Chapter 27 Credit Risk

Default Concepts and Terminology What is a default? Default probability Recovery rate Credit spread Credit default swaps

The Merton Default Model If we assume that assets of a firm are lognormally distributed, then we can use the lognormal probability calculations to compute either the risk-neutral or actual probability that the firm will go bankrupt This approach to bankruptcy modeling is called the Merton model

The Merton Default Model (cont’d) Suppose we assume that the assets of the firm, A, follow the process (27.6) where a is the expected return on the firm, and d is the cash payment made to claim holders on the firm

The Merton Default Model (cont’d) Suppose we assume also that the firm has issued a single zero-coupon bond that matures at time T and makes no payouts is the promised payment on the bond

The Merton Default Model (cont’d) The probability of bankruptcy at time T, conditional on the value of assets at time t, is (27.7) The expected recovery rate, conditional on default, is

The Merton Default Model (cont’d) If we replace  with r in equation (27.7), we obtain the risk-neutral probability of default

Bond Ratings and Default Experience Bond ratings are attempts to assess the probability that a company will default One way to measure bankruptcy probabilities is by looking at the frequency with which bonds experience a ratings change, also called a ratings transition Highly-rated firms are unlikely to suffer a default The default probability increases as the rating decreases

Ratings Transitions Credit ratings transition matrix

Ratings Transitions (cont’d) Under the assumption that ratings transitions are independent, we can use the table to compute the probability that after s years a firm will transfer from one rating to another Let p(i, t; j, t+s) denote the probability that, over an s- year horizon, a firm will move from the rating in row i to that in column j Suppose there are n ratings Given the s – 1-year transition probabilities, the s-year probability of moving from rating i to rating j is (27.12)

Recovery Rates Recovery rate (per $ 100 of par value) for different kinds of bonds, 1982-2010

Credit Risk Credit risk is the risk that a counterparty will fail to meet a contractual payment obligation Most commonly, credit risk is the possibility that a borrower will declare bankruptcy

Credit Risk (cont’d) The classic tools for dealing with bankruptcy include diversification across borrowers, collateral requirements, and statistical tests based on borrower characteristics designed to predict the likelihood of bankruptcy Among recent developments are credit-based derivatives claims, such as credit default swaps, that pay when a firm defaults. Thus, they effectively permit the trading of default risk the derivative pricing models that can be adapted for modeling default

Credit Default Swaps Credit risk can be hedged with credit derivatives The outstanding notional principal covered by credit default swaps grew significantly between 2004 and 2010

The Structure of a Credit Default Swap Cash flows and parties involved in a credit default swap

The Structure of a Default Swap (cont’d) If a credit event occurs, the protection buyer receives It is common for CDS contracts to settle in cash The payment for a CDS can have two components A lump sum payment at the initiation of the contract Annual premium paid quarterly until expiration or the occurrence of a credit event Note that there is still credit risk in the default swap. The default swap buyer faces the possibility that the swap writer will go bankrupt at the same time as a default occurs on the reference asset

Pricing a Default Swap How is the premium on a default swap determined? A simple argument suggests that the default swap premium should equal the difference between the yield on the reference asset and the yield on an otherwise equivalent default-free bond In other words, the default swap premium equals the credit spread

Pricing a Default Swap (cont’d) There are several issues that complicate determining of the premium on a default swap Time variation in the credit spread Bonds with fixed coupons instead of floating rates Transaction costs (such as costs of short-selling) What is an “otherwise equivalent default-free bond”? This yield is unlikely to be the government yield curve and may not be directly observable

Credit Default Swap Indices A credit default swap (CDS) index is an average of the premiums on a set of individual CDSs A CDS index provides a way to track credit for a market segment It is possible to replicate a CDS index by holding a pool of CDSs

Credit Default Swap Indices (cont’d) As with a single CDS, one party is a protection seller, receiving premium payments The other party is a protection buyer, making the payments but receiving a payment from the seller if there is a credit event There are many ways in which a CDS index product can be structured and traded

Credit Default Swap Indices (cont’d) A CDS index can be funded or unfunded The index contracts can trade based on tranches The underlying assets can represent different countries, currencies, maturities, or industries

Credit-Linked Notes A credit-linked note is a bond issued by one company with payments that depend upon the credit status of a different company Banks can issue credit-linked notes to hedge the credit risk of loans Credit-linked notes can be paid in full even if the company that issued the notes defaults This is because funds raised by the issuance of these notes are invested in bonds with a low probability of default, which are held in a trust Therefore, the interest rate on credit-linked notes is determined by the credit risk of the company that initially borrowed money

Tranched Structures A process called securitization provides a mechanism for reselling difficult to sell assets by pooling together many of them and creating securities bas on the pool When an asset is securitized, one structure is to reapportion the returns on the asset pool in such a way that different claims to the asset pool have differing priorities with respect to the cash flows. Such a structure is said to be tranched A collateralized debt obligation (CDO) is a financial structure that repackages the cash flows from a set of assets Tranching makes it possible to take a pool of low-rated assets and create some tranches that are highly rated

Tranched Structures (cont’d)

Tranched Structures (cont’d)