Credit Default Swaps

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Credit Default Swaps

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GGY AXIS 5001 Yonge Street Suite 1300 Toronto, ON M2N 6P6 Phone: 416-250-6777 Toll free: 1-877-GGY-AXIS Fax: 416-250-6776 Email: [email protected] Web: www.ggy.com

Background

A CDS is much like insurance against a bond default. More precisely, a CDS is a derivative contract under which one party, the protection seller, agrees to make a payment to another party, the protection buyer, in case of a credit event affecting a specified reference entity. In exchange, the protection buyer pays a recurring fee or coupon to the protection seller. There may also be an up-front payment.

A CDS has a notional amount and a defined term. Following a credit event, the protection seller pays the difference between the notional amount and the recovery value of the defaulted reference debt, less the accrued CDS coupon. The decision as to whether a credit event has occurred is made by an ISDA committee, and the recovery rate is established at an auction conducted under ISDA supervision.

A CDS does not refer to a specific bond or debt issue, but to all debt of a specified type issued by the reference entity – for example, all senior debt. (In practice, prices of different issues converge on default because of cross-default and maturity acceleration provisions). This means that a single CDS can cover a wide range of different debt issues, and CDSs are often more liquid than the underlying debt.

If the owner of a risky bond buys CDS protection then they are in almost (but not quite) the same position as the owner of a risk-free bond. Likewise, if the owner of a risk-free bond sells CDS protection then they are in much the same position as the owner of a risky bond. The main differences are:

 The CDS compensates the protection buyer for the loss of principal if a bond defaults, but there is a

timing difference, because payment is made at the time of default, not the original maturity date.

 The protection buyer is exposed to counterparty default risk. However, CDSs are almost always fully

collateralized, and it is increasingly common for CDSs to be executed through bankruptcy-remote

clearinghouses.

Because of the similarities between CDSs and risky bonds, the quoted CDS coupon rate is usually close to the yield spread on risky bonds. The CDS coupon is often referred to as the CDS spread.

CDS Index Transactions

A CDS index transaction is similar to a single-name CDS except that it references a static basket of issuers, not a single issuer. The total notional amount is subdivided among the underlying issuers. Unlike a single-name CDS the transaction does not terminate following a credit event, but the total notional amount is reduced by the notional amount of the defaulted issuer. The coupon rate remains unchanged in percentage terms, but reduces in dollar terms because of the reduced notional amount.

Pricing and Valuation

Standard CDS contracts have a recurring coupon of 100 bps p.a. (500 bps for below-investment-grade names), and a negotiated up-front payment. However, CDS prices are usually quoted as par spreads, i.e. a hypothetical coupon rate that would result in a zero up-front payment. This is analogous to quoting bond prices in the form of par yields.

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have a model of defaults and recovery rates. The model is calibrated to reproduce the quoted spread, and once calibrated the model is used to calculate a market value, or the other way around. The model implemented in AXIS is consistent with the standard ISDA model used for market quotations (see

www.markit.com/cds/documentation/resource/converter_guide_sep2009.pdf and

www.markit.com/converter.jsp). In technical terms, this is a flat hazard rate model, meaning that the survival probability over any period [t, T] is given by exp[–λ.(T–t)], where the hazard rate λ is a constant. The value of λ is determined by AXIS based on the given par spread or market value.

Note that this is a market-implied (risk-neutral) hazard rate model that is used only for market value calculations. It is not intended as a realistic description of defaults, but is simply a market convention for converting between quoted spreads and trade settlement amounts. This is similar to the way that option prices are often quoted in terms of Black-Scholes implied volatilities, despite the known shortcomings of the Black-Scholes model.

The recovery rate for market value calculations is specified directly by the AXIS user. The convention for market quotes is to assume 40% recoveries for senior debt and 20% for subordinated debt. The user is free to specify other values, but the resulting model values will likely be inconsistent with market prices.

AXIS uses the same flat hazard rate model for CDS index transactions as for single-name CDSs. Again, this is a market convention and is not intended as a realistic description of each underlying issuer’s survival probabilities.

