Credit default swap

A credit default swap ( CDS ) or credit default swap is a credit derivative in which credit risk of loans , bonds or borrower names ge concerns are. Another German term for this is credit default insurance - however, this term is sometimes also used for residual debt insurance .

General

A CDS is a contract between two parties that refers to a reference entity (as an underlying ). Reference entities are typically large, publicly listed companies. One contracting party, the so-called protection buyer , pays an ongoing premium as well as an additional one-time premium. In return, he receives a compensation payment from his contractual partner, the so-called security seller, if the reference debtor specified in the CDS contract fails.

The CDS is thus similar to credit insurance . However, the collateral taker receives the compensation payment regardless of whether the default of the reference debtor causes him any damage at all . Credit default swaps are therefore an instrument with which credit risks can be traded independently of existing credit relationships and long and short can be taken.

functionality

CDS are off-exchange transactions (English over the counter , abbreviated OTC). To simplify tradability, however, they are generally standardized to a certain extent by means of framework agreements . With CDS, the framework agreements of the International Swaps and Derivatives Association (ISDA) are common.

When concluding a credit default swap, the following points in particular are agreed (illustration based on):

• Reference debtor ( underlying ),
• Nominal value of the transaction (e.g. EUR 200 million),
• Duration of the transaction (e.g. six years),
• Price that the protection buyer pays the protection seller for assuming the risk,
• Type of credit events to be secured by the CDS (e.g. insolvency , default in payment and rescheduling ), if the occurrence of which the protection seller has to pay, as well as, if applicable, the reference assets ( bonds , loans ) of the reference debtor, on the basis of which certain credit events (e.g. B. default in payment) can be determined.
• Type of performance by the protection seller when the credit event occurs (usually payment ).

Reference debtor

The reference entity is the underlying of the credit default swap derivative. He is the legal person whose default as a debtor is "insured" by the CDS. In addition, CDS indices can also be the base value of a CDS. Common Reference Entities are companies or countries that bonds issued or greater have taken loans.

A CDS ends at the agreed end time or as soon as a credit event occurs. Due to the standardization through the ISDA framework agreement, only the following deadlines are generally agreed for CDS: March 20, June 20, September 20 or December 20. These are also called IMM dates” based on the closely related expiration dates of futures .

Also due to the standardization, CDS generally only start on the day following one of the IMM dates. If a CDS was not concluded on that date, the contract will be backdated to the last of the days following one of the IMM dates. This can lead to the conclusion of a CDS for which an insured credit event has already occurred.

The usual terms for CDS are 3 to 10 years. The most heavily traded term is 5 years.

The protection buyer must compensate the protection seller for the protection it receives. This is achieved by paying a regular premium and a one-off service, the so-called upfront:

• Payment flow of ongoing premium payment
• Payment flow upon conclusion of the CDS (upfront)
At the beginning of the contract, one of the two parties may make a one-off payment, or “upfront”. The height of the upfront is given in percentage points . An upfront of 2% to a nominal volume of 200 million euros corresponds to a payment of 4 million euros.

The amount of the net benefits to be paid by the protection buyer to the protection seller (i.e. the balance of upfront and current premium) of a CDS depends on

• the expected probability of default of the reference debtor and
• the expected recovery rate . The recovery rate is a kind of “bankruptcy rate”: it indicates what proportion of the nominal value of the reference assets the creditors will still get back if the debtor defaults.

The higher the probability of default of the reference debtor and the lower the expected recovery rate, the higher the costs of securing this risk with a CDS. Since the premium amounts are standardized, if the debtor's creditworthiness changes, the amount of upfront payments observable on the market for new CDSs to be concluded generally changes. This can mean that the upfront can also be negative, i.e. that the protection seller pays the protection buyer.

Fictional example

For example, a CDS on Riskant AG could be concluded the day before yesterday for a term of 5 years for the payment of a running spread of 500 bp and the payment of an upfront of 0.1%. Due to the increased credit rating, a CDS for a running spread of 500 bp and an upfront of 0 was possible yesterday. Due to the fact that the creditworthiness has increased again today, the CDS has to be taken out for an upfront of −0.1% with the same premium.

