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A credit default swap (CDS) is a swap contract in which the buyer of the CDS makes a series of payments to the seller and, in exchange, receives a payoff if a credit instrument (typically a bond or loan) goes into default (fails to pay). Less commonly, the credit event that triggers the payoff can be a company undergoing restructuring, bankruptcy, or even just having its credit rating downgraded.

CDS contracts have been compared with insurance, because the buyer pays a premium and, in return, receives a sum of money if one of the events specified in the contract occurs. However, there are a number of differences between CDS and insurance, for example:
• The buyer of a CDS does not need to own the underlying security or other form of credit exposure; in fact the buyer does not even have to suffer a loss from the default event. In contrast, to purchase insurance, the insured is generally expected to have an insurable interest such as owning a debt obligation;
• the seller need not be a regulated entity;
• the seller is not required to maintain any reserves to pay off buyers, although major CDS dealers are subject to bank capital requirements;
• insurers manage risk primarily by setting loss reserves based on the Law of large numbers, while dealers in CDS manage risk primarily by means of offsetting CDS (hedging) with other dealers and transactions in underlying bond markets;
• in the United States CDS contracts are generally subject to mark to market accounting, introducing income statement and balance sheet volatility that would not be present in an insurance contract;
• Hedge Accounting may not be available under US Generally Accepted Accounting Principles (GAAP) unless the requirements of FAS 133 are met. In practice this rarely happens.

## Description

A "credit default swap" (CDS) is a credit derivative contract between two counterparties. The buyer makes periodic payments to the seller, and in return receives a payoff if an underlying financial instrument defaults.

As an example, imagine that an investor buys a CDS from AAA-Bank, where the reference entity is Risky Corp. The investor will make regular payments to AAA-Bank, and if Risky Corp defaults on its debt (i.e., misses a coupon payment or does not repay it), the investor will receive a one-off payment from AAA-Bank and the CDS contract is terminated. If the investor actually owns Risky Corp debt, the CDS can be thought of as hedging. But investors can also buy CDS contracts referencing Risky Corp debt, without actually owning any Risky Corp debt. This may be done for speculative purposes, to bet against the solvency of Risky Corp in a gamble to make money if it fails, or to hedge investments in other companies whose fortunes are expected to be similar to those of Risky.

If the reference entity (Risky Corp) defaults, one of two things can happen:
• Either the investor delivers a defaulted asset to AAA-Bank for a payment of the par value. This is known as physical settlement.
• Or AAA-Bank pays the investor the difference between the par value and the market price of a specified debt obligation (even if Risky Corp defaults, there is usually some recovery, i.e., not all your money will be lost.) This is known as cash settlement.

The "spread" of a CDS is the annual amount the protection buyer must pay the protection seller over the length of the contract, expressed as a percentage of the notional amount. For example, if the CDS spread of Risky Corp is 50 basis points, or 0.5% (1 basis point = 0.01%), then an investor buying $10 million worth of protection from AAA-Bank must pay the bank$50,000 per year. These payments continue until either the CDS contract expires or Risky Corp defaults.

All things being equal, at any given time, if the maturity of two credit default swaps is the same, then the CDS associated with a company with a higher CDS spread is considered more likely to default by the market, since a higher fee is being charged to protect against this happening. However, factors such as liquidity and estimated loss given default can impact the comparison.

Credit spread rates and credit ratings of the underlying or reference obligations are considered among money managers to be the best indicators of the likelihood of sellers of CDSs to have to perform under these contracts.

## Uses

Like most financial derivatives, credit default swaps can be used by investors for speculation, hedging and arbitrage.

### Speculation

Credit default swaps allow investors to speculate on changes in CDS spreads of single names or of market indices such as the North American CDX index or the European iTraxx index. Or, an investor might believe that an entity's CDS spreads are either too high or too low relative to the entity's bond yields and attempt to profit from that view by entering into a trade, known as a basis trade, that combines a CDS with a cash bond and an interest rate swap. Finally, an investor might speculate on an entity's credit quality, since generally CDS spreads will increase as credit-worthiness declines, and decline as credit-worthiness increases. The investor might therefore buy CDS protection on a company in order to speculate that the company is about to default. Alternatively, the investor might sell protection if they think that the company's creditworthiness might improve.

