Contents

CDR Liquid Index data as at 27 February 2007

Source: Credit Derivatives Research

CDR Liquid Indices
The CDR Liquid indices represent the CDS levels of the most-liquid names in their respective markets and ratings classes. Liquidity is measured by the number of bid-offers a credit receives. Index values are simple averages of on-the-run five year CDS levels.

CDR Global Market Depth™
The CDR Global Market Depth Index is a daily measure of how many names are actively traded. Liquidity is measured by the number of bid-offers a credit receives. Index values are counts of the number of names that exceed CDR's Liquidity Floor.

CDR Global Market Activity™
The CDR Global Market Activity Index is a daily measure of activity within the global CDS market. Liquidity is measured by the number of bid-offers a credit receives. Index values are simple averages of total bid-offers of all names that exceed CDR's Liquidity Floor multiplied by CDR's Global Base Liquidity Constant.

CPDOs being cranked up

Floodgates set to open as CPDO issuance comes back on the agenda

Bankers are now re-starting their CPDO-related activities in anticipation of the end of the rating agency-enforced hiatus (SCI passim). While there is no official move from the agencies, some banks have already begun to market new deals.

"It's beginning to be a more reasonable thing to do, but still a little bit aggressive versus where the rating agencies actually are. However, we are getting to a point where these trades are actually going to come to market," says one structurer.

Moody's is understood to have released some new assumptions in connection with its CPDO ratings methodology, although a spokesperson at the agency says that there has not yet been any official change in the firm's position. Those assumptions are now being input into banks' CPDO models and all fifteen banks that had previously been working on CPDOs are believed to be utilising them to establish what is now possible with the product.

"Some banks were out early with transactions and have re-circulated presentations, while everyone else is working on them," confirms one dealer. "Overall, you are going to see a flood of deals hitting the market again and it will be interesting to see how investors differentiate between them and how many of them end up getting printed, as there will perhaps be an oversupply of the product," he adds.

Fitch and S&P are believed to be further behind in the process than Moody's, so the first new CPDOs are likely to be single agency rated at first. "I would expect to see a whole bunch of Moody's deals coming out and those that are brave may tack on a speculative S&P and Fitch targeted rating without knowing whether or not they have it at the point at which they begin marketing," the dealer says.

The structurer suggests that there will, however, be a wide variety of types of new CPDO on offer. "Some people will either not have the relationships or simply make the decision that it's best just to go out with a mechanical deal – a variation on the previous product just using the new rating agency methodology. But others will come out with managers offering an index-based product where the manager can control the roll of the indices and go long or short single names, and some will go for a bespoke portfolio where the CPDO references a static pool or a managed one," he says.

The structurer argues that each type of deal has its pros and cons, so it is likely that there will quickly be examples across the spectrum. "Something in the middle makes most sense to me – a managed index position – but some will go for the straight index position because it is cheapest to manufacture. And others will offer a product with a managed bespoke position, as it will give the most diversification but is also probably going to be the most expensive to construct because there is less liquidity in the bespoke single name market than in the index market."

Whatever firms go for, the rating agencies will need to be comfortable that their second generation models are able to cope with the structures being proposed to ensure there is no further market freeze. "I think they will be happy with most of what's currently being put together, but if some bank comes up with a structure where outsized spreads are being generated, they might take another look at their methodology in that context," the dealer warns.

MP

Taste of CCOs to come

New deal a sign of impending increase in commodities-based issuance

Credit Suisse International has begun marketing a synthetic collateralised commodities obligation (CCO) – the US$200m SIRENS Series 2007-2 transaction. The new deal is a precursor to the increasing volume and globalisation of such structures.

The deal has two tranches of triple-A notes – US$100m Class As due 20 March 2012 and US$100m Class Bs due 20 March 2010 – rated by Derivative Fitch. It references a diverse pool of 17 commodities through a portfolio of 100 long and 100 short trigger swaps, and follows in the footsteps of a handful of public deals and considerably more private ones seen in the past year or so.

But there are more CCO transactions to come, according to Lars Jebjerg, senior director at Derivative Fitch. "Since towards the end of last year we have had a good volume of enquiries on CCOs. Obviously, there are always a few deals that never come through, but we would expect to rate more in the reasonably near future. We are already talking to a number of arrangers that will in all likelihood issue CCOs in the next three months or so."

SIRENS is also an indicator of the increasingly global appeal of CCOs, being arranged out of Asia. "Originally it was very much a London market, but there is now significant interest in Asia – and New York has also picked up on the structures as well. So, for this deal we had to develop a pan-regional approach, with work being done out of our Beijing, London and New York offices," explains Jebjerg.

Investors in the product are expected to come from around the world too. A large proportion of SIRENS is expected to be snapped up by European institutional investors, whereas anecdotal evidence suggests that previous CCOs had been dominated by an Asian investor base.

At closing, Credit Suisse International will enter into commodity trigger swaps with the issuer. The commodity trigger swaps (CTS) are based on the provisions of the 2005 ISDA Commodity Definitions. The portfolio comprises 100 European CTS transactions each referencing a single commodity, in respect of which the issuer sells a CTS with a predefined trigger level to the swap counterparty (the long portfolio) and a portfolio of 100 European CTS transactions each referencing a single commodity in respect of which the issuer buys a CTS with a predefined trigger level from the swap counterparty (the short portfolio).

The proceeds from the note issuance will be invested in triple-A rated collateral. The issuer will pass on all interest earned on the collateral to Credit Suisse. In return, the bank as swap counterparty will fund the quarterly interest to noteholders.

The principal of the notes will be reduced at maturity if the total net loss to the portfolio is greater than the available credit enhancement. Any losses caused by long triggers could be offset by short triggers where applicable. A 15% credit enhancement for the Class A five-year maturity tranche and a 10% credit enhancement for the Class B three-year maturity tranche has been provided for the transaction.

MP

Property boom?

US, Asian and European initiatives continue to appear

Notwithstanding the continued heavy pressure on the US sub-prime mortgage market, property remains a key area of focus for those involved in the structured credit markets. Consequently, real estate products look set to continue to proliferate.

The long-awaited launch of standardised property CDS in the US (see SCI issue 10) is understood to be very close, though no official announcement has yet been made. Meanwhile, ABN AMRO and Sun Hung Kai Financial have executed the first-ever Asian property derivative based upon Hong Kong residential properties. The Asia deal follows on from a growing number of such trades seen in the UK and to a lesser extent continental Europe.

Neither property CDS nor property swaps are expected to emerge as direct competition for ABS-based property structures, however. "Property derivatives and instruments such as ABX or CMBX are very much complementary products. You can use them both to take general or specific views, but they are different enough to be unlikely to encourage arbitrage between them," says one dealer.