As the CDS always ends on one of the dates March 20, June 20, September 20 or December 20, the regular premiums are also paid on these days. Premiums are always paid for 3 months. This also applies to the first premium payment. This means that even if the CDS only runs for a shorter period, it must be paid for the entire 3 months. For example, for a CDS concluded on March 1, the premium for the period December 21 of the previous year to March 20 must be paid on March 20. The premium not due to the protection seller for the unsecured period is also offset via the upfront payment. This method of paying the first premium is known as a full coupon .

Definition of Credit Events

The ISDA defines possible credit events as:

• Insolvency of the reference debtor (English bankruptcy )
• Default of the reference entity (English failure to pay )
• Possible early maturity of debts ( obligation default )
• Premature maturity of debts (English obligation acceleration )
• Non-recognition or postponement of payment obligations by the reference debtor (English repudiation / moratorium )
• Restructuring of debt (English restructuring )

It should be noted that in a standardized CDS often only part of these credit events is collateralized. The events " bankruptcy " and " failure to pay " are common. How the event “ restructuring ” is handled is inconsistent and is indicated by the following abbreviations:

• Restructuring is not an insured credit event (“XR” or “NR”). It is the usual form of CDS with American underlyings.
• In the original version, restructuring is an insured credit event (“CR”). This means that the credit event is no different from any other insured credit event. CR is a common expression for CDS on states.
• In the modified version, restructuring is an insured credit event (“MR” for “ modified restructuring ”). If this variant is selected, only bonds with a remaining term of less than 30 months at the time of the credit event are considered when the credit event restructuring occurs. MR was the usual form for North American CDS until 2009.
• The second modified version of the restructuring is an insured credit event (“MM” for “ modified modified restructuring ”). If a credit event occurs, bonds with a remaining term of up to 60 months are considered. MM is common for CDS on European underlyings.

Detect the occurrence of a credit event

An independent committee decides whether a specific event in the environment of the reference debtor fulfills the definition of a credit event in the sense of a CDS and thus a compensation payment has to be made by the protection seller. This body is part of the ISDA and is called the Determinations Committee (DC). The DC deals with the decision on a credit event only upon request. The application must be accompanied by publicly available information about the credit event applied for for recognition.

As a first step, the DC then decides whether it wants to deal with the decision on a credit event. If this is the case, the DC makes a binding decision for all CDS on the reference debtor whether a credit event has occurred or not. This decision therefore also affects all other market participants who have acted as collateral sellers or buyers on this reference debtor in a CDS.

There is a period of 6 weeks for submitting a credit event request, known as the lookback period , from the availability of publicly available information. If this period is exceeded, no further payment can be requested due to the occurrence of a credit event. The lookback period has a side effect: if you take out a CDS, the last 60 days before you take out a CDS are also “insured”. For example, a credit event that occurred 30 days before the CDS was concluded, but was already public knowledge 3 days before the CDS was concluded, would result in a payment by the collateral provider and the CDS being terminated.

Recognize the occurrence of a follow-up event

During the term of a CDS, the reference debtor may merge , be taken over or split up . This event is called a successor event (freely translated as a successor event ). In such a case, it is often necessary to clarify which of the units resulting from the old debtor is the new reference debtor of the corresponding CDS.

This decision is also made by the Determinations Committee upon request (for all existing CDS contracts for the relevant reference debtor) . In addition to defining the new reference debtor, a possible decision can also be to split the existing CDS contract into several CDS contracts (with units resulting from the reference debt as reference debtors).

Compared to the credit events, the follow-up events have an extended lookback period of 90 days.

Benefit when the credit event occurs

When the credit event occurs, the protection seller provides the protection buyer with the contractually agreed service. Possible types of benefits are