For example, a hedge fund believes that Risky Corp will soon default on its debt. Therefore it buys $10 million worth of CDS protection for two years from AAA-Bank, with Risky Corp as the reference entity, at a spread of 500 basis points (=5%) per annum. • If Risky Corp does indeed default after, say, one year, then the hedge fund will have paid$500,000 to AAA-Bank, but will then receive $10 million (assuming zero recovery rate, and that AAA-Bank has the liquidity to cover the loss), thereby making a profit. AAA-Bank, and its investors, will incur a$9.5 million loss unless the bank has somehow offset the position before the default.

• However, if Risky Corp does not default, then the CDS contract will run for two years, and the hedge fund will have ended up paying $1 million, without any return, thereby making a loss. Note that there is a third possibility in the above scenario; the hedge fund could decide to liquidate its position after a certain period of time in an attempt to lock in its gains or losses. For example: • After 1 year, the market now considers Risky Corp more likely to default, so its CDS spread has widened from 500 to 1500 basis points. The hedge fund may choose to sell$10 million worth of protection for 1 year to AAA-Bank at this higher rate. Therefore over the two years the hedge fund will pay the bank 2 * 5% * $10 million =$1 million, but will receive 1 * 15% * $10 million =$1.5 million, giving a total profit of $500,000. • In another scenario, after one year the market now considers Risky much less likely to default, so its CDS spread has tightened from 500 to 250 basis points. Again, the hedge fund may choose to sell$10 million worth of protection for 1 year to AAA-Bank at this lower spread. Therefore over the two years the hedge fund will pay the bank 2 * 5% * $10 million =$1 million, but will receive 1 * 2.5% * $10 million =$250,000, giving a total loss of $750,000. This loss is smaller than the$1 million loss that would have occurred if the second transaction had not been entered into.

Transactions such as these do not even have to be entered into over the long-term. If Risky Corp's CDS spread had widened by just a couple of basis points over the course of one day, the hedge fund could have entered into an offsetting contract immediately and made a small profit over the life of the two CD contracts.

### Hedging

Credit default swaps are often used to manage the credit risk (i.e., the risk of default) which arises from holding debt. Typically, the holder of, for example, a corporate bond may hedge their exposure by entering into a CDS contract as the buyer of protection. If the bond goes into default, the proceeds from the CDS contract will cancel out the losses on the underlying bond.

Pension fund example: A pension fund owns $10 million of a five-year bond issued by Risky Corp. In order to manage the risk of losing money if Risky Corp defaults on its debt, the pension fund buys a CDS from Derivative Bank in a notional amount of$10 million. The CDS trades at 200 basis points (200 basis points = 2.00 percent). In return for this credit protection, the pension fund pays 2% of $10 million ($200,000) per annum in quarterly installments of $50,000 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 million back after five years from Risky Corp. Though the protection payments totaling $1 million reduce investment returns for the pension fund, its risk of loss due to Risky Corp defaulting on the bond is eliminated. • If Risky Corporation defaults on its debt three years into the CDS contract, the pension fund would stop paying the quarterly premium, and Derivative Bank would ensure that the pension fund is refunded for its loss of$10 million (either by physical or cash settlement - see above). The pension fund still loses the $600,000 it has paid over three years, but without the CDS contract it would have lost the entire$10 million.