Indeed, the development of synthetic indices for the commercial mortgage-backed securities market in Europe (see SCI issue 21) continues to move forward. There is not yet a confirmed timeframe for their launch, but it remains targeted at Q2 this year.

Rob Ford, MD of European ABS trading at Barclays Capital, says: "Everyone in the market is now very much on board and wants the same things to happen. There now just remain legal and documentation issues to be resolved."

To this end, all of the 20-plus dealers who will contribute index pricing and trade the proposed four European CMBX indices are pushing ahead with their internal legal requirements, as well as with market-wide discussions. "We continue to be in dialogue with ISDA in combination with the other people who will be involved in the business, such as Markit on such matters as defining a final version of the standard terms for a European CDS of ABS PAUG format - which is a pre-requisite for the creation of the index product - as well as the standard form of confirmation for the index itself," explains Ford.

When the European CMBX index does arrive, it is hoped that the breadth of coverage of the indices will ensure that it doesn't suffer the current difficulties faced by the ABX.HE products. "ABX is being driven by people who can afford to push it and push it, but that wouldn't be the case if there were enough index constituents to attract natural investors. What's unfortunate is that - having worked to create a product which promotes more liquidity by restricting the number of reference obligations - ABX has ended up as one that generates less," concludes the dealer.

MP

Pioneering reinsurance CDO launched

Risk management vehicle for reinsurer expected to be the first of many

Société Générale has launched the debut European synthetic CDO of insurance and reinsurance companies – Merlin CDO I. Arranged for Hannover Re, the transaction provides credit protection on a portfolio with a notional size of €1bn, comprising of 99 reference entities.

A total of €95m of notes rated triple-A, double-A, single-A and triple-B by S&P will be issued with a scheduled maturity of five years and a legal maturity of six years. The notes cover losses to the portfolio of €95m in excess of the €60m first loss retained by Hannover Re.

"Working with S&P we have been able to determine specific correlation and default assumptions that mean the CDO methodology can be applied to a portfolio consisting solely of insurance and reinsurance entities," comments Billy Radicopoulos, director in the cash CDO team at Société Générale.

A fixed recovery rate of 35% provides transparency for investors, and a simple payout mechanism for Hannover Re. Credit event definition covers insolvency, bankruptcy and inability to pay reinsurance debts. It ensures that the cover is appropriate for Hannover Re, while providing a clear and simple loss mechanism for investors.

"A key challenge was to define a credit event that is meaningful for Hannover Re and is clear for investors. By combining our expertise of the insurance industry and capital markets, we have found a solution that provides an effective risk management tool for insurers and reinsurers and an attractive, diversifying asset for investors", adds Clare Hennings, md in charge of insurance products at Société Générale.

The book of European and Asian investors that participated in the transaction was characterised by financial institutions attracted by the benefit of exposure to the insurance and reinsurance industry. These investors were predominantly comprised of banks and fund managers who had not had prior exposure to the sector.

"As part of [our] approach to insurance capital optimisation (regulatory, rating, economic capital), the Merlin approach can be tailored for other insurers and reinsurers: some will transfer the majority of the risk to the capital markets to improve economic capital, some will transfer only part of the risk, while others will concentrate on placing the super senior tranches as an alternative to cat bonds or systemic risk protection. It is therefore an extremely powerful tool," concludes David Aubin, md and head of debt capital market insurance origination at Société Générale.

There are thought to be more such transactions in the pipeline currently being considered by the rating agencies, with demand primarily being driven by entities that want to improve their capital model scores. As analysts at RBS note, such tools should boost return on equity for the insurance companies involved – although the real cost of this protection is more difficult to evaluate.

Hannover Re also recently launched a privately placed loan for US$200m which will function in the same way as a catastrophe bond and transfer some of its exposure to the sector.

MP

Operationally challenged

Vanilla CDS backlogs may have diminished, but buy-side firms still have other processing concerns

Buy-side firms continue to have concerns over credit derivatives processing, particularly with bespoke deals. In addition, poorly executed related operational services have caused some to re-assess who they deal with.

Nevertheless, some aspects of the way the credit derivatives market is dealing with operational backlogs and trade and settlement issues are deemed adequate by investors. "We have had no problems with confirming CDS transactions with the DTCC, which is helping the market move to a more paperless environment," says Everett Crawford, operations manager at Rockview Capital Management in New York.

A hedge fund manager in London concurs: "About 95% of our single-name confirms come off with no problem. There may be mismatches on ISIN numbers or updates and amendments to reference obligations, but this is a manageable risk."

Furthermore, the incorporation of ISDA standard master confirmation terms directly into the DTCC operating procedures is making it easier to process trades. This is true for some newer instruments such as CDS of ABS in the US, which have something of a track record, but is not the case with products that do not or are without standardised documentation such as CDS on CDOs or loan CDS in Europe.

Consequently, William Lavelle, coo at Credaris in London believes that operational issues have switched from vanilla to more structured instruments. "There are still significant backlogs because there is more activity in the bespoke CDS space. The majority of automated systems in the market are geared towards the single-name structure, meaning the more complex trades are still paper dependent," he says.

Lavelle notes that Credaris receives a good chunk of its structured trade confirmations and associated payments via paper and fax. "It could be easy to rest on one's laurels and say we have done a great job with single-name processing but it is a constantly evolving marketplace and it is essential that technological innovation keeps up with innovation within the actual market," adds Lavelle.

Receiving timely portfolio valuations is also an ongoing concern. However, third-party providers, which are often able to provide valuations in a matter of days, have contributed much to alleviating this concern and accelerating the reporting process.

Another bone of contention is that firms do sometimes still receive statements that include other managers' portfolios. "This is far from ideal. As a result we are increasingly focusing our trading activity on those banks which treat their valuations group as a client servicing function," Lavelle says.

Some firms have factored OTC derivatives into their broker review process which has resulted in changes to the counterparties they deal with, notes Sunil Chadda, head of the hedge fund and derivatives practice at consultancy Citisoft in London. "Investors require a fully rounded service especially with complex highly risky instruments and they are moving their business elsewhere if firms won't play ball and confirm and settle in a timely fashion," he says.

Rockview is one such firm that has voted with its feet, switching its administration duties from one bank to another to gain a better service. "We integrated with another fund administrator's system to receive better reconciliation and monitoring of our securities," says Crawford.

Citisoft's Chadda believes that a lack of strategy and investment in infrastructure for processing OTC derivatives is constraining fund management and hedge fund companies from scaling their derivatives capabilities. "Many are looking for solutions but investment is needed. The effect of this it that it is limiting front-office innovation, adding to costs and increasing operational risk," he says.