Payment flow when the credit event occurs in the case of "payment and delivery"
• "Payment and delivery" or "physical delivery": the protection seller pays the protection buyer the nominal value of the contract (in the example EUR 200 million), while the protection buyer pays the protection seller assets (claims on the reference debtor, e.g. bonds or loans) this nominal value is transferred. Which claims the protection buyer can deliver is determined when the contract is concluded. This is generally a subset of the reference assets. The disadvantage of this type of benefit is that if the protection buyer does not have the claim in his portfolio when the credit event occurs, he must first buy it on the market. If numerous market players have speculated on the default of a debtor in this way, the sudden demand for the defaulted assets can drive their price up sharply (“ squeeze ”).
Payment flow upon occurrence of the credit event in the case of cash settlement or auction settlement
• "Cash settlement" or "Cash Settlement": the protection seller pays the protection buyer the loss in value of the reference asset. To do this, the market price of the reference asset after the credit event (the recovery rate ) is first determined. The protection seller then reimburses the protection buyer for the difference between the market price and the nominal value of the asset. The protection buyer does not have to deliver the asset to the protection seller and can sell it separately on the market. The sum of the sales price and compensation payment should correspond to the nominal and thus have the same security effect as "payment and delivery". The advantage of this type of service compared to "payment and delivery" is that the processing of the credit event does not include the delivery or acceptance of an asset and thus the collateral buyer does not have to ensure that a defaulted asset is delivered and the collateral provider does not have to accept it and then dispose of it . However, one difficulty with cash settlement is the determination of the loss in value of the reference asset based on its market price, since the defaulted instruments are then often illiquid. The revenue quota is therefore usually formed from the mean value of the prices of several dealers over several days.
• "Auction Settlement": This is very similar to cash settlement. Here, too, the loss in value of the reference asset or all assets of the reference debtor that are of at least a certain quality are paid. The determination of the current value of these assets and thus also the determination of the loss in value is achieved via an auction. The price that the assets reach in this auction is regarded as the current market price (i.e. as determining the recovery rate). The protection seller has to pay the difference between the original value and the protection buyer. The collateral taker is free to participate in the auction. If he has claims against the debtor, he can alternatively try to sell these at a later point in time on terms that are more favorable to him.

Until the first half of 2009, the usual form of contract was the form of “payment and delivery” due to the difficulties with “cash settlement”. In order to solve the problems with “payment and delivery” again, “auction settlement” became the usual form of contract in the first half of 2009.

Since the current premium payment is usually made quarterly in arrears and the CDS ends when the credit event occurs, the protection buyer still has to pay the pro-rata premium for the current period. This is usually offset against the claim on the protection seller, so that only one payment is made from the difference between the two claims.

Areas of application of a CDS

Like all derivatives, CDS can be used for hedging , speculation and arbitrage . These basic forms of application can also be used, in particular, for risk diversification in credit portfolios. These techniques are used in particular with regard to large, capital market-oriented borrowers (large industrial companies, banks and states), as there is a liquid CDS market for them.

validation

CDSs can be used to hedge the credit risk of credit exposures. If an investor has granted a loan to a debtor A or bought bonds from A, he can enter a CDS with A as the underlying as collateral buyer. If the debtor defaults, the investor receives the agreed service from the collateral provider from the CDS. This is a compensation for loss that arises from the write-off of the credit exposure. In return, the investor, as security buyer, pays the premiums that ultimately reduce his interest income from the credit exposure.

For the best possible protection, the CDS must be concluded with the same term and with the same nominal value as the loan to be hedged. Nevertheless, the CDS does not represent a complete hedge in every case. On the one hand, the investor could suffer a loss from the loan due to an event that is not covered as a credit event in the CDS. In addition, the performance in the event of default does not necessarily correspond to the loss in value from the credit exposure, unless “payment and delivery” has been agreed and the investor can tender his credit exposure to the protection seller. The residual risks that remain because the hedge is not perfect are also referred to as basic risks.

The investor can also undertake a partial hedge by not taking out the CDS for the entire amount or the entire term of the credit exposure. Has his credit exposure z. B. a term of 7 years and he concludes a CDS with a term of 5 years, he is only protected against a possible default of the debtor for the next 5 years.

speculation

CDS can also be used to speculate on changes in the traded spread or the creditworthiness of a reference debtor. In this case, the investor concludes CDS without necessarily having previously had a corresponding credit exposure. If the investor is of the opinion that the creditworthiness of reference debtor B will deteriorate, he enters a CDS as protection buyer. If the creditworthiness of B then actually deteriorates, the CDS premiums traded on the capital market increase. The investor will then conclude another CDS on reference debtor B, this time as collateral provider. Since the premiums have risen, the investor receives more from the second CDS than he paid for the first CDS. You can say that he bought the hedge cheaply and resold it at a profit.

However, if the market develops contrary to expectations, the investor makes a loss because the second CDS brings in less than the first.

