}{4} (\delta_1 + \delta_2 + \delta_3) ]$
		$-p_1 p_2 p_3 p_4 ( \delta_1 + \delta_2 + \delta_3 + \delta_4 ) \frac{Nc}{4}$

In the 'no-arbitrage' model proposed by both Duffie, and Hull and White, it is assumed that there is no risk free arbitrage. Duffie uses the LIBOR as the risk free rate, whereas Hull and White use US Treasuries as the risk free rate. Both analyses make simplifying assumptions (such as the assumption that there is zero cost of unwinding the fixed leg of the swap on default) which may invalidate the no-arbitrage assumption. However the Duffie approach is frequently used by the market to determine theoretical prices. Under the Duffie construct, the price of a credit default swap can also be derived by calculating the asset swap spread of a bond. If a bond has a spread of 100, and the swap spread is 50 basis points, then a CDS contract should trade at 50. However owing to inefficiencies in markets, this is not always the case. The difference between the theoretical model and the actual price of a credit default swap is known as the basis. There is very little academic research which identifies the factors that cause the basis to expand and contract.

[edit] Levels and flows

The Bank for International Settlements reported the notional amount on outstanding credit forwards and swaps to be $3.846 trillion in end-June 2004, up from $536 billion at the end of June 2001.

The Office of the Comptroller of the Currency reported the notional amount on outstanding credit derivatives from 882 reporting banks to be $5.472 trillion at the end of March, 2006.

The International Swaps and Derivatives Association (ISDA) reported the notional amount of credit default swaps grew by 52% in the first half of 2006, to $26.0 trillion.

[edit] Criticisms

Warren Buffett famously described derivatives bought speculatively as "financial weapons of mass destruction." In Buffett's annual report to shareholders he said "Unless derivatives contracts are collateralized or guaranteed, their ultimate value also depends on the creditworthiness of the counterparties to them. In the meantime, though, before a contract is settled, the counterparties record profits and losses -often huge in amount- in their current earnings statements without so much as a penny changing hands. The range of derivatives contracts is limited only by the imagination of man (or sometimes, so it seems, madmen)." In that very same report to shareholders, however, Warren Buffet has stated that he uses derivatives to hedge.

The market for credit derivatives is now so large, in many instances the amount of credit derivatives outstanding for an individual name are vastly greater than the bonds outstanding. For instance, company X may have $1 billion of outstanding debt and $10 billion of CDS contracts outstanding. If company x were to default, and recovery is 40 cents on the dollar, then the loss to investors holding the bonds would be $600 million. However the loss to credit default swap sellers would be $6 billion. Instead of spreading risk, credit derivatives in fact are amplifying losses in the event of default.

[edit] Operational Issues in Settlement

In the US, the settlement and processing of a CDS contract is currently the subject of concern by the US Federal Reserve. In 2005, the Federal Reserve obtained a commitment by 14 major dealers to upgrade their systems and reduce the backlog of "unprocessed" CDS contracts. As of January 31, 2006, the dealers had met their commitment and achieved a 54% reduction.^[2]

In addition, growing concern over the sheer volume of CDS contracts potentially requiring physical settlement after credit events for names actively traded in the single-name and index-trade market where the notional value of CDS contracts dramatically exceeds the notional value of deliverable bonds has led to the increasing application of cash settlement auction protocols coordinated by ISDA. Successful auction protocols have been applied following credit events in respect of Collins & Aikman Products Co., Delphi Corporation , Delta Air Lines and Northwest Airlines, Calpine Corporation, Dana Corporation and Dura Operating Corp..