He adds that a number of buy-side firms trading credit and OTC derivatives in volume still do not have ISDA documentation management systems in place. "Some include this into their trading systems so only Isda-compliant trades can be traded and receive electronic sign off, but many do not have such systems, which increases risk and time to trade," says Chadda.

HD

McEneny joins Lloyds TSB

The latest company and people moves

McEneny joins Lloyds TSB
Credit derivatives law specialist Greg McEneny has joined Lloyds TSB Corporate Markets as head of legal, products & markets. He was previously legal counsel, credit trading & distribution at the Royal Bank of Scotland.

Citi adds to exotics
Tejasvi Mohanram has left his position as exotics correlation trader at Deutsche Bank and will be joining Citigroup as vp, to trade exotic products in credit correlation. He reports to Keith Crider, head of European credit correlation.

Cournot expands
Frank Iacono, who joined Cournot Capital as ceo last year from Lehman Brothers, has hired a number of staff to the credit derivatives product company (CDPC) and is looking to add more. The Morgan Stanley offshoot will act as a principal investor in structured credit, via special purpose vehicle Cournot Financial Products, and is beefing up staffing levels to broaden its product offering.

RBS doubles up
Steve Hewlett has left Lehman Brothers to join RBS. He is understood to have been hired to run the UK bank's ABS and CDO distribution business. Also, it is understood that Paul Ashcroft has left Bear Stearns to join RBS in CDS flow trading.

Huang goes to Highland
Highland Financial Holdings Group has hired Sheila Huang, as director and portfolio manager of the firm's high-grade strategies. Huang joins from Credit Suisse Asset Management, where she was MBS portfolio manager and responsible for all MBS security selection and trading. The firm expects to add at least seven additional positions in the investment team and back office to support its growth in 2007.

HVB hires Kitzmüller
Agnes Kitzmüller has joined the credit strategy and structured credit team of Unicredit MIB's global credit research from Pioneer Investments where she was a portfolio manager for ABS. At MIB she will be responsible for structured credit research and reports to Jochen Felsenheimer, head of credit strategy and structured credit.

Codefarm and Fitch team up
Codefarm has signed an agreement with Derivative Fitch to enable customers of Codefarm's Galapagos Structurer product to have the option of using the semi-analytic and Monte-Carlo Gaussian copula CDO models from Fitch's RAP CD pricing and risk analytics platform for CDOs. This incorporates the former Reoch Credit Pricing Model library which was acquired by Derivative Fitch in July 2006.

The library covers a wide range of structures including CDO, CDO^2, long/short, variable subordination, zero coupon and forward starting, and is based on semi-analytical and Monte Carlo factor models calibrated from the observable index tranche market.

Wachovia promotes Asian structured credit head
Wachovia Securities has promoted Yu-Ming Wang to head of fixed income Asia. In this newly created role, Wang will execute the firm's corporate business strategy and manage all fixed income origination, distribution, and trading as the Fixed Income Division's senior leader in Asia. He will be based in Hong Kong.

Wang will report to Curtis Arledge, head of fixed income in this new role. Wang is currently an md and head of structured credit products for Wachovia Securities. In addition to his new role, Wang will maintain his current responsibilities, reporting to Tom Wickwire, head of structured products.

HD & MP

Euromax VI on the road

A round up of this week's structured credit news

Euromax VI on the road
Collineo Asset Management is bringing a new CDO of ABS that aims to take advantage of the currently beneficial markets in mezzanine ABS. The deal, Euromax VI, is being marketed by joint-lead managers Citigroup and UniCredit (HVB).

Euromax VI ABS Ltd is a €425m refinancing of Euromax I and Euromax II. Consequently, the combined portfolios of Euromax I and II plus a number of additional assets will constitute the initial portfolio for Euromax VI. That portfolio initially will be made up of 64.8% RMBS, 29.1% CMBS and 6.1% ABS CDOs.

The transaction, rated by Fitch and S&P, will offer six classes of notes. They range from €333m of Class A triple-A rated notes to €3m of double-B Class Es, plus €20m of unrated subordinated notes.

The thinking behind the deal was straightforward, according to a banker close to the transaction. "There were call dates due for Euromax I and Euromax II around now and later in the year, and current market conditions mean cheaper funding compared to 5 or 6 years ago," he says.

Euromax VI is not the only CDO of ABS underway looking to access current attractive spreads, but the banker believes it has some key advantages. "It will be 100% ramped from the outset so there will be no chance of the market moving against the manager in the deal's early days; and the collateral is of higher quality than other deals – non-conforming RMBS as well as CDOs are restricted to 10% each, for example; and assets are generally subject to a double-B minus minimum."

Furthermore, he says: "The assets are 100% European and euro-denominated, so the deal offers a rare opportunity to invest in pure European mezzanine ABS. Finally and most importantly, Collineo has a strong track record in this type of transaction going back to 2001."

Euromax VI is expected to close in April. It is being marketed to a wide range of investors and the leads will be roadshowing the deal for the next two weeks in Europe, the Middle East and Asia.

S&P launches new version of Accelerator
S&P Ratings Services has launched the latest version of its synthetic CDO tool, CDS Accelerator. Incorporating the same methodology used in the S&P synthetic CDO ratings process, CDS Accelerator is intended to enable managers, investors and structurers to quickly and efficiently determine the risk profile of potential or actual transactions.

"Since CDS Accelerator was first launched in December 2005, its development has been guided by close collaboration with the CDO community. The emphasis in this latest version has been placed on incorporating the growing needs of CDO managers and their credit teams in today's increasingly complex global structured markets," says md in the CDO team, Pat Jordan.

The key enhancement of CDS Accelerator 2007 is the addition of scenario analysis reporting. Users can define their own stress-test scenarios from a greater number of fields. "Using consistent, objective measures of credit quality, the results allow ever-more sophisticated transactions to be easily compared with each other," Jordan adds.

Other improvements that have been made to the latest version of the tool include the introduction of a rating change report and historical rating analysis. In addition, ABS-referenced assets have been extended to include the US, starting with US home-equity loans, which makes the tool ideal for stressing CDOs of ABS portfolios and assessing the effect of making substitutions, according to Jordan.

Bumper year ahead for SIVs
A report on the global SIV market published by S&P says that another bumper year is expected for the sector in 2007, following record growth in 2006. The key factors behind this record-breaking increase have been the emergence of new vehicles, while others have sought to strengthen their position by increasing their portfolio sizes, according to credit analyst Stephen Wallis.