Conversely, the investor can also speculate on the improvement in creditworthiness. To do this, he first enters a CDS as collateral provider. If the creditworthiness of the reference debtor actually improves, he can buy back the sold protection with a second CDS more cheaply.

arbitrage

In arbitrage , CDSs are used to exploit price imbalances between the cash market and the derivatives market or within the derivatives market by taking positions with little or no market price risk in order to achieve secure profits. For example, the risk premium of a bond from a company could be higher than the premium of a CDS of the same maturity on that company. This situation can be exploited through an arbitrage strategy like a cash-and-carry arbitrage : The arbitrageur buys the company's bonds and hedges them with a CDS. With the risk premium compared to the high risk, the arbitrageur can pay the costs of the CDS protection and still retain a profit margin. He is protected against the risk of the bond defaulting by the CDS. The arbitrage opportunity increases demand for both the bond and hedging. As a result, the bond price rises due to demand - i.e. H. the risk premium falls - as does the CDS premium. This eliminates the price imbalance and the possibility of arbitrage.

Risk diversification

A CDS can also be used to reduce cluster risks . In this way, an investor can hedge part of his existing cluster risk through a CDS in which he is the security recipient. At the same time, the investor finances the costs incurred by taking out another CDS on a completely different reference debt in which the investor is the security provider.

For example, a bank has credit risks of EUR 200 million through its credit exposure to Riskant AG. She has secured this with a CDS of EUR 100 million. It pays 500 bp annually and an upfront of 1%. It refinances the costs of a one-off EUR 1 million and EUR 5 million annually through the conclusion of a further CDS in the amount of EUR 100 million as collateral provider. The reference debtor in this second CDS is Waghalsig & CO KG. Although this is to be rated as similarly risky as Riskant AG, it operates in a different industry. Thus, a decline in demand for products from Riskant AG has no connection with the change in demand for products from Waghalsig & Co KG. The income from assuming the credit risk from the 2nd CDS amounts to a one-off 1% (EUR 1 million) and 500 bp (EUR 5 million) annually.

After the two CDSs have been concluded, the bank's risk position amounts to EUR 100 million (EUR 200 million credit exposure - EUR 100 million risk assumption) credit risk of Riskant AG and EUR 100 million (through the 2nd CDS) credit risk of Waghalsig & Co KG. The CDS premium payments to be paid and to be collected are reduced to zero EUR.

In terms of volume, the overall risk position is still as large as it was before the CDS transactions. Because the two companies operate in different markets, it is unlikely that both companies will have a credit event at the same time. Thus, the expected default volume could be reduced significantly, but at the same time with an increased probability of the occurrence of a credit event.

Risks

The main risk driver for a CDS is the premium traded on the market (the so-called CDS spread), which in turn depends mainly on the market participants' assessment of the creditworthiness of the underlying. An improvement in the credit rating leads to a reduction in the CDS spread, which causes the market value of the CDS to fall for the protection buyer and rise for the protection seller; these changes in value are generally assigned to the market price risk. Alternatively, this main risk can also be viewed as a credit risk : the protection seller bears the risk of the costs of default of the underlying asset.

As a further market price risk, a CDS is subject to a certain risk of changes in interest rates , since the present value of future payments (premium payments and any compensation payment by the protection seller) depends on the level of interest rates on the capital markets.

Further, a CDS as each containing derivative of a counterparty risk (replacement risk).

• For the protection buyer, this consists in the fact that in the event of the failure of the protection seller - his counterparty - he has to conclude a replacement transaction with a higher premium, possibly due to negative developments in the underlying, or, in the worst case, does not receive a compensation payment in the event of a credit event.
• For the collateral seller, the replacement risk is comparatively low. It consists in the fact that the protection buyer defaults and the protection seller may only receive a lower premium from the replacement transaction.

In order to minimize the replacement risk, it is common with CDSs, as with other derivatives, for the party for whom the CDS has a negative present value to provide security, also known as collateral . Since the CDS is periodically re-evaluated with the latest market data, on the one hand the amount of the collateral fluctuates and on the other hand the contracting party that has to provide it may change.

In order to reduce the operational risks when processing CDSs, especially legal risks , these are usually concluded under a framework agreement.

Special forms

Digital Credit Default Swap

In the case of a digital credit default swap or digital default swap (DDS), the protection seller pays a fixed, previously agreed compensation payment in the event of a credit event. The value of a DDS therefore only depends on the expected probability of default, not on the expected recovery rate.