Hedging issues related to banks and corporations subject to taxation or using US GAAP for financial reporting: While the economics of entering into a CDS contract to hedge the credit risk in an asset are the same for a pension fund, a bank and a corporation, there are two significant practical differences in how hedges using CDS contracts affect banks and corporations compared to pension plans:
• Taxes - - for tax purposes the loss incurred on the Risky Corp.'s debt may be treated very differently from the payout by Derivative Bank to either a corporation or a bank. If the loss on the asset is taxed at a different rate from the profit made on the hedge, then the amount of the CDS swap needed to create a hedge of the Risky Corp.'s debt to the bank or corporation will differ from the [principal] amount of the debt. See Tax Treatment following.
• Financial reporting treatment may not parallel the economic effects. For example, GAAP generally require that Credit Default Swaps be reported on a mark to market basis, and assets that are held for investment, such as a commercial loan or bonds, be reported at cost unless a probable and significant loss is expected. Thus, hedging a commercial loan using a CDS can induce considerable volatility into the income statement and balance sheet as the CDS changes value over its life due to market conditions and due to the tendency for shorter dated CDS to sell at lower prices than longer dated CDS. Clearly, one can try to account for the CDS as a hedge under FASB 133 but in practice that can prove very difficult unless the risky asset owned by the bank or corporation is exactly the same as the Reference Obligation used for the particular CDS that was bought.

### Risk

When entering into a CDS, both the buyer and seller of credit protection take on counterparty risk. Examples of counter party risks:
• The buyer takes the risk that the seller will default. If Derivative Bank and Risky Corp. default simultaneously ("double default"), the buyer loses its protection against default by the reference entity. If Derivative Bank defaults but Risky Corp. does not, the buyer might need to replace the defaulted CDS at a higher cost.
• The seller takes the risk that the buyer will default on the contract, depriving the seller of the expected revenue stream. More important, a seller normally limits its risk by buying offsetting protection from another party - that is, it hedges its exposure. If the original buyer drops out, the seller squares its position by either unwinding the hedge transaction or by selling a new CDS to a third party. Depending on market conditions, that may be at a lower price than the original CDS and may therefore involve a loss to the seller.

As is true with other forms of over-the-counter derivative, CDS might involve liquidity risk. If one or both parties to a CDS contract must post collateral(which is common), there can be margin calls requiring the posting of additional collateral. The required collateral is agreed on by the parties when the CDS is first issued. This margin amount may vary over the life of the CDS contract, if the market price of the CDS contract changes, or the credit rating of one of the parties changes.

### Arbitrage

An interesting situation in which the inverse correlation between a company's stock price and CDS spread breaks down is during a Leveraged buyout (LBO). Frequently this will lead to the company's CDS spread widening due to the extra debt that will soon be put on the company's books, but also an increase in its share price, since buyers of a company usually end up paying a premium.

Another common arbitrage strategy aims to exploit the fact that the swap adjusted spread of a CDS should trade closely with that of the underlying cash bond issued by the reference entity. Misalignments in spreads may occur due to technical reasons such as specific settlement differences, shortages in a particular underlying instrument, and the existence of buyers constrained from buying exotic derivatives. The difference between CDS spreads and asset swap spreads is called the basis and should theoretically be close to zero. Basis trades can aim to exploit any differences to make risk-free profits.

## History

### Conception

Forms of Credit Default Swaps had been in existence from at least the early 1990s, but the modern Credit Default Swaps were invented in 1997 by a team working for JPMorgan Chase. They were designed to shift the risk of default to a third party, and were therefore less punitive in terms of regulatory capital. The first CDS involved JPMorgan selling the credit risk of Exxon to the European Bank of Reconstruction and Development.

Credit Default Swaps became largely exempt from regulation by the U.S. Securities and Exchange Commission (SEC) with the Commodity Futures Modernization Act of 2000, which was also responsible for the Enron loophole.

### Market growth

As the market matured, CDSs came to be used less by banks seeking to hedge against default and more by investors wishing to bet for or against the likelihood that particular companies or portfolios would suffer financial difficulties - see above as well as those seeking to profit from perceived mispricing; the rapid growth of index compared with single name CDS after 2003 reflected this change. The market size for Credit Default Swaps began to grow rapidly from 2003; by the end of 2007, the CDS market had a notional value of $45 trillion. But notional amount began to fall during 2008 as a result of dealer "portfolio compression" efforts, and by the end of 2008 notional amount outstanding had fallen 38 percent to$38.6 trillion.

### Market as of 2008

It is important to note that since default is a relatively rare occurrence (historically around 0.2% of investment grade companies will default in any one year), in most CDS contracts the only payments are the premium payments from buyer to seller. Thus, although the above figures for outstanding notionals are very large, in the absence of default the net cashflows will only be a small fraction of this total: for a 100 bp = 1% spread, the annual cash flows are only 1% of the notional amount.