"There were four new entrants into the market throughout 2006: Kestrel Funding, Vetra Finance, Zela Finance and Hudson-Thames Capital – bringing the total number of vehicles that we rate in Europe to 23," Wallis continues.

"This trend will likely continue in 2007 and we can only expect further growth, probably on the same scale as last year, leading to each manager seeking new ways to enhance investor returns," he concludes.

Servicing US CREL CDOs deviates from the norm
The role of servicers in US CREL (commercial real estate loan) CDOs is still evolving and is far from being standardised, according to Fitch in a new report. CREL CDO issuance has grown exponentially in recent years because of its ability to accommodate commercial real estate loans that weren't otherwise securitisable through a CMBS REMIC structure.

According to Derivative Fitch md and CRE CDO group head Jenny Story, this creates more unique servicing challenges in the process. "The high-touch nature of the loans and changing collateral composition of CREL CDOs make it that much more challenging to service the portfolios underlying these deals," says Story.

Whereas CMBS servicing is delineated between primary, master and special servicers and is fairly standardised due to the maturity of the industry, the role of the servicer in a CDO is anything but standardised. "Servicers should be sure to determine their role up front when pursuing servicing assignments for CRE CDOs," says Fitch senior director Richard Carlson. "Servicers should look to their core competencies to determine which additional functions are most likely to add value to an asset manager's platform."

Asia Pacific CDOs hit by global factors
Moody's first annual study of Asia Pacific structured finance rating transitions finds that overall ratings for the instruments in the region show greater stability than global trends. However, CDOs have suffered more downgrades than any other securitisation asset class.

In 2006 Moody's did not downgrade any CMBS, RMBS or ABS, while the only downgrades – a total of 17 – were restricted to CDOs. Explaining the synthetic arbitrage CDO downgrades, Debjani Dutta Roy, a co-author of the report, says: "The performance of CDO securities often relates to changes in global credit market conditions, whereas that of non-CDO securities is mostly driven by changes in local economic conditions."

The heightened downgrade activity evident for the CDO segment was highly correlated to an increase in the global corporate downgrade rate, which rose to 8.9% in 2006, from 8.3% in 2005 and 8.1% in 2004, adds Roy.

MP

Trading ideas - diving in

Dave Klein, research analyst at Credit Derivatives Research, looks at a negative basis trade on Devon Energy Corp

Our survival-based valuation framework – which implicitly judges how rich or cheap bonds are to the CDS curve – allows us to screen our universe of CDS tenors and bonds for the cheapest bonds. On this occasion it suggests a negative basis trade on Devon Energy Corp (DVN).

Based on this approach DVN's 6.875's of Sept 2011 bond is about US$0.40 cheap to fair value. Exhibit 1 indicates the 'price-based' term structure of DVN and indicates that both of DVN's bonds are trading cheap.

Exhibit 1

DVN is active in the credit derivative markets and has liquid cash bonds. We do note that Devon Financing Corp. is the issuer of this bond and we advise clients to have the bond declared a deliverable for the CDS in this package.

Even if this is not achieved, the bond and CDS have traded with a high degree of correlation (as we shall see below in Exhibit 3). Additionally, make sure to choose the 6.875's of Sept 30 2011 and not the 7.25's of October 1 2011 (an Ocean Energy issue).

Based on our analysis of bond cheapness and market activity, the 6.875's of September 2011 is viable for the long bond leg of our negative basis trade. We must now look at the actual spreads to judge whether we are actually trading at a negative basis, and, maybe more importantly, can position ourselves with positive carry.

Comparing the bond z-spreads (for the active bonds) with the CDS term structure, Exhibit 2 shows that the bond is indeed trading wide of CDS. Importantly, we must note that the bond is trading wide of its interpolated maturity-equivalent CDS (five year) which reflects our second basis adjustment discussed above.

Exhibit 2

The DVN CDS curve is 'well-behaved' and has no serious inflexion points. There is also good liquidity in the five-year on-the-run maturity. Additionally, we see solid two-way pricing on Bloomberg's ALLQ screens for the 6.875's of September 2011.

Given that we have identified the DVN 6.875's of September 2011 bond as trading cheap to the CDS market (from our survival-based framework) and its z-spread as being wide of on- and off-the-run CDS levels, we must ensure that we account correctly for any premium or discount that the bond is trading at.

As seen in Exhibit 3, the basis between five-year CDS and the Sep 2011 bond has been both negative and positive over the past year. The bond sold off a bit in November and, although both securities have rallied, the basis remains nears its lows. 

Exhibit 3

As discussed previously, we must adjust for the impact of loss given default differences between the bond and CDS market. This maximum 'gearing' effect is translated into our adjusted basis and carry calculations. At current levels, the package has a raw basis of -12 basis points, and a positive adjusted carry of 10 basis points.

Over the hedge
There are two significant risks that need to be hedged in a bond-CDS negative basis trade. The first is default, which can be accounted for primitively in the adjustments we suggested previously to the CDS leg notional amount. In a perfect world, we would suggest frequent re-hedging of the CDS leg to account for changes in the bond price, but this is impractical in reality.

The approach most frequently used by practitioners is to hedge based on the price of the bond. A bond trading at USUS$110 would mean we buy 1.1 times the notional protection as we bought face value of the bond. A bond trading at US$90 would mean we buy 0.9 times the notional protection as we bought face value of the bond. This approximation is, somewhat surprisingly, close to optimal in terms of a single CDS static hedge.

This default risk hedge amount – based broadly on the bond price change – is important to understand in that if the bond is trading a premium (over par) then we will be over-hedged in the CDS as the bond pulls 'down' to par over time. Correspondingly, if the bond trades at a discount (under par) then we will be under-hedged as the bond pulls 'up' to par as maturity approaches.

We have seen different approaches discussed as to how to solve this dilemma but we prefer to 'keep it simple'. A practical approach is to hedge the bond's default risk with the most liquid (and closest in maturity) CDS according to the average of current and final bond price adjustments.

Our initial hedge amount should be based on a minimisation of expected loss in default– we calculate the initial hedge as (Bond Price – Recovery)/(Par – Recovery). For a bond trading at US$110 and assuming a 40% recovery, the initial hedge amount should (110-40)/(100-40)=117%. We should buy US$11.7m protection for each US$10m of face value bond we buy.

This hedge will, obviously, be over-hedged as the bond pulls to par at maturity. We would want to hold a 100% weighting in the CDS as we get close to maturity. So we simply average our initial and final hedge amounts – (117-100)/2= 108.5% - to arrive at our 'simple' initial hedge. We therefore buy US$10.85m protection for each US$10m of bond face value we buy. This hedge is, on 'average' our most optimal hedge.