Recovery swap

A recovery swap or recovery rate swap is a combination of a normal credit default swap and a digital default swap, whereby the counterparties are protection sellers for one component and protection takers for the other. The compensation payment from the DDS is agreed in such a way that the premium payments from the CDS and DDS cancel each other out (so no premium payments are made during the term of the transaction). In the event of a credit event, the protection seller pays the loss in value of the reference asset from the CDS and receives the fixed compensation payment from the protection seller of the DDS. He has thus exchanged the actual loss in value for the expected one, which was reflected in the determination of the compensation payment of the DDS. Recovery rate swaps thus offer the possibility of trading the expected recovery rate regardless of the probability of default.

Index Credit Default Swaps

Index credit default swaps do not relate to a single underlying, but to a portfolio of reference entities. These reference entities are those that can also be found in the corresponding credit default swap index . If a credit event occurs for one of the reference borrowers during the term of the CDS, the nominal amount due pro rata to this borrower is settled: A compensation payment is made from the protection seller to the protection buyer. The debtor is then removed from the index and the CDS is continued with the nominal amount reduced by the nominal that falls on this debtor.

For example, the index consists of 50 reference entities, which are represented in equal parts in the index. A CDS has been concluded on the index with a volume of EUR 100 million. The debtor Riskant AG is represented in the index and suffers a credit event. Auction Settlement establishes a recovery rate of 20%. The reference debtor Riskant AG will then have a nominal value of EUR 2 million (EUR 100 million nominal of the CDS / 50 reference debtor). A compensation payment of 1.6 million (EUR 2 million nominal on Riskant AG * (100% - 20% recovery rate)) will be made by the protection seller to the protection buyer. The CDS will then be continued with 49 reference borrowers and a reduced nominal of EUR 98 million (EUR 100 million - EUR 2 million).

Common indices are iTraxx for Europe, CDX for America and iTraxx Asia for Asia and Australia.

Basket credit default swaps are an extension of the index CDS concept and also do not relate to a single underlying, but to a portfolio ("basket") of reference borrowers. In the case of a first to default swap , an agreed equalization payment is made if a credit event occurs for any of the debtors. The premium for a basket CDS is comparatively high, as the probability of a credit event is higher than if only one debtor were considered.

Another variant are nth-to-default swaps , in which a compensation payment is only made from the underlying portfolio on the nth credit event. For the pricing and valuation of basket CDS, not only the expected probability of default and the expected recovery rate of the individual portfolio components must be taken into account, but also the expected correlation of the individual default probabilities. Basket CDS thus offer the opportunity to trade expected default correlations. So you can z. B. can be used to hedge corresponding correlation risks from purchased ABS tranches.

History and market

The ISDA has had a framework agreement for CDS since 1999 . In 2003 the ISDA presented a revised version of the framework agreement.

The year 2009 was marked by changes to the framework agreements for CDS and changes in trading practices (see below), which were aimed at increasing liquidity in the CDS markets and reducing counterparty risks. At the same time, the introduction of central counterparties was pushed ahead. Since March 9, 2009, the Intercontinental Exchange has been the world's first clearing house to offer the corresponding CDS clearing.

In the course of time, various service providers have established themselves in the field of CDS trading. In particular, Markit provides CDS market data. Markit also offers debtor referencing. Each underlying is assigned a unique code - similar to the securities identification number for shares. This is RED or RedCode (of English " R eference E ntity D atabase" called). This allows easy referencing to a specific debtor while entering into a CDS. Depository Trust & Clearing Corporation (DTCC) has established itself as a quasi-standard for the processing of closed CDS contracts . DTCC offers a matching service. This simplifies the written confirmation of the traded CDS contract, which usually follows the conclusion by telephone.

The market for CDS grew rapidly from 2007 until the financial crisis . Since CDS are over-the-counter, sales are not recorded centrally, but the market is regularly recorded through studies by various institutions (e.g. the ISDA, the British Bankers' Association , the Bank for International Settlements and Fitch Ratings ). In 2001, the ISDA recorded the volume of CDS separately in its statistics for the first time. At the end of 2001 it was just under 1 trillion. USD. The volume rose to around 50 trillion by mid-2006. USD. In 2008 it went back for the first time in history, from around 60 bio. USD to around 40 trillion. USD. The reason for this is presumably the crisis-related distortions on the CDS market, but also the fact that transactions were offset against each other as a result of the financial crisis.

