Credit Risk Pricing Flashcards
(25 cards)
When does credit risk arise?
Credit risk arises from a positive probability that a borrower cannot meet her obligations.
This can take the form of not repaying the full loan, not paying the interest, etc.
Probability of default
In a given time interval, the probability of default is proportional to the time length considered.
Prob of default = λ∆t
The coefficient of proportionality is the hazard rate (or default intensity).
How to estimate default probabilities?
The default rate must be estimated using available data.
The best publicly available data are market prices, e.g., bond or asset prices.
Problems arise when assets are not liquid enough, or when they are not traded in markets.
Bond Yields
Bond yields are the average rate of return, that if applied to every cash flow of the bond, obtains the bond price.
A bond yield is the return an investor expects to earn if they buy the bond at its current price and hold it to maturity (total return including coupon interest and any price changes).
If bond prices rise, yields fall.
If two bonds have the same time to maturity and coupons, which bond has a lower price?
A bond with a higher yield will have a lower price.
Recovery Rate
When a company goes bankrupt (or a country declares default), investors can file claims and recover part of their money (either via reduced coupons, lower final payment, extended maturity).
-> debt restructuring.
The recovery rate is what is able to be recovered in the default.
What is the hazard rate equal to?
The hazard rate equals the spread between high corporate bond yield and risk-free yield.
When the recovery rate is zero.
What is the spread equal to?
With a positive rate of recovery R>0?
λ(1-R)=s
(1-R) is what is not recovered in the default.
The spread is the likelihood of default and the loss.
In general, the spread given in the market is slightly below the hazard rate because of a positive recovery rate.
What is the probability of default if the recovery rate is 1?
If R=1, there is a full recovery and there is no default.
The probability of default tends to zero.
What is a spread?
Corporate bonds have yields above that of government bonds.
The difference in yields is called the spread.
What does a spread tell us?
The spread incorporates default probability and expresses potential losses in case of default.
It is a measure of risk.
Government bonds themselves have a spread measured against the most ‘safe’ country… Germany for EU zone, US in general.
What does the yield curve show?
The yield curve of a given borrower is the collection of interest rate levels at different maturity times.
The curve is a collection of theoretical zero-coupon bond rates.
Countries are borrowers and each has its sovereign debt yield curve.
How to construct a yield curve?
Using bonds with different maturities issued by the borrower.
Using market prices of available bonds, or the money market for short maturities.
‘Bootstrapping’ to interpolate prices for unavailable dates.
How can investors trade the spread?
Trading the spread = trading the slope.
Short a short-term AAA bond and long a long-term AAA bond.
The price of the long-term bond needs to rise by more than the short-term bond.
Measures of sensitivity of bond prices to changes in the yield?
The price value of a basis point is a measure of sensitivity.
If the yield of 30 years moved by 1bp, the price fluctuation is much larger than the price fluctuation of a short maturity bond.
Sensitivity differs.
Increasing yield curve reflects?
Normal times and normal conditions.
Increasing yield curve = positive spread for bonds of longer maturities.
Reflects:
* Time preferences
* Risk - more events can happen in a longer time period that prevents the borrower from repaying debt.
When does an inverted yield curve occur?
Expectation of a worsening economic outlook.
Possibility of debt restructuring.
Why are default rates estimated from bond prices higher than historical default rates?
This is a drawback to using bond prices to estimate default probabilities.
Liquditiy premium for corporate bonds causes a larger spread.
Higher correlations of defaults in times of market stress make a higher premium necessary.
What is a liqudity premium?
Corporate bonds are less liquid than government bonds during stressful market environments.
Investors require a higher yield as compensation for this illiquidity.
Bid-ask spread is high.
Creates a bias in the price that is used to estimate default.
What is the premise of the Merton model (1974)?
A company’s equity is see as an option on the company’s assets.
Equity is a call option on the value of the company’s assets with the strike price euql to its debt.
Apply the Black-Scholes model to Merton (1974): what is N(-d2)?
1-N(d2)=N(-d2) expresses the probability of default Q(T).
N(d2) is seen as the risk-neutral probability of being “in-the-money” with the company’s shares seen as a call option on its survival event.
How to calculate relative expected loss?
L = prob of default x prob of no recovery
= λT(1-R)
What is distance to default?
Measures how many standard deviations the asset value can move before triggering a default.
Value is given by d2 - denotes how big the losses can be before triggering a default (normalised value).
1-N(d2) determines the probability of default.
What is a Credit Default Swap?
A CDS is a contract in which the buyer makes continuous payments to the seller in return for a payment in case of a specified credit event.
The payments cover any losses arising from default.
Credit event is commonly the default of the company.