#### Regulatory concerns over CDS

The market for Credit Default Swaps attracted considerable concern from regulators after a number of large scale incidents in 2008 , starting with the collapse of Bear Stearns..

In the days and weeks leading up to Bear's collapse, the bank's CDS spread widened dramatically, indicating a surge of buyers taking out protection on the bank. It has been suggested that this widening was responsible for the perception that Bear Stearns was vulnerable, and therefore restricted its access to wholesale capital which eventually led to its forced sale to JP Morgan in March. An alternative view is that this surge in CDS protection buyers was a symptom rather than a cause of Bear's collapse; i.e., investors saw that Bear was in trouble, and sought to hedge any naked exposure to the bank, or speculate on its collapse.

In September the bankruptcy of Lehman Brothers caused a total close to $400 billion to become payable to the buyers of CDS protection referenced against the insolvent bank. However the net amount that changed hands was around$7.2 billion This difference is due to the process of 'netting'. Market participants co-operated so that CDS sellers were allowed to deduct from their payouts the inbound funds due to them from their hedging positions. Dealers generally attempt to remain risk-neutral so their losses and gains after big events will on the whole offset each other.

Also in September American International Group (AIG) required a federal bailout because it had been excessively selling CDS protection without hedging against the possibility that the reference entities might decline in value, which exposed the insurance giant to potential losses over $100 Billion. The CDS on Lehman were settled smoothly, as was largely the case for the other 11 credit events occurring in 2008 which triggered payouts. And while it is arguable that other incidents would have been as bad or worse if less efficient instruments than CDS had been used for speculation and insurance purposes, the closing months of 2008 saw regulators working hard to reduce the risk involved in CDS transactions. In 2008 there was no centralized exchange or clearing house for CDS transactions; they were all done over the counter (OTC). This led to recent calls for the market to open up in terms of transparency and regulation. In November, DTCC, which runs a warehouse for CDS trade confirmations accounting for around 90% of the total market, announced that it will release market data on the outstanding notional of CDS trades on a weekly basis. The data can be accessed on the DTCC's website here: [40225]The U.S. Securities and Exchange Commission granted an exemption for IntercontinentalExchange to begin guaranteeing credit-default swaps. The SEC exemption represented the last regulatory approval needed by Atlanta-based Intercontinental. Its larger competitor, CME Group Inc., hasn’t received an SEC exemption, and agency spokesman John Nester said he didn’t know when a decision would be made. ### Market as of 2009 The early months of 2009 saw several fundamental changes to the way CDSs operate, resulting from concerns over the instruments' safety after the events of the previous year. According to Deutsche Bank managing director Athanassios Diplas "the industry pushed through 10 years worth of changes in just a few months"By late 2008 processes had been introduced allowing CDSs which offset each other to be cancelled. Along with termination of contracts that have recently paid out such as those based on Lehmans, this had by March reduced the face value of the market down to an estimated$30 trillion.The Bank for International Settlements estimates that outstanding derivatives total $592 trillion. U.S. and European regulators are developing separate plans to stabilize the derivatives market. Additionally there are some globally agreed standards falling into place in March 2009, administered by International Swaps and Derivatives Association (ISDA). Two of the key changes are: 1. The introduction of central clearing houses, one for the US and one for Europe. A clearing house acts as the central counterparty to both sides of a CDS transaction, thereby reducing the counterparty risk that both buyer and seller face. 2. The international standardization of CDS contracts, to prevent legal disputes in ambiguous cases where its not clear what the payout should be. Speaking before the changes went live , Sivan Mahadevan, a derivatives strategist at Morgan Stanley in New York, stated In the US central clearing operations began in March 2009 , operated by InterContinental Exchange (ICE). A key competitor also interested in entering the CDS clearing sector is CME Group. Details for a European clearing are still being hammered out. #### Government approvals relating to Intercontinental and its competitor CME The SEC's approval for ICE's request to be exempted from rules that would prevent it clearing CDSs was the third government action granted to Intercontinental in one week. On March 3, its proposed acquisition of Clearing Corp., a Chicago clearinghouse owned by eight of the largest dealers in the credit-default swap market, was approved by the Federal Trade Commission and the Justice Department. On March 5, the Federal Reserve Board, which oversees the clearinghouse, granted a request for ICE to begin clearing. Clearing Corp. shareholders including JPMorgan Chase & Co., Goldman Sachs Group Inc. and UBS AG, received$39 million in cash from Intercontinental in the acquisition, as well as the Clearing Corp.’s cash on hand and a 50-50 profit-sharing agreement with Intercontinental on the revenue generated from processing the swaps.