The largest share of the market is made up of normal CDS (on individual reference entities) and index CDS, i. H. made up of simple, liquid products. This trend intensified over the financial crisis, so that at the end of 2008 both products accounted for 80% of the market. Another effect of the financial crisis was that the need for security increased as the counterparty risk received much more attention.

Before the crisis, banks were, on average, protection buyers from CDS, while the insurance industry and other market participants such as hedge funds were protection providers. However, this does not necessarily apply to individual banks. Over time, the position of the banks has more and more balanced. This is probably due to the fact that banks are increasingly assuming the role of broker ( financial intermediary ) on the CDS market . The top 5 CDS traders in 2009 were JP Morgan , Goldman Sachs , Morgan Stanley , Deutsche Bank and Barclays .

In the Federal Republic of Germany, between May 19 and July 27, 2010, it was prohibited as protection buyer to conclude a CDS on countries in the euro zone , provided that the protection buyer did not have open risk positions in these countries (e.g. if he is protection seller in an existing CDS or holds government bonds).

Changes in trade practices and framework agreements in 2009

In order to ensure greater transparency and integrity in the market and to take the first step towards a central clearing house by standardizing the contracts, there were several changes to the framework agreements and trading practices from spring 2009 .

Big Bang Protocol

Under the working title “Big Bang Protocol”, the ISDA revised the procedure defined in the framework agreement in the spring of 2009 when a credit event occurs (settlement).

The procedure applicable up to this point in the event of a credit event was characterized by bilateral procedures between the protection seller and protection buyer. Both had to mutually agree that a credit event had occurred. This could lead to situations where an investor who had concluded a CDS on a company with two protection providers could agree with one protection seller on the occurrence of a credit event but not with the other protection seller on the occurrence of a credit event. Legal disputes were therefore possibly the result.

In addition, the usual type of settlement was payment and delivery . As described above, this could mean that not all collateral takers were in possession of an asset that they had to deliver in order to receive the compensation payment. An unlikely short-term increase in the price of the assets was also a possible consequence.

To solve these problems, the Big Bang Protocol introduced a new framework agreement and at the same time added to the old framework agreements. The key points were:

• Introduction of the Determinations Committee, which replaced bilateral negotiations on credit events with a central decision
• Use auction settlement as the settlement method to solve payment and delivery problems
• Introduction of the lookback period.

The new framework agreement was introduced on April 8, 2009. From March 7th to April 7th, 2009, the market participants were able to inform the ISDA beforehand whether the new framework agreement should also apply to their old contracts. If both contractual partners had accepted the new framework agreement for a CDS, this replaced the framework agreement originally negotiated for this CDS.

Small Bang Protocol

The “Small Bang Protocol” is a specification of the Big Bang Protocol for the restructuring credit event, especially for the European market. While it is common for companies in the US to restructure their liabilities through laws such as Chapter 11 in the event of financial difficulties , there is no similar cross-country legislation in Europe. The problems of defining an auction settlement for this initial situation were solved with the Small Bang Protocol.

The protocol was introduced in July 2009. From July 14th to July 24th, 2009, the market participants were able to inform the ISDA beforehand whether the new framework agreement should also apply to their old contracts.

In addition to the introduction of the Big Bang Protocol, the ISDA proposed changing trading practices. While the changes to the protocols affected the framework agreements, the commercial usages involved changing the "usual" agreements within a CDS contract. This was therefore more suggestive than normative. The proposed changes were widely accepted and prevailed. In addition, the usual suggestions only apply to new CDSs to be concluded, since the existing transactions have already been traded, while the protocols are also used for old transactions.

The changes in usages were proposed by the ISDA for the various local CDS markets at different times. At the same time as the Big Bang Protocol, conventions for normal North American CDS ( Standard North American Contracts (SNAC)) were introduced. Usages for European CDS followed on June 20, 2009, those for Asian CDS, for example, on December 21, 2009.

