Credit derivative

A credit derivative transfers exposure to deterioration of credit quality or a specified credit event of a reference borrower without necessarily transferring the underlying loan or bond. Credit default swaps transfer a defined loss exposure; total return swaps transfer a wider asset return. Funded structures such as credit-linked notes combine the exposure with an investor's initial principal. Documentation specifies the reference entity, obligations, credit events and settlement; a hedge can leave counterparty credit risk and mismatch with the original exposure.

A synthetic collateralized debt obligation creates portfolio credit exposure using credit default swaps rather than necessarily owning a pool of cash loans or bonds. Losses are allocated to tranches with different attachment and exhaustion levels. A tranche can be funded, unfunded or partly funded depending on structure. Individual default probabilities alone do not price it: dependence among defaults and recovery outcomes changes the portfolio loss distribution.

For aggregate monetary loss $L$ and monetary attachment/exhaustion levels $A<D$, this is the loss allocated to the tranche. It is zero until attachment, rises with losses between $A$ and $D$, and is capped at $D-A$. Expected tranche losses and surviving tranche notional determine protection and premium legs. For basket products whose payoff occurs at a first default, the joint default-time distribution matters as well as the final loss distribution.

A funded note whose coupons or principal depend on specified credit events of a reference entity or portfolio. In a simple structure, the investor supplies principal and receives enhanced coupon for economically selling credit protection; a reference default reduces principal repayment. The investor may also face the note issuer's own credit risk. This is not automatically the same exposure as directly holding the reference borrower's bond.

The total-return receiver obtains a reference asset's income and price gains, pays its price losses, and pays an agreed funding leg to the total-return payer. This supplies economic exposure without buying the reference asset outright. The transfer includes ordinary market-price risk as well as credit risk, distinguishing it from a credit default swap. Both parties can have counterparty credit risk as the swap's replacement value changes.

The protection buyer pays a contractual premium in exchange for compensation upon a defined credit event of the reference entity. In a simple cash-settled contract of notional $N$, a default loss with fractional recovery $\mathcal{R}$ gives payment $N(1-\mathcal{R})$. Physical settlement instead exchanges an eligible defaulted obligation for par. Payments, accrued premium, maturity and eligible obligations depend on the contract. The protection buyer need not own the reference debt; the seller earns premium while taking the specified credit risk.

A basket credit contract whose protection payment is triggered by the first specified default among its reference entities. The loss and settlement terms refer to the defaulting name according to the contract. Premium generally stops at that first default or maturity. Pricing requires the joint default-time distribution; separate marginal default probabilities alone do not determine the first-default law.

Assume deterministic discount factors, deterministic risk-neutral default intensity $\lambda$, fixed fractional recovery $\mathcal{R}$, and continuous premium until default or maturity. Survival is $G(t)=\exp (-{\int }_0^t\lambda (u)du)$. Expected discounted protection is $N(1-\mathcal{R})\int B\lambda G$, while premium is $Ns\int BG$. Equating them gives the par spread. Constant intensity gives $s=(1-\mathcal{R})\lambda$. Discrete premiums, default accrual, stochastic recovery and counterparty losses require changing the corresponding cash-flow expectations.