SEC spokesperson John Nestor stated

Other proposals to clear credit-default swaps have been made by NYSE Euronext, Eurex AG and LCH.Clearnet Ltd. Only the NYSE effort is available now for clearing after starting on Dec. 22. As of Jan. 30, no swaps had been cleared by the NYSE’s London- based derivatives exchange, according to NYSE Chief Executive Officer Duncan Niederauer.

• Cash settlement: The protection seller pays the buyer the difference between par value and the market price of a debt obligation of the reference entity. For example, a hedge fund has bought $5 million worth of protection from a bank on the senior debt of a company. This company has now defaulted, and its senior bonds are now trading at 25 (i.e. 25 cents on the dollar) since the market believes that senior bondholders will receive 25% of the money they are owed once the company is wound up. Therefore, the bank must pay the hedge fund$5 million * (100%-25%) = $3.75 million. The development and growth of the CDS market has meant that on many companies there is now a much larger outstanding notional of CDS contracts than the outstanding notional value of its debt obligations. (This is because many parties made CDS contracts for speculative purposes, without actually owning any debt for which they wanted to insure against default.) For example, at the time it filed for bankruptcy on 14 September 2008, Lehman Brothers had approximately$155 billion of outstanding debt but around $400 billion notional value of CDS contracts had been written which referenced this debt. Clearly not all of these contracts could be physically settled, since there was not enough outstanding Lehman Brothers debt to fulfill all of the contracts, demonstrating the necessity for cash settled CDS trades. The trade confirmation produced when a CDS is traded will state whether the contract is to be physically or cash settled. ### Auctions When a credit event occurs on a major company on which a lot of CDS contracts are written, an auction (also known as a credit-fixing event) may be held to facilitate settlement of a large number of contracts at once, at a fixed cash settlement price. During the auction process participating dealers (e.g., the big investment banks) submit prices at which they would buy and sell the reference entity's debt obligations, as well as net requests for physical settlement against par. A second stage Dutch auction is held following the publication of the initial mid-point of the dealer markets and what is the net open interest to deliver or be delivered actual bonds or loans. The final clearing point of this auction sets the final price for cash settlement of all CDS contracts and all physical settlement requests as well as matched limit offers resulting from the auction are actually settled. According to the International Swaps and Derivatives Association (ISDA), who organised them, auctions have recently proved an effective way of settling the very large volume of outstanding CDS contracts written on companies such as Lehman Brothers and Washington Mutual. Below is a list of the auctions that have been held since 2005. ## Pricing and valuation There are two competing theories usually advanced for the pricing of credit default swaps. The first, referred to herein 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. The second model, proposed by Darrell Duffie, but also by John Hulland White, uses a no-arbitrage approach. ### Probability model Under the probability model, a credit default swap is priced using a model that takes four inputs: • the "issue premium", • the recovery rate (percentage of notional repaid in event of default), • the "credit curve" for the reference entity and • the "LIBOR curve". If defaultevents never occurred the price of a CDS would simply be the sum of the discountedpremium 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_0with four quarterly premium payments occurring at times t_1, t_2, t_3, and t_4. If the nominal for the CDS is Nand the issue premium is cthen the size of the quarterly premium payments is Nc/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 valueof 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 Ris the recovery rate, or it survives without a default being triggered, in which case a premium payment of Nc/4is 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. The probability of surviving over the interval t_{i-1}to t_iwithout a default payment is p_iand the probability of a default being triggered is 1-p_i. The calculation of present value, given discount factorsof \delta_1to \delta_4is then Date Name Final price as a percentage of par 2005-06-14 Collins & Aikman - Senior 43.625 2005-06-23 Collins & Aikman - Subordinated 6.375 2005-10-11 Northwest Airlines 28 2005-10-11 Delta Airlines 18 2005-11-04 Delphi Corporation 63.375 2006-01-17 Calpine Corporation 19.125 2006-03-31 Dana Corporation 75 2006-11-28 Dura - Senior 24.125 2006-11-28 Dura - Subordinated 3.5 2007-10-23 Movie Gallery 91.5 2008-02-19 Quebecor World 41.25 2008-10-02 Tembec Inc 83 2008-10-06 Fannie Mae - Senior 91.51 2008-10-06 Fannie Mae - Subordinated 99.9 2008-10-06 Freddie Mac - Senior 94 2008-10-06 Freddie Mac - Subordinated 98 2008-10-10 Lehman Brothers 8.625 2008-10-23 Washington Mutual 57 2008-11-04 Landsbanki - Senior 1.25 2008-11-04 Landsbanki - Subordinated 0.125 2008-11-05 Glitnir - Senior 3 2008-11-05 Glitnir - Subordinated 0.125 2008-11-06 Kaupthing - Senior 6.625 2008-11-06 