Chapter 18: Credit risk Flashcards
Credit event
An event that will trigger the default of a bond.
Recovery rate
In the event of a default, the fraction δ of the defaulted amount that can be recovered through bankruptcy proceedings or some other form of settlement is known as the recovery rate.
Structural models
Models for a company issuing both shares and bonds, which aim to link default events explicitly to the fortunes of the issuing company.
Reduced-form models
Statistical models that use observed market statistics such as credit ratings, as opposed to specific data relating to the company.
Intensity-based models
A particular type of continuous-time reduced-form model.
They typically model the “jumps” between different states using transition intensities.
Merton model for risk: Type
The Merton model is a structural model for credit risk.
Merton model for risk: Assumption
It assumes that the shareholders are entitled to net assets of the company after redemption of the loan
Merton model for risk: How are Gross assets modelled
Gross assets are modelled as the share price in a Black-Scholes market
Thus, if the loan matures at time T:
- Lt is the loan value at time t,
- Ft is the gross asset value,
- Et is the equity value at time t ,
Then Lt = min(L, Ft) where L is the nominal amount of the loan.
It follows that Et is the value of a call option on the gross assets with strike L and Ft = Et + Lt
relationship between the current equity value of the company
and FT, the final gross value of the company’s assets
E₀ = Eₚ exp{rT}(FT - L)*
3 Types of credit risk models
- structural
- reduced form
- intensity-based
Describe how the Merton model can be used to estimate the risk-neutral probability of default.
In the Merton model, the company is modelled as having
… a fixed debt, L
… and variable assets Ft.
This means the equity holders can be regarded as holding a
….European call on the assets with a strike of L.
It follows from the Black- Scholes model that we can deduce the (risk-neutral) default probability from the share price.
Describe the 2-state model for credit derivatives
The company defaults at time-dependent rate λ(t) if it hasn’t previously defaulted.
Once it defaults, it remains permanently in the default state. It is assumed that after default, all bond payments will be reduced by a known factor, (1 − δ), where δ is the recovery rate.
Default-free bond
A bond is default-free if the stream of payments due from the bond will definitely be paid in full and on time
4 Possible Outcomes of a default
The outcome of a default may be that the contracted payment stream is:
- Rescheduled
- Cancelled by the payment of an amount which is less than the default-free value of the original contract
- Continued but at a reduced rate
- Totally wiped out
4 examples of a credit event
- Failure to pay either capital or a coupon
- Loss event (when it becomes clear the borrower is not going to make a full payment on time)
- Bankruptcy
- Ratings downgrade of the bond by a rating agency such as S&P or Moody’s
