Types of Credit Derivatives
A credit derivative is a financial instrument that transfers credit risk related to an underlying entity or a portfolio of underlying entities from one party to another without transferring the underlying(s). The underlyings may or may not be owned by either party in the transaction. The common types of credit derivatives are Credit Default Swaps, Credit Default Index Swaps (CDS index), Collateralized Debt Obligations, Total Return Swaps, Credit Linked Notes, Asset Swaps, Credit Default Swap Options, Credit Default Index Swaps Options and Credit Spread Forwards/Options.
Credit Default Swaps
In a credit default swap the seller agrees, for an upfront or continuing premium or fee, to compensate the buyer when a specified event, such as default, restructuring of the issuer of the reference entity, or failure to pay, occurs. Buyers of credit default swaps can remove risky entities from their balance sheets without selling them. Sellers can gain higher returns from investments or diversify their portfolios by entering markets that are otherwise difficult to get into.
The value of a default swap depends not only on the credit quality of the underlying reference entity but also on the credit quality of the writer, also referred to as the counterparty. If the counterparty defaults, the buyer of a default swap will not receive any payment if a credit event occurs. We also note that if a counterparty defaults, the premium payments end. Hence, the value of a default swap depends on the probability of counterparty default, probability of entity default and the correlation between them.
Credit default swaps are composed of the following four types: credit default swaps on single entities, credit default swaps on a basket of entities, credit default index swaps, and first-loss and tranche-loss credit default swaps.
Total Return Swaps
A total return swap is a means to transfer the total economic exposure, including both market and credit risk, of the underlying asset. The payer of a total return swap can confidentially remove all the economic exposure of the asset without having to sell it. The receiver of a total return swap, on the other hand, can access the economic exposure of the asset without having to buy the asset. Typical reference assets of total return swaps are corporate bonds, loans and equities.
A credit-linked note, also known as a credit default note, is a fixed or floating rate note where the principal and/or coupon payments are referenced to a credit or a basket of credits. If there is no credit event of the reference credit(s), all the coupons and principals will be paid in full. However, if there is a credit event, the payments of the principal and, possibly, also the coupon of the note will be reduced.
Credit Default Swap Options
A credit default swap option is also known as a credit default swaption. It is an option on a credit default swap (CDS). A CDS option gives its holder the right, but not the obligation, to buy (call) or sell (put) protection on a specified reference entity for a specified future time period for a certain spread. The option is knocked out if the reference entity defaults during the life of the option. This knock-out feature marks the fundamental difference between a CDS option and a vanilla option. Most commonly traded CDS options are European style options.
Similar to the credit default swaps, CDS options can be: CDS options on a single entity with a regular payoff for the default leg; CDS options on a single entity with a binary payoff for the default leg; CDS options on a basket of entities with regular payoff for the default leg; and CDS options on a basket of entities with a binary payoff for the default leg.
Credit Default Index Swap Options
A credit default index swap option (CD index swap option, or CD index swaption, or CDS index option) is an option to buy or sell the underlying CDIS at a specified date. A payer swaption gives the holder of the option the right to buy protection (pay premium) and a receiver swaption gives the holder of the option the right to sell protection (receive premium). Unlike a CD index swap, which is a natural extension of a CDS on a single-entity to a CDS on a portfolio of entities, a CD index swaption is significantly different from a CDS option, an option on a single-entity CDS. In the case of an option on a single-entity, if the reference entity defaults before the option's expiry, the option will be knocked out and become worthless. For an option on a CDIS, when a reference entity defaults before the option's expiry, the loss will be paid by the protection seller to the protection buyer when the option is exercised. Even if there is only one entity in the portfolio, a CD index swaption is still different from a single-entity CDS option: if the entity defaults before expiry, the option's seller will pay to the protection buyer the lost amount at expiry. Clearly, a CD index swaption is always more valuable than a single-entity CDS option.
Credit Spread Options and Forwards
Credit spread options are options where the payoffs are dependent on changes to credit spreads. The transaction may be either based on changes in a credit spread relative to a risk-free benchmark (e.g. LIBOR or US Treasury) or changes in the relative spread between two credit instruments. A credit spread option may be a vanilla option or an exotic option, such as an Asian option, a lookback option, etc. The option style may be European or American. Valuation of credit spread options can be based on modeling the two underlying instruments or modeling the credit spread only.
An asset swap is a combination of a defaultable bond with a fixed-for-floating interest rate swap that swaps the coupon of the bond into the cash flows of LIBOR plus a spread. In the case of a cross currency asset swap, the principal cash flow may also be swapped. In a typical asset swap, a dealer buys a bond from a customer at the market price and sells to the customer a floating rate note at par. The dealer then enters into a fixed-for-floating swap with another counterparty to offset the floating rate obligation and the bond cash flows. For a premium bond, the dealer pays to the customer the difference of the bond price and its par. For a discount bond, the customer pays to the dealer the difference of the par and the bond price. In the swap with the counterparty the dealer pays a fixed bond coupon and receives LIBOR + a spread. The spread can be determined from the cash that the dealer pays/receives and from the difference of the bond coupon and the par swap rate.
Synthetic Collateralized Debt Obligations (CDOs)
Synthetic CDOs are credit derivatives on a pool of reference entities that are "synthesized" through more basic credit derivatives, mostly, credit default swaps (CDSs) and credit linked notes (CLNs). A common structure of CDOs involves slicing the credit risk of the reference pool into a few different risk levels. The level with a higher credit risk supports the levels with lower credit risks. The risk range of two adjacent risk levels is called a tranche. The lower bound of the risk level of a tranche is often referred to as an attachment point and the upper bound a detachment point. The most common CDO credit derivatives are CDSs on CDO tranches and CDO notes (tranche-linked notes or CLN on tranches). The most popular synthetic CDOs are the so-called standardized CDOs (sometimes are simply called standardized tranches). For a standardized CDO its reference entities are homogenous, i.e., all the reference entities have the same notional and the same recovery rate. Due to the complexity and the large sizes of reference pools of synthetic CDOs, their valuation is much more complicated and resource intensive than the ordinary single-entity or basket CDSs and CLNs. Monte Carlo methods have been the most reliable methods in CDO valuation but they are not efficient in computation. Recently, thanks in part to the standardization of the synthetic CDO market, quasi-analytic methods, such as the fast Fourier transform (FFT), are gaining popularity. These methods are much more efficient than Monte Carlo simulation for CDOs whose reference entities have "good" homogeneity and, particularly, when the one-factor copula model is used for modeling credit correlation.
Correlations are one of the key factors in CDO valuation. Given the spread of a tranche one would like to back out, when the one-factor Gaussian copula model is used, the correlation that gives the tranche's par spread as the given spread. Such a correlation is called a tranche correlation. Research shows that tranche correlation is not unique except for the equity tranche. For this reason the implied correlations of tranches that have an attachment of 0 have become more attractive than tranche correlations. Such correlations are known as base correlations. Since market quotes are available only for regular tranches, to back out the base correlations of all trachea of a synthetic CDO, the so-called bootstrapping algorithm must be used.