Download
1 / 16
E N D
2. Outline
3. Credit Derivatives Market Overview Credit derivatives market took of in 1997 and reached now a notional size of over 5,000 billion
The biggest players in the markets are
banks- use credit derivaties to achieve capital relief and hedge their loan portfolio‘s
Hedge who engage in capital structure arbitrage
And insurance companies who use credit derivatives to diversify their investment portfolios and enhance their returns
The market is expected to further grow in this rate
A lot of banks have to revalue their loan portfolio‘s
Credit derivatives market took of in 1997 and reached now a notional size of over 5,000 billion
The biggest players in the markets are
banks- use credit derivaties to achieve capital relief and hedge their loan portfolio‘s
Hedge who engage in capital structure arbitrage
And insurance companies who use credit derivatives to diversify their investment portfolios and enhance their returns
The market is expected to further grow in this rate
A lot of banks have to revalue their loan portfolio‘s
4. Credit Derivatives Market Overview Most basic product is the CD swap
CDO, First to default baskets….
For example they have to much exposure to one client ….
Wieso CDS so erfolgreich….
Die zwei hauptgruende:
Most basic product is the CD swap
CDO, First to default baskets….
For example they have to much exposure to one client ….
Wieso CDS so erfolgreich….
Die zwei hauptgruende:
5. Credit Default Swap (CDS) Was ist ein Credit Default Swap
…eigentlich nichts anderes als eine Versicherung gegen ein Credit Event
Was ist ein Credit Default Swap
…eigentlich nichts anderes als eine Versicherung gegen ein Credit Event
6. Mechanics of a CDS Credit event is bancruptcy, failure to pay, restructuring etc.
(equivalent to paying 1-T, R=recovery rate)
This is done as price discovery in default is not easy…illiquid trading
Cheapest to delivery option
(equivalent to paying 1-T, R=recovery rate)
This is done as price discovery in default is not easy…illiquid trading
Credit event is bancruptcy, failure to pay, restructuring etc.
(equivalent to paying 1-T, R=recovery rate)
This is done as price discovery in default is not easy…illiquid trading
Cheapest to delivery option
(equivalent to paying 1-T, R=recovery rate)
This is done as price discovery in default is not easy…illiquid trading
7. Credit Models
8. ‘ for countries national stock index as proxy
Black scholes assumptions: constant volatility and interest rates, complete markets, continous trading, no transaction costs
The bondholders have sold the shareholders an option to put the firm back to them
for the bond’s notional value at maturity T. It is this additional risk which makes
them demand a yield spread over the default-free zero coupon bond.
‘ for countries national stock index as proxy
Black scholes assumptions: constant volatility and interest rates, complete markets, continous trading, no transaction costs
The bondholders have sold the shareholders an option to put the firm back to them
for the bond’s notional value at maturity T. It is this additional risk which makes
them demand a yield spread over the default-free zero coupon bond.
9. However, stock price and stock volatility are observable.
From ito’s lemma we get
From the balance sheet equation asset value= equity + liabilities
D is an expression for the leverage of the firm , the higher the d, the higher the risk
Numerically solve for both equations....
Link between equity and debt markets
However, stock price and stock volatility are observable.
From ito’s lemma we get
From the balance sheet equation asset value= equity + liabilities
D is an expression for the leverage of the firm , the higher the d, the higher the risk
Numerically solve for both equations....
Link between equity and debt markets
10. Once we have the value of the risky bond it is easy to calculate the credit spread:
...and build a spread curve
Example: (K=100; AV=140,115,98)
Merton Model
11. -Default can only occur at maturity
credit spreads tends to go to zero as the maturity of the bond goes to infinity, where
Fitting a term structure of bonds means fitting requires a term structure of asset value volatilities and asset values, which are not observable
E.g if company has two bonds outstanding, the price of the longer bond depends on the wheter the company is solvent when the shorter bond matures (similar to pricing a compound option). The pricing formula becomes very complicated and the pricing of credit derivatives with more exotic payoffs is beyond the limit of the model.
As the diffusion model of the firm value is continous, default is never a surprise event....this fact means that short term spreads are too small is contradictionary to practise where it sometimes is...eg. Sovereigns unwillingness to pay
‘If the real capital structure is taken into account, then all claims on the asset need to be taken into account, which is unfeasible
You cannot fit a term structure of spreads bonds to model…it is not arbitrage free
Cannot be easily extendend to price exotic derivatives
-Default can only occur at maturity
credit spreads tends to go to zero as the maturity of the bond goes to infinity, where
Fitting a term structure of bonds means fitting requires a term structure of asset value volatilities and asset values, which are not observable
E.g if company has two bonds outstanding, the price of the longer bond depends on the wheter the company is solvent when the shorter bond matures (similar to pricing a compound option). The pricing formula becomes very complicated and the pricing of credit derivatives with more exotic payoffs is beyond the limit of the model.