Coinciding with the changes for American CDS ISDA published the source code and Excel - Addin a CDS evaluation program (English Pricer ) as open source . This had previously been donated to her by the JP Morgan investment bank . The ISDA suggested that all market participants should use this pricer to rate their CDS. If the same remaining parameters of the pricer were used, all market participants would receive the same evaluation results for given CDS. Correspondingly, as part of the adjustment of trading practices, a flat credit curve and expected recovery rates of either 40% (senior loan, English senior ordinated debt ) or 20% (subordinated loan, English sub ordinated debt ) were proposed. It should be noted that the expected recovery rates have nothing to do with the recovery rates determined by auction when a credit event occurs. The expected recovery rates are only one parameter in the assessment of CDSs that have not yet failed.

The evaluation parameters are not agreed between the contracting parties. Ultimately, each contracting party can determine how it would like to rate a CDS. An agreement on the parameters for converting the variable current spreads into a fixed spread and an upfront payment is only necessary when converting old CDS contracts into CDSs with current trading practices, known as recouponing . These parameters are precisely the recovery rate, the yield curve and the structure of the credit curve.

Usages for standard North American contracts include, in addition to the definition of the valuation parameters, a fixed spread of 100 or 500 basis points (and thus a varying upfront payment). Up to this point in time, CDS were traded with non-standardized premium levels without paying an upfront. Upfronts were only used for Itraxx CDS to offset the coupon amounts set for the Itraxx issue up to this point in time.

In addition, the Restructuring credit event is no longer included than the credit event insured in the CDS.

The change in the convention for European CDS is based on the provisions for SNAC. The biggest difference between the new European usages and the American ones is on the one hand that restructuring is included as modified modified restructuring, as well as in the number of possible fixed spreads. There are fixed spreads of 25, 100, 500 or 1000 basis points, as well as an additional 300 and 750 basis points when reclassifying existing contracts.

The following is a brief overview of the differences in usage between non-SNAC, SNAC and the new European convention:

 Classification of Credit Default Swaps Non-SNAC (before April 8, 2009 or June 20, 2009) SNAC (from April 8, 2009) Europe (from June 20, 2009) CDS type North American, European or State north american European ongoing premium variable constant 100 or 500 bps constant 25, 100, 500 or 1000 bps (300 and 750 possible for existing contracts) Start of coupon payment Long first, short first, full Full Full Start of coupon accumulation Trading day +1 last IMM day last IMM day Restructuring as a Credit Event MM, MR, CR or XR not included ("XR") modified-modified restructuring ("MM") Credit curve at valuation flat or complete curve flat curve flat curve Recovery rate agreed by contracting parties 40% for senior loans, 20% for subordinated loans 40% for senior loans, 20% for subordinated loans rating variable uniformly uniformly

rating

There are several theoretical methods of pricing a CDS, such as no- arbitrage models by both Darrell Duffie and John Hull . In general, however, the following model based on probabilities of failure is used.

The model requires the following input parameters

• the recovery rate , percentage of the nominal amount that is repaid by the debtor in the event of a credit event,
• the "Credit Curve" (vector of current market prices of CDS on these debtors with different terms)
• the corresponding swap curve, for example Euribor for European CDS or USD - Libor for USD-CDS

Would occur unless no credit event that would present value (PV or of English present value ) of the CDS only the sum of the discounted premium payments. Accordingly, the probability of a credit event occurring between the day the CDS started and the day it ended must be taken into account.

For the sake of clarity, it is assumed, for the sake of simplicity, that a CDS is to be assessed starting with a remaining term of one year . This CDS has 4 payment dates for the premium. These are , , and . Let the nominal of the CDS be and the premium to be paid . Thus, a quarterly premium is paid. ${\ displaystyle t_ {0}}$${\ displaystyle t_ {1}}$${\ displaystyle t_ {2}}$${\ displaystyle t_ {3}}$${\ displaystyle t_ {4}}$${\ displaystyle N}$${\ displaystyle c}$${\ displaystyle Nc / 4}$

For the sake of simplicity, it is also assumed that a credit event can only occur on one of the premium payment days. Then there are five ways the CDS contract can end:

• Either no credit event occurs - then the 4 premium payments are made and the CDS runs until the agreed final term -,
• or a Credit Event occurs on the first, second, third, or fourth Premium Payment Day.

In order to evaluate this CDS, the probabilities of these five possibilities are needed. Then the present value of each of these options can be calculated. Then only the five present values ​​have to be multiplied and added by the respective probability of occurrence.

