Two Categories
- Default Risk
- Spread Risk
Default risk
S&P’s definition of corporate default
“A default is recorded upon the first occurrence of a payment default on any financial obligation, rated or unrated, other than a financial obligation subject to a bona fide commercial dispute; an exception occurs when an interest payment missed on the due date is made within the grace period. Preferred stock is not considered a financial obligation; thus, a missed preferred stock dividend is not normally equated to a default. Distressed exchanges, on the other hand, are considered defaults whenever the debt holders are offered substitute instruments with lower coupons, longer maturities, or any other diminished financial terms.”
– Ratings Performance 1999: Stability & Transition (2000)
Default Risk is comprised of a number of distinct default events that may occur in isolation or as a combination namely;
- bankruptcy
- insolvency
- repudiation
- restructuring
- moratorium
- failure -to-pay
- cross default
- cross acceleration
Although default is defined and agreed by negotiation at the outset, there is some risk of disagreement over whether the credit event has occurred.
S&P’s definition of sovereign default
” Sovereign debt is considered in default in any of the following circumstances:
• For local and foreign currency bonds, notes, and bills, when either scheduled debt service is not paid on the due date, or an exchange offer of new debt contains terms less favorable than the original issue.
• For central bank currency, when notes are converted into new currency of less than equivalent face value.
• For bank loans, when either scheduled debt service is not paid on the due date, or a rescheduling of principal and/or interest is agreed to by creditors at less favorable terms than the original loan. Such rescheduling agreements covering short- and long-term bank debt are considered defaults even when, for legal or regulatory reasons, creditors deem forced rollover of principal to be voluntary.
In addition, many rescheduled sovereign bank loans are ultimatively extinguished at a discount from their original face value. Typical deals have included exchange offers (such as for those linked to the issuance of Brady
bonds), debt/equity swaps related to government privatization programs, and or buybacks for cash. Standard & Poor’s considers such transactions as defaults because they contain terms less favorable to creditors than the original obligation.”
– Ratings Performance 2000: Default, Transition, Recovery, and Spreads
(2001)
Modeling for Credit Risk – Elements that Must be Considered
- Exposure at default
- Transition probabilities
- Default probabilities
- Recovery Rates
- fractional recovery of par
- fractional recovery of market value
- fractional recovery of default free equivalent bond
- For portfolios, joint default probabilities and joint transition probabilities
Modeling for Credit Risk – Stochastic Processes
- Martingales
- Brownian Motion
- $\mathcal{F}_{t}$ adapted process
- Forward default probability
- Markov Process
- Bernoulli Process
- Copulas
Further Reading
Bernd Schmid, Credit Risk Pricing Models – Theory and Practice. Second edition (2004)