As the diffusion model of the firm value is continous, default is never a surprise event....this fact means that short term spreads are too small is contradictionary to practise where it sometimes is...eg. Sovereigns unwillingness to pay
‘If the real capital structure is taken into account, then all claims on the asset need to be taken into account, which is unfeasible
You cannot fit a term structure of spreads bonds to model…it is not arbitrage free
Cannot be easily extendend to price exotic derivatives
12. Reduced Form Model Purpose: Arbitrage free valuation of default linked payoffs
Default is treated as exogenous event
Default event is the first event of a Poisson counting process.
Conditional probability of default is defined as hazard rate:
...integration leads to the survival probality:
Jarrow/Turnbull 1995
Do not attempt to explain default in terms of underlying fundamentals, default is treated as exogenous event
Can fit a whole term structure of spreads and therefore can be used to price more exotic derivatives
Usually we are only interested in the first time to default
Survival probability under the risk neutral measure p is not directly related to historical default frequencies but where the default risk can be hedged in the market
Default probabilities
The default probabilities calculated for
pricing purposes can be quite different
from those calculated from historical
default rates of assets with the same rating.
These real-world default probabilities
are generally much lower. The reason for
this is that the credit spread of an asset
contains not just a compensation for pure
default risk; it also depends on the market’s
risk aversion expressed through a risk
premium, as well as on supply-anddemand
imbalances.
One should also comment on the market’s
use of Libor as a risk-free rate in pricing.
Pricing theory shows that the price of a
derivative is the cost of replicating it in a riskfree
portfolio using other securities. Since
most market dealers are banks which fund
close to Libor, the cost of funding these
other securities is also close to Libor. As a
consequence it is the effective risk-free rate
for the derivatives market.
Such expectations are only available from
price information, and the problem in credit
is that given one price, it is difficult to separate
the probability of default from the recovery
rate expectation.
The market standard is therefore to revert to
rating agency default studies for estimates of
recovery rates. These typically show the average
recovery rate by seniority and type of
credit instrument, and usually focus on a US
corporate bond universe
Jarrow/Turnbull 1995
Do not attempt to explain default in terms of underlying fundamentals, default is treated as exogenous event
Can fit a whole term structure of spreads and therefore can be used to price more exotic derivatives
Usually we are only interested in the first time to default
Survival probability under the risk neutral measure p is not directly related to historical default frequencies but where the default risk can be hedged in the market
Default probabilities
The default probabilities calculated for
pricing purposes can be quite different
from those calculated from historical
default rates of assets with the same rating.
These real-world default probabilities
are generally much lower. The reason for
this is that the credit spread of an asset
contains not just a compensation for pure
default risk; it also depends on the market’s
risk aversion expressed through a risk
premium, as well as on supply-anddemand
imbalances.
One should also comment on the market’s
use of Libor as a risk-free rate in pricing.
Pricing theory shows that the price of a
derivative is the cost of replicating it in a riskfree
portfolio using other securities. Since
most market dealers are banks which fund
close to Libor, the cost of funding these
other securities is also close to Libor. As a
consequence it is the effective risk-free rate
for the derivatives market.
Such expectations are only available from
price information, and the problem in credit
is that given one price, it is difficult to separate
the probability of default from the recovery
rate expectation.
The market standard is therefore to revert to
rating agency default studies for estimates of
recovery rates. These typically show the average
recovery rate by seniority and type of
credit instrument, and usually focus on a US
corporate bond universe
13. Pricing of contingent claims
if payment is made at time T:
where
if payment is made when default occurs:
Probability of defaulting in time interval from t to t+dt is
...and by integrating over the density of default time
Reduced Form Model Assumption here is the that default time tau is independent of Payoff and the term structure of interest rate.
This is a questionable assumption as companies default more often in a recession. In a recession interest rates are usually low. Therefore there should be a negative correlation between interest rates and default probability. But for firms who have floating rate debt its the other way around.
Under the independence assumptions the price of a defaultable claim is
We can
Assumption here is the that default time tau is independent of Payoff and the term structure of interest rate.
This is a questionable assumption as companies default more often in a recession. In a recession interest rates are usually low. Therefore there should be a negative correlation between interest rates and default probability. But for firms who have floating rate debt its the other way around.
Under the independence assumptions the price of a defaultable claim is
We can
14. Reduced Form Model Pricing CDS Spreads
Present Value Protection leg
Present Value Premium leg
You cannot separate default intensity and recovery value.......
Assumption interest rate and default intensity are deterministic constant
You cannot separate default intensity and recovery value.......
Assumption interest rate and default intensity are deterministic constant
15. Reduced Form Model
16. Recovery Rates Predict future distribution and price the financial productsPredict future distribution and price the financial products
17. Conclusion There is a lot to learn for me
But the rewards are high
