Chapter 18 - Credit Risk Flashcards
Credit event
A credit event is an event that will trigger the default of a bond and includes the following:
- failure to pay either capital or a coupon
- loss event (ie where the company says that it is not going to make a payment)
- bankruptcy
- rating downgrade of the bond by a rating agency such as Standard and Poor’s and Moody’s.
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 recovery rate.
Structural models
Structural models are models for a company issuing both shares and bonds, which aim to link default events explicitly to the fortunes of the issuing company.
The models are simple and cannot be realistically used to price credit risk. However, studying them does give an insight into the nature of default and the interaction between bondholders and shareholders.
Reduced-form models
Reduced-form models are statistical models that use observed market statistics such as credit ratings, as opposed to specific data relating to the company.
The credit rating agencies that issue the credit ratings will have used detailed data specific to the issuing corporate entity when setting their rating. They will also regularly review the data to ensure that the rating remains appropriate and will re-rate the bond either up or down as necessary.
Reduced form models use market statistics along with data on the default-free market to model the movement of the credit rating of the bonds issued by a corporate entity over time. The output of such models is a distribution of the time to default.
Intensity-based models
Intensity-based models are a particular type of continuous-time reduced-form models. They typically model the “jumps” between different states (usually credit ratings) using transition intensities.
The Merton model
Merton’s model is a structura model. It assumes that a company has issued both equity and debt such that its total value at time t is F(t). This value varies over time as a result of actions by the corporate entity, which does not pay dividends on its equity or coupons on its bonds. The total value of the bonds issued and the shareholders’ interest equals F(t).
Part of the corporate entity’s value is zero-coupon debt with a promised repayment amount of L at a future time T. At time T, the remainder of the value of the corporate entity will be distributed to the shareholders and the corporate entity will be wound up.
The corporate entity will default if the total value of its assets F(t) is less than the promised debt repayment at time T. In this situation, the bondholders will receive F(T) instead of L and the shareholders wil receive nothing. This can be regarder as treating the shareholders of the corporate entity as having a European call option on the assets of the company with maturity T and a strike price equal to the value of the debt.
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.
Possible outcomes of a default (4)
The contracted payment stream:
- is rescheduled
- is 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
- is totally wiped out
Credit spread
Credit spread is a measure of the excess of the yield on a risky security over a risk-free yield. It largely relates to the expected cost of default, as referred to here. However, in practise it will also typically reflect other factors, such as a risk premium relating to the risk of default and a liquidity premium.
State the circumstances under which the implied risk-neutral transition intensities can be determined
Knowing both the default-free and bond term structures and making an assumption about the recovery rate enables the implied risk-neutral transition intensities to be determined.
Explain fully how a two state model can be enhanced with the use of a stochastic transition intensity
We can assume that the transition intensity between states, λ(t), is stochastic and dependent on a separate state variable process, X(t).
Using this approach in a situation where there are just two states the tume of default τ will be the first jump time in a Cox process with intensity λ(t).
By using a stochastic approach, λ(t) can be allowed to vary with company fortunes and other economic factors. For example, a rise in interest rates may make default more likely, so X(t) could include appropriate allowance for changes in interest rates.
This approach can be used to develop models for credit risk that combine the structural modelling and intensity-based approaches.
Describe the JLT model
This is a more general and more realistic model, with multiple credit ratings, rather than the simplistic default/no default model. In this model there are n-1 credit ratings plus default. We define the transition intensity, under the real world measure P, from state i to state j at time t to be λij(t).
In this n-state model, transfer is possible between all states except for the default state n, which is absorbing.