This is shown in the diagram below. On each premium payment day, either a credit event occurs and the CDS thus ends with an insurance payment of . This is symbolized by red. Or the CDS survives since no credit event occurs. In this case, a premium of . This is shown in blue. ${\ displaystyle N (1-R)}$${\ displaystyle Nc / 4}$

The probability of surviving the interval from to without a credit event occurring is . That of a credit event at the same interval . The calculation of the present value, on the assumption that the respective discount factors to be added, is given by ${\ displaystyle t_ {i-1}}$${\ displaystyle t_ {i}}$${\ displaystyle p_ {i}}$${\ displaystyle 1-p_ {i}}$ ${\ displaystyle \ delta _ {1}}$${\ displaystyle \ delta _ {4}}$

description Cash value premium payment Cash value compensation payment probability
Credit event at the time ${\ displaystyle t_ {1}}$ ${\ displaystyle 0 \,}$ ${\ displaystyle N (1-R) ​​\ delta _ {1} \,}$ ${\ displaystyle 1-p_ {1} \,}$
at the time ${\ displaystyle t_ {2}}$ ${\ displaystyle - {\ frac {Nc} {4}} \ delta _ {1}}$ ${\ displaystyle N (1-R) ​​\ delta _ {2} \,}$ ${\ displaystyle p_ {1} (1-p_ {2}) \,}$
at the time ${\ displaystyle t_ {3}}$ ${\ displaystyle - {\ frac {Nc} {4}} (\ delta _ {1} + \ delta _ {2})}$ ${\ displaystyle N (1-R) ​​\ delta _ {3} \,}$ ${\ displaystyle p_ {1} p_ {2} (1-p_ {3}) \,}$
at the time ${\ displaystyle t_ {4}}$ ${\ displaystyle - {\ frac {Nc} {4}} (\ delta _ {1} + \ delta _ {2} + \ delta _ {3})}$ ${\ displaystyle N (1-R) ​​\ delta _ {4} \,}$ ${\ displaystyle p_ {1} p_ {2} p_ {3} (1-p_ {4}) \,}$
no credit event ${\ displaystyle - {\ frac {Nc} {4}} (\ delta _ {1} + \ delta _ {2} + \ delta _ {3} + \ delta _ {4})}$ ${\ displaystyle 0 \,}$ ${\ displaystyle p_ {1} \ cdot p_ {2} \ cdot p_ {3} \ cdot p_ {4}}$

The probabilities , , and are from the Credit Curve (this includes the Running spreads for different maturities as well as the up-front payment), the swap curve and the recovery rate determined in advance. The riskier the underlying debtor, the higher the probability of default and the values ​​of the credit curve. ${\ displaystyle p_ {1}}$${\ displaystyle p_ {2}}$${\ displaystyle p_ {3}}$${\ displaystyle p_ {4}}$

To obtain the present value of the CDS, the present values ​​of the individual CDS outputs are multiplied by the probability of each output and then added.

 ${\ displaystyle PV \,}$ ${\ displaystyle = \,}$ ${\ displaystyle (1-p_ {1}) N (1-R) ​​\ delta _ {1} \,}$ ${\ displaystyle + p_ {1} (1-p_ {2}) \ left [N (1-R) ​​\ delta _ {2} - {\ frac {Nc} {4}} \ delta _ {1} \ right ]}$ ${\ displaystyle + p_ {1} p_ {2} (1-p_ {3}) \ left [N (1-R) ​​\ delta _ {3} - {\ frac {Nc} {4}} (\ delta _ {1} + \ delta _ {2}) \ right]}$ ${\ displaystyle + p_ {1} p_ {2} p_ {3} (1-p_ {4}) \ left [N (1-R) ​​\ delta _ {4} - {\ frac {Nc} {4}} (\ delta _ {1} + \ delta _ {2} + \ delta _ {3}) \ right]}$ ${\ displaystyle -p_ {1} p_ {2} p_ {3} p_ {4} (\ delta _ {1} + \ delta _ {2} + \ delta _ {3} + \ delta _ {4}) { \ frac {Nc} {4}}}$

literature

• Darrell Duffie, Kenneth J. Singleton: Credit Risk: Pricing, Measurement, and Management . Princeton University Press, 2003, ISBN 0-691-09046-7 .
• Phillip J. Schönbucher: Credit Derivatives Pricing Models: Models, Pricing and Implementation . Wiley Finance Series, May 2003, ISBN 0-470-84291-1 .