We have a slightly more directional perspective on this hedge. Given that we are basically hedging the impact of default on our position, if we felt strongly that the credit was unlikely to default, then we would prefer to receive more carry for more default risk. Vice versa, if we felt that fundamentals were weakening and the credit was more likely to default, then we might prefer to be slightly over-hedged.

Utilising Gimme Credit's Credit Scores – which reflect the fundamental outlook for the issuer, we adjust our single CDS hedge. If the outlook is improving then we will prefer to hedge only 100% of face value to maturity. If the outlook is deteriorating then we would hedge at our maximum current hedge amount (117% in our example). If the outlook is stable then we will choose our mid-point optimal hedge (108.5% in our example).

Once this hedge is put on, we will monitor bond price levels and default risks to ensure that our hedge is still 'close' to default neutral. This is more reasonable than adjusting frequently and paying the bid-offers, and even more importantly can often provide more carry in the short-term on a credit that is a low default risk.

In our specific trade today, the bond is trading at US$106.00 (best ask) and so our maximum hedge would be (106.00 – 40)/(100-40) = 110%. Given our stable fundamental outlook for DVN, the optimal hedge would be 105%. In reality, it is often difficult to transact in odd lot size, and given the minimal differential between our optimal hedge and face value, we feel it is more realistic to assume a 100% hedge and be slightly under-hedged.

Adding in mid-dated CDS to balance the hedge is possible and we are happy to discuss the use of a second CDS position with any investors who prefer to be more 'perfectly' hedged. Since the bond matures about 6 months before the current five year on-the-run CDS maturity and is trading above par, we suggest the single CDS to bond 100% hedge and a less frequent but vigilant re-hedging programme. We can generate a forward-based price projection for the bond based on the CDS curve – to show how we expect the bond price to drop (premium) or rise (discount) until maturity – which may help some investors with their hedging strategies.

The second (and often overlooked) hedge is the simple interest rate hedge on the bond. Our basis trade is positioned to benefit from any convergence of the credit risk perspectives of the cash and CDS markets and further, the bond is cheap on the basis of its CDS curve (only credit-risk based).

We therefore must ensure that our bond is hedged against interest rate movements and the impact these will have on the price of the cash instrument. Note that the CDS is exposed to interest rate movements but only in the discounting of cashflows and this interest rate sensitivity is minimal (and we ignore it in this case).

Investors could choose to asset swap the bond to minimise the interest rate sensitivity but we suggest otherwise. The asset swap has a number of shortcomings (not the least of which are lack of liquidity, premium/discount bond price errors, and default cash flow timing mismatches). We suggest buying the bond outright – benefiting from the most positive carry – and hedging interest rate risk on a portfolio basis.

We assume that many investors will not be carrying a single bond exposure and therefore it is more efficient to manage overall interest rate risks in a portfolio context. Also, assuming that investors will be over-, or under-weight issuers against their bogeys (in the traditional fixed income shops), this portfolio-based interest rate risk management allows for a more direct allocation of funds that reflects the interest rate 'view' of the manager.

Given the cheapness of DVN's bonds, relatively wide basis and positive carry of our overall position, we suggest this negative basis trade (long bond and long protection) as a default-neutral way to pick up 12 basis points and more importantly potentially realise the bond's relative value differential.

Risk analysis
This position is close to default-neutral and spread duration-neutral. There is a slight maturity mismatch since the bond matures in a bit less than five years. This does not concern us as we expect convergence long before our CDS position matures.

We do, notably, understand that many investors would still prefer to understand the interest rate risks associated with this position. Exhibit 4 shows the overall and key-rate sensitivities for the bond that can be used to specifically hedge any residual interest rate risk and offers the investor some more insights into the price sensitivities of the position. 

Exhibit 4

The trade has moderate positive carry – given the current levels. This carry cushion protects the investor from any short-term mark-to-market losses.

Entering and exiting any trade in these maturities carries execution risk, but this is not a major risk with DVN CDS in this maturity as it is increasingly liquid. Our largest concern is execution in size in the bond markets.

Liquidity
Liquidity is a major driver of any longer-dated trade – i.e. the ability to transact effectively across the bid-offer spread in the bond and CDS markets. Our data on liquidity, created from the volume of bids, offers, and trades we see each day, provide us with significant comfort in both the ability to enter a trade in DVN and the bid-offer spread costs.

DVN shows good liquidity in the five-year maturity and bid-offer spreads are narrowing to around 3 basis points. Recent bids and offers (seen on Bloomberg's ALLQ) for the September 2011 DVN bonds have shown good availability in both directions. We recommend the bond leg of the basis be worked first, looking for a price below US$106.37 (our model fair-value).

Fundamentals
While this trade is technical in nature and not necessarily impacted by fundamentals, we must confirm there are no surprises in the short-term that could cause divergence between cash and CDS markets such as LBOs or major M&A activity. The trade is based on the bond market being mispriced relative to the CDS curve, rather than an expectation of general curve movements.

Summary and trade recommendation
Although DVN missed its numbers this past quarter, both its CDS and bonds have tightened significantly since the autumn. With CDS leading the rally, the traditional z-spread-to-CDS raw basis is negative and our 'curve and bond price'-adjusted basis remains negative and shows positive carry.

Given a stable fundamental outlook, we feel a default-neutral negative basis trade is an excellent opportunity to earn modest carry while waiting for the bonds to converge to fair value. With market realities, and the bond trading reasonably close to par, we recommend a slightly under-hedged basis package using a single CDS static hedge to pick up 12 basis points of carry.

Buy US$1m notional Devon Energy Corp. 5 Year CDS protection at 16bps and

Buy US$1m notional (US$1.06m cost) Devon Financing Corp. 6.875% of September 2011 bonds at a price of US$106.00 (z-spread of 28bps) to gain 12 basis points of positive carry.

For more information and regular updates on this trade idea go to: www.creditresearch.com

Copyright © 2007 Credit Derivatives Research LLC. All Rights Reserved.

Note: This article is intended for general information and use and does not constitute trading advice from Structured Credit Investor (see also terms and conditions, below, section 12).

Credit default swaps - part 1

This, the first of a two part primer by Michael Hampden-Turner, Panayiotis Teklos, Michael Sandigursky, Hans Lorenzen, Matt King and Peter Goves of the European quantitative credit strategy and analysis group at Citigroup, looks at CDS contracts and their valuation

By any benchmark, the recent growth of credit derivatives has been remarkable, developing from a niche to a highly liquid OTC market within a few years. As Figure 1 illustrates, the International Swaps and Derivatives Association (ISDA) estimates that, as of July 2006, the CDS market has US$26tr contract notional outstanding, having grown more than seven times in the last three years.