Kaupthing - Subordinated 2.375 2008-12-09 Masonite [40226] - LCDS 52.5 2008-12-17 Hawaiian Telcom - LCDS 40.125 2009-01-06 Tribune - CDS 1.5 2009-01-06 Tribune - LCDS 23.75 2009-01-14 31.375 2009-02-03 Millennium America Inc 7.125 2009-02-03 Lyondell - CDS 15.5 2009-02-03 Lyondell - LCDS 20.75 2009-02-03 EquiStar 27.5 2009-02-05 Sanitec [40227] - 1st Lien 33.5 2009-02-05 Sanitec [40228] - 2nd Lien 4.0 2009-02-09 British Vita [40229] - 1st Lien 15.5 2009-02-09 British Vita [40230] - 2nd Lien 2.875 2009-02-10 Nortel Ltd. 6.5 2009-02-10 Nortel Corporation 12 2009-02-19 Smurfit-Stone CDS 8.875 2009-02-19 Smurfit-Stone LCDS 65.375 2009-02-26 Ferretti 10.875 2009-03-09 Aleris 8 2009-03-31 Station Casinos 32 2009-04-14 Chemtura 15 2009-04-14 Great Lakes 18.25 2009-04-15 Rouse 29.25 2009-04-16 LyondellBasell 2 2009-04-17 Abitibi 3.25 2009-04-21 Charter Communications CDS 2.375 2009-04-21 Charter Communications LCDS 78 2009-04-22 Capmark 23.375 2009-04-23 Idearc CDS 1.75 2009-04-23 Idearc LCDS 38.5 2009-05-12 Bowater 15 2009-05-13 General Growth Properties 44.25 2009-05-27 Syncora 15 2009-05-28 Edshcha 3.75 2009-06-09 HLI Operating Corp LCDS 9.5 2009-06-10 Georgia Gulf LCDS 83 2009-06-11 R.H. Donnelley Corp. CDS 4.875 2009-06-12 General Motors CDS 12.5 2009-06-12 General Motors LCDS 97.5 2009-06-18 JSC Alliance Bank CDS 16.75 2009-06-23 Visteon CDS 3 2009-06-23 Visteon LCDS 39 2009-06-24 RH Donnelley Inc LCDS 78.125 2009-07-09 Six Flags CDS 14 2009-07-09 Six Flags LCDS 96.125 2009-07-21 Lear CDS 38.5 2009-07-21 Lear LCDS 66 2009-11-10 METRO-GOLDWYN-MAYER INC. LCDS 58.5 2009-11-20 CIT Group Inc. 68.125 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+\Delta t decays exponentially with a time-constant determined by the credit spread, or mathematically p=exp(-s(t) \Delta t/(1-R)) 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 multiply 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} ### No-arbitrage model In the 'no-arbitrage' model proposed by both Duffie, and Hull-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 70 basis points, then a CDS contract should trade at 30. However there are sometimes technical reasons why this will not be the case, and this may or may not present an arbitrage opportunity for the canny investor. The difference between the theoretical model and the actual price of a credit default swap is known as the basis. ## Criticisms Credit default swaps lower the yield on bonds since owners of credit default swaps will accept a lower bond yield knowing that they have insurance on the default of that bond. This harms small investors unable to buy credit default swaps because bond yields are lower as bonds are priced with the insurance value of credit default swaps included. Critics of the huge credit default swap market have claimed that it has been allowed to become too large without proper regulation and that, because all contracts are privately negotiated, the market has no transparency. Furthermore, there have even been claims that CDSs exacerbated the 2008 global financial crisis by hastening the demise of companies such as Lehman Brothers and AIG. In the case of Lehman Brothers, it is claimed that the widening of the bank's CDS spread reduced confidence in the bank and ultimately gave it further problems that it was not able to overcome. However, proponents of the CDS market argue that this confuses cause and effect; CDS spreads simply reflected the reality that the company was in serious trouble. Furthermore, they claim that the CDS market allowed investors who had counterparty risk with Lehman Brothers to reduce their exposure in the case of their default. Credit default swaps have also faced criticism that they contributed to a breakdown in negotiations during the GM bankruptcy, because bondholders would benefit from the credit event of a GM bankruptcy due to their holding of CDSs. Critics speculate that these creditors were incentivized into pushing for the company to enter bankruptcy protection. Due to a lack of transparency, there was no way to find out who the protection buyers and protection writers were, and they were subsequently left out of the negotiation process. It was also reported after Lehman's bankruptcy that the$400 billion notional of CDS protection which had been written on the bank could lead to a net payout of $366 billion from protection sellers to buyers (given the cash-settlement auction settled at a final price of 8.625%) and that these large payouts could lead to further bankruptcies of firms without enough cash to settle their contracts. However, industry estimates after the auction suggested that net cashflows would only be in the region of$7 billion. This is because many parties held offsetting positions; for example if a bank writes CDS protection on a company it is likely to then enter an offsetting transaction by buying protection on the same company in order to hedge its risk. Furthermore, CDS deals are marked-to-market frequently. This would have led to margin calls from buyers to sellers as Lehman's CDS spread widened, meaning that the net cashflows on the days after the auction are likely to have been even lower.Senior bankers have argued that not only has the CDS market functioned remarkably well during the financial crisis, but that CDS contracts have been acting to distribute risk just as was intended, and that it is not CDSs themselves that need further regulation, but the parties who trade them.