AXIS Interface

Several new options and inputs have been added to the AXIS asset cell.

 Asset Features

o Calculation type has a new option, “25 – Credit Default Swap”.

o Payment timing has a new option, “4 – Based on maturity date (CDS convention)”. The reason for

this option is that CDS contracts usually have a short initial stub period, so as to align the coupon

payment dates and maturity dates with standard IMM dates (March 20, June 20, September 20 or

December 20). With this setting there is a full coupon payment at the end of the initial stub

period, partially offset by an accrued coupon payment on the start date. This only makes a

difference to AXIS projections if the first CDS coupon payment is still in the future. Otherwise, this

setting is effectively the same as “3 – Based on maturity date”.

 Asset Features – Credit Default Swap: This is a new section with two inputs. Position can be “0 -

Protection seller” or “1 - Protection buyer”. CDS spread/premium is the annualized CDS coupon rate.

This is the contractual spread established at the start of the contract, not the current market spread

used for valuation purposes. For a standard contract this will be either 100 bps or 500 bps.

 Pricing/Projections – CDS Underlying and Margins – CDS Underlying: These are new sub-sections

with two inputs, CDS default and CDS recovery. These inputs are specified in the same way as default

rates and salvage values for bonds. If default and salvage value tables have been set up for bonds they

can be re-used for CDSs. The reason for the new sub-sections is to emphasize that these assumptions

refer to the CDS reference entity, not the CDS counterparty.

 Central Clearing: If beta feature 331 (“variation margin”) has been enabled, then the Central clearing

and Price alignment interest switches can be used for a CDS.

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Credit Default Swaps Page 3 of 3

 Accounting Basis – Amort Cost Basis Method: For a CDS this can be “0 – Zero”, “1 – Cost”, “2 – Simple

amortized cost” or “6 – Market value”.

 Market Value

o Market value method can be “0 – Zero” or “10 – PV of cashflows to maturity date”.

o Calibration has a new option, “3 – Solve for par CDS spread/premium”. This is similar to solving for

a yield spread based on an in-force market value (or a future purchase price). As with yield

spreads, the calibrated CDS spread can either be held constant or graded down over time,

depending on the Spread method switch.

Regardless of the calibration switch, AXIS still solves for a hazard rate so as to convert between

par CDS spreads and market values. The calibration switch determines whether or not the par

spread is calibrated to match a given in-force market value, not whether AXIS solves for a hazard

rate.

o CDS par spread: This can be a flat spread, a table specifying a par spread curve, or both. A CDS

spread table takes the same form as a yield spread table for bonds, and spread tables that have

already been set up for bonds can be re-used for CDSs. If a table is specified then the CDS par

spread is an interpolated value based on the CDS maturity. For details of AXIS’ interpolation

methodology see

www.ggy.com/htmlhelp/axis/75423.htm

.

If the Calibration switch is set to “3 – Solve for par CDS spread” and a spread table is specified

then AXIS solves for a flat spread that is in addition to the interpolated table value.

o CDS par spread maturity: This is a new switch that affects the interpretation of a CDS par spread

table.

 If the switch is set to “0 - Next IMM date after nominal maturity in CDS par spread

table” then each column in the spread table is taken to refer to the next IMM date

after the nominal maturity date. For example, as of Dec 31, 2015 the “5-year” column

would refer to a Mar 20, 2021 maturity date. This is consistent with CDS market

quotation conventions.

With this setting it is not necessary to populate every column in the spread table. For

example, if CDS spread quotes are only available for 3 and 5-year nominal maturities

then the other columns can be left blank. AXIS will ignore the blank columns when

calculating interpolated spreads.

 If the switch is set to “1 - Same as nominal maturity date in CDS par spread table” then

the spread table is interpreted in the same way as for bonds. In the above example,

the “5-year” column would refer to a maturity of Dec 31, 2020.

Sample Asset Cell

Dataset “CDS Sample Cell” includes a sample cell that illustrates this feature. To use this dataset, you will require the activation codes for beta features “462 – Credit Default Swap” and “331 – Variation margin”. Please contact GGY for these activation codes.

Credit Default Swaps