Figure 2 illustrates how single-name and index CDSs make up the bulk of this volume, outstripping the underlying cash market on which the derivatives are written. The evolution continues with interest now sufficient for the most liquid of CDS contracts to become exchange-traded on Eurex in March 2007.

There are a number of factors behind this growth rate:

Firstly, the flexibility of credit derivatives has revolutionised a large and idiosyncratic market for investors. CDSs typically offer greater liquidity and flexibility than underlying cash instruments, such as bonds issued by the same credit entity. Investors can go long or short any maturity and in any currency they choose, regardless of actual bond issuance in the underlying entity. The market is standardised to aid liquidity while still accommodating bespoke trades. As physical assets are no constraint on traded volumes, the notional of CDS contracts on a single entity is typically a substantial multiple of the outstanding debt on the same name.

Secondly, this growth has been rapid in part because it has benefited from the expertise and infrastructure that was created by the growth of other derivatives markets, such as interest rate swaps. Many institutions that started to trade CDS in the late 1990s had already invested in trading, risk management, accounting and operational systems for interest rate swaps (IRSs). Many of the same processes were required for a CDS business and many financial institutions were able to benefit from what was already in place. This inherited advantage helped to facilitate the rapid development of the CDS market.

What are some of the other reasons CDSs have become so popular? Better liquidity and increased flexibility are important, but the main thrust behind the exponential pickup are the new types of trading strategies and products that derivative instruments facilitate in what was previously a long-only market. CDSs enable investors to take quite specific views on names without foreign exchange (FX) or interest rate exposure, name by name or to a whole portfolio.

It is this ability to take exposure to whole portfolios of credit quickly and efficiently that was a huge step forward. For example, CDS indices such as iTraxx in Europe and CDX in the United States enable investors to hedge/take credit risk to a diversified portfolio of 125 investment names in a single trade. Bid-offer spreads in these index CDS markets are typically as low as 0.25bp in sizes up to US$200m.

The liquidity in these indices facilitates structured credit that allows investors to take bespoke diversified credit exposure. For example, an investor can take leveraged exposure to well-rated credits or de-leveraged exposure to risky names.

Structured credit enables a much greater precision in the balance between risk and reward. Therefore, many more investors can take exposure to whole new areas of credit that previously would have been too risky, or not risky enough.

Many more investors can access a much broader spectrum of credit in a manner that exactly matches their risk appetite. It is this matching of lenders and borrowers that has been revolutionary. Single-name and index CDSs are the building blocks of structured credit and therefore structured credit helps to drive volume in the CDS market.

Barriers to understanding how CDSs work are much less substantial than many investors typically assume. The primary mechanics are quite similar to the bond or IRS markets: yield curves, discounting cash flows and concepts of duration, for example. As with many areas of finance, simplicity of the product is somewhat obfuscated by the use of jargon and some of the detail, but we hope that this primer will help lighten the burden by explaining some of these features in an accessible manner.

Product overview

A CDS can be thought of as an insurance policy on a risky asset. CDS investors talk about buying and selling protection on names. Buying protection on a bond insures the CDS holder against loss owing to default on that name (or, more accurately, a default among a pool of eligible reference assets on that name).

In the case of default, the protection holder delivers the defaulted bond to the seller and receives the par value of the asset (traditionally, CDSs have been a physically settled derivative, but contracts increasingly specify the cash equivalent of this transaction). In return, the buyer pays the seller regular premia (fixed at inception) for this protection. This payment is expressed as a notional spread in basis points and is paid quarterly in arrears over the pre-agreed-to life of the CDS contract or until a default event occurs.

A CDS is a bilateral contract between two parties and it cannot be broken without compensation. Therefore, the net present value (NPV) is dependent on the cost of cancelling or hedging the CDS. As a result, CDS contracts are also a hedge against a deterioration of credit quality. If an investor buys protection when spreads are tight, it will become more valuable as spreads widen. Therefore, a CDS can be used to hedge mark-to-market (MTM) changes of a bond (because of credit spread change) or as a vehicle to take a credit view in its own right.

Unwinding a CDS before maturity
There are three ways to unwind a CDS before the maturity of the contract (similar to an IRS).

Termination: "Tearing up" the contract with the original counterparty has to be done with mutual agreement and requires the settlement of the MTM value of the CDS. It has the advantage of freeing counterparty credit lines, reducing operational burden and removing any further legal risk.

Novation: The CDS is assigned to a third counterparty (with MTM settlement). This is operationally more intensive than alternatives and requires all parties to consent to the arrangement.

Offsetting position: An opposite or offsetting trade is made with another counterparty. This has the advantage of being independent of the first transaction. The disadvantage is that it uses up credit lines. In addition, financial loss as a result of a legal mismatch between contracts is rare but not unheard of.

Offsetting positions, however, is the most common method of unwind — hence, the exponential growth of CDS outstanding in Figure 1.

Standardised versus bespoke CDS
CDSs are over-the-counter (OTC) derivatives and a considerable degree of customization is possible. However, highly bespoke contracts tend to hinder liquidity because bespoke CDSs have to be specially valued and are not fungible.

For example, an investor who bought protection for exactly five years and sold five-year protection after six months would end up with a maturity mismatch. For a very active investor this would soon become a highly complex mismatch. Furthermore, investors would rather trade a single liquid 5yr spread rather than a series of spreads for 5yr, 4.5yr and 4yr, for example.

Therefore, the majority of CDSs trade on standardised maturity dates to reduce this problem. However, maturity is not the only detail that requires matching: legal detail, payment frequencies and market conventions are all standardised to facilitate liquidity. Completely bespoke contracts still trade, but the liquidity of non-standard contracts is much reduced.

Maturities and premium payments are aligned by having standardised quarterly roll dates so all CDS premiums coincide. These dates are 20 September, 20 December, 20 March and 20 June. So an investor buying 5yr protection on the 10 January 2007 roll date will actually be buying protection that starts T+1 and expires five years from the next roll date — that is, 20 March 2012.

Thus, investors who want to trade names actively need to "roll" their contracts every three months. This involves simultaneously buying/selling contracts maturing — for example, 20 March 2012 and 20 June 2012. Such an exchange normally involves some MTM because of bid/offer spread, but rolls are usually reasonably efficient as desks are also keen to roll their positions.

5yr contracts are the most liquid, but all CDS maturities have the concept of "on-the-run" and "off-the-run" contracts from one to ten years. Contracts that become off the run typically lose liquidity more rapidly than other contracts and prices for them are harder to observe. Liquidity also varies considerably from name to name.