Some general criticism of financial derivatives is also relevant to credit derivatives. Warren Buffett famously described derivatives bought speculatively as "financial weapons of mass destruction." In Berkshire Hathaway's annual report to shareholders in 2002, 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)." It is true thatentering a CDS transaction gives you counterparty risk, but bear in mind that it is also possible to hedge this risk by buying CDS protection on your counterparty! Furthermore, it is not strictly true to say that profit and loss is recorded without any money changing hands since positions are marked-to-market daily and collateral will pass from buyer to seller (or vice versa) to protect both parties against counterparty default. It is also worth noting that Buffett seems to have since changed his stance on derivatives since he made this statement, since in October 2008 Berkshire Hathaway was forced to reveal to regulators that it has entered into at least \$4.85 billion in derivative transactions. In addition, Berkshire Hathaway was a large owner of Moody's stock during the period that it was one of two primary rating agencies for subprime CDOs, a form of mortgage security derivative dependant on the use of credit default swaps.

### Systemic risk

The risk of counterparties defaulting has been amplified during the 2008 financial crisis, particularly because Lehman Brothers and AIG were counterparties in a very large number of CDS transactions. This is an example of systemic risk, risk which threatens an entire market, and a number of commentators have argued that size and deregulation of the CDS market have increased this risk.

For example, imagine if a hypothetical mutual fund had bought some Washington Mutual corporate bonds in 2005 and decided to hedge their exposure by buying CDS protection from Lehman Brothers. After Lehman's default, this protection was no longer active, and Washington Mutual's sudden default only days later would have led to a massive loss on the bonds, a loss that should have been insured by the CDS. There was also fear that Lehman Brothers and AIG's inability to pay out on CDS contracts would lead to the unraveling of complex interlinked chain of CDS transactions between financial institutions. So far this does not appear to have happened, although some commentators have noted that because the total CDS exposure of a bank is not public knowledge, the fear that one could face large losses or possibly even default themselves was a contributing factor to the massive decrease in lending liquidity during September/October 2008.

Chains of CDS transactions can arise from a practice known as "netting". Here, company B may buy a CDS from company A with a certain annual "premium", say 2%. If the condition of the reference company worsens, the risk premium will rise, so company B can sell a CDS to company C with a premium of say, 5%, and pocket the 3% difference. However, if the reference company defaults, company B might not have the assets on hand to make good on the contract. It depends on its contract with company A to provide a large payout, which it then passes along to company C. The problem lies if one of the companies in the chain fails, creating a "domino effect" of losses. For example, if company A fails, company B will default on its CDS contract to company C, possibly resulting in bankruptcy, and company C will potentially experience a large loss due to the failure to receive compensation for the bad debt it held from the reference company. Even worse, because CDS contracts are private, company C will not know that its fate is tied to company A; it is only doing business with company B.

As described above, the establishment of a central exchange or clearing house for CDS trades would help to solve the "domino effect" problem, since it would mean that all trades faced a central counterparty guaranteed by a consortium of dealers.

## Tax treatment

The U.S federal income tax treatment of credit default swaps is uncertain.Nirenberg, David Z. & Steven L. Kopp. “Credit Derivatives: Tax Treatment of Total Return Swaps, Default Swaps, and Credit-Linked Notes,” Journal of Taxation, Aug. 1997: 1. Peaslee, James M. & David Z. Nirenberg. Federal Income Taxation of Securitization Transactions: Cumulative Supplement No. 7, November 26, 2007, http://www.securitizationtax.com: 85. Retrieved July 28, 2008. Ari J. Brandes. A Better Way to Understand Credit Default Swaps. Tax Notes (July 21, 2008). Earlier version of paper available at: [40231]. Commentators generally believe that, depending on how they are drafted, they are either notional principal contracts or options for tax purposes, but this is not certain. There is a risk of having credit default swaps recharacterized as different types of financial instruments because they resemble put options and credit guarantees. In particular, the degree of risk depends on the type of settlement (physical/cash and binary/FMV) and trigger (default only/any credit event). If a credit default swap is a notional principal contract, periodic and nonperiodic payments on the swap are deductible and included in ordinary income. If a payment is a termination payment, its tax treatment is even more uncertain. In 2004, the Internal Revenue Service announced that it was studying the characterization of credit default swaps in response to taxpayer confusion, but it has not yet issued any guidance on their characterization. A taxpayer must include income from credit default swaps in ordinary income if the swaps are connected with trade or business in the United States.

## LCDS

A new type of default swap is the "loan only" credit default swap (LCDS). This is conceptually very similar to a standard CDS, but unlike "vanilla" CDS, the underlying protection is sold on syndicated secured loans of the Reference Entity rather than the broader category of "Bond or Loan". Also, as of May 22, 2007, for the most widely traded LCDS form, which governs North American single name and index trades, the default settlement method for LCDS shifted to auction settlement rather than physical settlement. The auction method is essentially the same that has been used in the various ISDA cash settlement auction protocols, but does not require parties to take any additional steps following a credit event (i.e., adherence to a protocol) to elect cash settlement. On October 23, 2007, the first ever LCDS auction was held for Movie Gallery.[40232]

Because LCDS trades are linked to secured obligations with much higher recovery values than the unsecured bond obligations that are typically assumed to be cheapest to deliver in respect of vanilla CDS, LCDS spreads are generally much tighter than CDS trades on the same name.

## References

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