A customer enquiring about a CDS trading on standard terms might hear the following: "BAE is trading 19/21". The following assumptions about the CDS trade are made:

• The customer can buy protection for 21bp and sell protection for 19bp
•  Premia are paid quarterly in arrears on an ACT/360 basis
• The quote assumes 5yr maturity protection on the next nearest roll date
• The trade starts at T+1
• The standard market size is 10m dollar/euro notional
• ISDA 2003 documentation will be used
• The physical settlement is assumed (see next section)

CDS default events
Defaults are not necessarily as "binary" as one might initially think. Therefore, there is carefully constructed legal documentation surrounding what constitutes a credit event that can trigger the protection element of a CDS.

CDS can be either cash or physically settled — that is, either an investor is compensated for loss by a cash payment or a physical bond is delivered to the protection seller in return for par. There are a number of key terms:

A CDS is written on a reference entity, which is the corporate or sovereign entity on whose credit the contract is based. Contracts typically specify a reference obligation, issued or guaranteed by the reference entity; if none is specified then a senior unsecured obligation is assumed. However, any deliverable obligation that satisfies a set of requirements can qualify for delivery following a credit event (see the section that follows on physical settlement).

Credit events
Credit events are strictly defined by a standard ISDA 2003 agreement. The credit events for corporate names are:

• Bankruptcy: administration, winding up, dissolution, insolvency, receivership or an agreement with creditors
• Failure to pay: failure by entity to make, when due, payments equal to US$1m or equivalent on one or more of its obligations (grace periods apply)
• Restructuring: or rescheduling of payments in respect to any one or more obligations of the entity (other than in accordance with the initial terms of the obligations). The aggregate amount of obligations affected must be more than US$10m.
• Obligation acceleration¹
• Obligation default¹
• Repudiation/Moratorium¹

[1. These events are used with Asian and EM corporates and sovereigns.]

Restructuring is the most controversial of the credit events. It was introduced initially to extend CDS coverage to loans but causes a problem because of a disparity of post-restructuring asset prices. In particular, short-dated assets tend to have a higher recovery rate than long-dated assets, with a potential hedging mismatch for investors. Therefore, a number of clauses in the CDS contract have been introduced to resolve this.

Trigger events under restructuring
Modified modified restructuring (Mod Mod R): A trigger event must be followed by the delivery of an asset less than 30 months in duration (remaining). This is common in Europe.

Modified restructuring (Mod R): A trigger event must be followed by the delivery of an asset less than 60 months in duration (remaining). This is common in the United States.

Restructuring (R): A trigger event leads to delivery of an asset of any duration. This is common in Asia and Japan.

No restructuring (No R): Restructuring is not a trigger event.

Cash versus physical settlement
Once a credit event has occurred, a CDS is settled in one of two ways: a physical or cash settlement.

Physically settled CDS
The protection buyer has 30 calendar days to deliver a Notice of Physical Settlement to the seller; this should include which qualifying reference obligation will be delivered. Some qualifying assets will be cheaper to deliver (CTD) than others.

Once the notice is delivered, the protection buyer has 30 business days to choose and deliver the reference obligation.

Physical settlement has a number of "fall-backs" to force settlement in situations where obtaining deliverable paper is problematic. Sellers are able to buy in a bond on behalf of the protection buyer.

Cash-settled CDS
At one time, cash settlement was more unusual for single-name CDSs but now is increasingly common. Contracts can vary but typically the calculation agent determines the Final Price (that is, the post-default price of the deliverable obligation) at 11 a.m. five business days after the credit event. This is done through an auction process whereby the calculation agent obtains prices from multiple market makers. Cash settlement of par minus Final Price is made three business days after that.

Succession rules
Some practical issues arise when the reference entity underlying a CDS changes significantly. To counter this there are some detailed definitions of succession events. Under 2003 ISDA definitions, a "succession event" means an event of a merger, consolidation, spin-off, or any other major change in capital structure, where one entity succeeds to the relevant obligations of another entity. Relevant obligations include bonds, loans and any other type of borrowed money.

The following are some rules of thumb regarding ISDA 2003 CDS reference entity (CDS RE) succession:

• If a single entity assumes the majority (that is, greater than 75%) of the CDS RE's debt or only one entity has more than 25% of the CDS RE's debt, then the RE of the CDS contract references this new entity.
• In the case where no single entity has more than 75%, but two or more have more than 25%, then the CDS splits equally among all the entities reaching the 25% threshold.
• If an entity has less than 25% and the CDS RE survives, then there is no change to the original CDS contract.
• If an entity has less than 25% and the CDS RE ceases to exist, then the sole successor is the entity with the highest percentage of relevant obligations.

Succession can have a dramatic effect on the MTM of a CDS and has been in the headlines recently. For example, to execute divestitures or takeovers, companies often have to take out all, or effectively all, of the debt of the existing reference entity. If the new debt financing the transaction is issued out of another entity (without a cross guarantee to the original entity), or for some reason it is not eligible to become a new reference obligation, then the original CDS contract becomes "orphaned". Since the reference entity only has a negligible amount of deliverable debt assigned to it, the CDS spreads tighten substantially.

Succession issues are explored more fully in Citigroup's High-Grade Strategy group's publication A Rough Guide to CDS Succession, by Dennis Adler, Mikhail Foux and Hiedy Kim, 2 August 2006.

Counterparty risk
CDSs are subject to counterparty risk, as are many derivatives. This is the risk that the party with which one has traded fails to fulfil its contractual obligations.

For the protection buyer this means that if the counterparty and reference entity in the CDS contract default simultaneously, then the loss is potentially quite large — identical to the loss that would be occurred from holding an asset of the defaulted company.

However, counterparty risk has an impact on protection sellers as well. Protection with a large positive MTM is at risk of counterparty default as well. For example, if an investor sold protection when spreads were wide and spreads then tightened dramatically, the CDS would have a large positive MTM. If the counterparty defaults, then the investor loses the value of the future cash flow. (Protection buyers are also at risk of MTM loss when a counterparty defaults.)

CDS Valuation

Premium and protection: a two-leg structure
It is a popular misconception that the value of a CDS is highly dependent on models. Actually, much of the valuation mechanics is similar to bonds or interest rate swaps (IRSs). Credit default swaps are so named because, like IRSs, they are considered to have two "legs" or parts: a premium leg and a protection leg. Consider the following from the perspective of the protection buyer (we will note the comparison with IRSs in brackets).

• The premium (pay fixed) leg is the series of premium payments that have been agreed upon throughout the life of the transaction. The present value (PV) of this leg is calculated by discounting the future cash flow.
• The protection (receive floating) leg is the insurance on the name. No payments are received on this leg unless there is a default event. The PV of the protection leg is considered to be the probability of the default event occurring multiplied by the loss-given default.

The NPV of the contract is the difference in PV between the two legs. At inception, the NPV of a CDS should be close to zero.

The fact that the fair value NPV of an at-market CDS is zero is an important building block in helping to conceptualise the value of the protection leg of a CDS. Consider an example where one buys protection on a name at 45bp and the spread for this name immediately widens to 48bp. The market now demands 48bp of premium to protect this name — that is, the PV of the 48bp premium leg discounted back to today must equal the value of the protection leg on the CDS. Therefore, the MTM must be equal to the difference between a 48bp premium leg and a 45bp premium leg.

To gain an accurate impression of how MTM has changed over time, one needs to fully price each leg in the manner described in the next section. However, it is also possible to think of the MTM of a CDS purely in terms of a combination of a spread move and DV01 (duration or sensitivity to spread move). Bloomberg provides a tool — which has become the market standard — to help with this sort of CDS scenario analysis. The screen can be accessed by typing CDSW [Go].

The CDSW screenshot has been set up to value our previous example: a US$10m 5yr CDS that was struck at 45bp and where the current market spread has risen to 48bp. The CDSW screen calculates that the sensitivity of the CDS to a movement in spread is US$4,372 per basis point. Therefore, the deal has a positive MTM of 3*4,372 = US$13,133.

Estimating DV01
It is possible to predict with reasonable accuracy how MTM on a CDS will change in certain scenarios by using a quick approximation for the DV01 in the following way:

where:

and  

and:
DV01 is the sensitivity of the CDS to a change in spreads (s)
r = interest rate
T = time in years to maturity
s = current market spread
R = assumed recovery rate

Consider the example from the CDSW page where the current market spread is 48bp, rates are 4.75% and the recovery rate is assumed to be 40%. Therefore, a = 0.0048/0.6 and the DV01 = US$4.324.

This needs to be scaled by the notional, so for US$10m we need to multiply it by US$10m*1bp = 1,000 giving us a DV01 of 4,324.

Therefore, if US$10m of our 5yr CDS widens by 3bp, then the change in MTM is: 3 * 4,324 = US$12,975

With this simple formula for duration we are able to deal with CDS purely in terms of DV01. However, by taking one's understanding a little bit further one can gain an important insight into the product and the foundation for pricing all sorts of bespoke and exotic transactions.

Valuing each leg
A crucial part of CDS valuation is the determination of probability of default of the underlying entity.

Rating agencies derive their estimates of probabilities of default by relying heavily on a statistical analysis of historical default data. Rating agencies employ a number of different types of analysis to determine the rating of an asset. But, once that rating is assigned, the probability of default for the asset is determined by the historical experience of assets of similar type, rating and maturity. This estimate has the advantage of being based on observations and market experience, but has the disadvantage of being retrospective rather than forward looking.

Market practitioners, on the other hand, follow the principles of risk neutral valuation for pricing any derivative. In other words, the probability of default of an entity is determined by the market value of a CDS. Furthermore, this probability of default is also valid for use in pricing exotics and structured credit transactions. It is a reality that market supply/demand determines at what cost a credit may be hedged, although this axiom may be questioned.

Therefore, if the market demands a premium of 50bp for protecting a name, this must be an accurate reflection of the loss that would occur should the name default and the probability of that event occurring over the lifetime of the CDS.

The first of these two parts is estimated via the recovery rate, which is the expected post-default value of the bond. This is typically described as the expected value of US$1 notional of debt of the credit post-default. So the loss in the event of default of a CDS is expected to be (1-R) where R is the recovery rate. This is typically estimated based on historical observation of data published by rating agencies. Most market participants will use the same assumed recovery rate for all senior unsecured debt.

The standard market approach is to model the probability of default as a Poisson process (that is, with a default intensity model). Although the detail can be intricate, the basic concept is straightforward. The intensity of default or hazard rate (h) is linked to the credit spread of the CDS (s) by the relationship:

From this we can calculate the survival rate at any time using the following formula: Survival rate = e^-ht

For example, the hazard rate on a credit with a spread of 50bp (assuming a recovery rate of 40%) becomes 0.005/(1-0.4) = 0.83%. The survival rate for one year is exp ( 0.0083) = 99.17% and for two years is exp (-0.0083*2) = 98.35%.

The marginal default probability is the probability of default conditional on survival in the previous periods. In our example, the marginal probability of default in year 2 is 99.17% - 98.35% = 0.823%.

Let's put it all together by trying to value the legs of US$10m 1yr CDS. This is quite short dated, but it makes the example more manageable. We will start with the premium leg:

Here, we define the categories in Figure 6:

• Premium coupon is calculated as 50bp*US$10m*(coupondays/360)
• Survival factor is the probability of surviving from the value date to coupon date e^-ht where h=s/(1-R)
• Marginal default probability is the probability of default in this time period conditional on survival in previous periods and is calculated by subtracting survival factors: sf_t-1-sf_t
• Survival premium is the product of the premium coupon and the survival factor
• Default premium is the product of the weighted average accrued premium that would fall due if default were to occur and the probability of a default occurring in that period. It is assumed that, on average, a default would occur halfway through a premium period. Therefore, default premium = premium coupon * marginal default probability * 0.5
• Adjusted premium is the sum of the survival premium and the default premium
• Discount factor is the risk free rate, which is assumed to be 4% in our example: e^-rt
• Premium PV is the product of the adjusted premium and the discount factor

To value the protection leg we use many of the same concepts:

In Figure 7, the categories are defined as follows:

• Loss given default (LGD) is assumed to be Notional*(1-R)
• The probability weighted LGD is the product of the marginal default probability and the loss given default

Term structure of default probabilities
Our example assumes that the probability of default is constant through time. In practice, probability of default is assumed to have a term structure that is determined by the relative spreads of CDS of different maturities. To get a complete term structure one needs a method to determine the probability of default for any maturity, not just those quoted.

Finally, a popular method of extracting the entire term structure of probabilities of default is known as the "bootstrap method". The idea behind this technique is to create a curve out of the available points by making some assumptions about the form of the hazard rate (for example, whether its form is linear or piecewise). Other methods are sometimes employed to avoid inconsistencies that can occur in the curve construction process, such as "negative default probability" or unrealistic discontinuities in the curve.

© 2007 Citigroup Global markets. All rights reserved. This Research Note was first published by Citigroup Global markets on 8 February 2007.