Name types of Credit risk:
- Default risk
- Risk of migration (downgrading)
- Spread risk (variation in spread curve)
- Risk of exposure (EAD increase near the default)
- Country / sovereign risk
- Counterparty risk or replacement (OTC derivatives)
What are the components of credit risk?
1. Exposure at default EAD
- Amount placed at risk
2. Default D
- Bernoulli r.v. taking value 1 w/ probability , and 0 w/ probability 1-PD
o PD depends on economic / financial characteristics & creditworthiness of borrower
o PD also called default rate
3. Severity SEV
- r.v. representing % loss in case of default
- depends on nature of bond
- E(SEV) = LGD (Loss given default)
Define the terms EL, UL and RR
Name some Major Rating Agencies, what they tell us and what they consider:
Moody’s, S&P, FitchRatings..
They tell:
rating (AAA, Aaa etc.)
Outlooks
likely direction of an issuer’s rating over medium term (usually 2a)
Watch
indicates that issuer has on or more rating under review for possible change
They consider:
business risk
economic environement, potentiality of market
financial risk
future budget, expected cash flow …
How are PD and ratings connected?
The PD can be obtained implicitly, by % of defaults occurred in the past in different classes.
We can use a Binomial or Multinomial model:
What is the default correlation? How does it influence the UL of Credit Portfolios?
tendency of two companies to fail simultaneously
—> important when analyzing benefits of diversifcation of credit risk or evaluating multiname credit derivatives (CDO tranches)
—> default correlation makes it complicated to compute UL of Credit portfolio since it cannot only by summed up like the EL
What is the Economic Capital?
The capital a financial services firm needs to protect against unexpected future losses.
—> also called the Credit Value at Risk
—> Decomposes risk into two components
o First = expected losses
o Second = unexpected losses
Explain the Un-/ conditional default probability:
Unconditional:
Condiitonal:
What is the Default Intensity?
Alternative way of characterizing the distribution of time to default: hazard rate / default intensity, i.e.: instantaneous probability of default in t, conditional of survival until t
with lamda being constant
How can we estimate PDs?
- Historical data
- Bond spreads
- CDS spreads
- Merton’s model
- Discriminant analysis
- Deep learning
What is the problem with using Historical Simulations for estimating PDs?
Implicit assumption: defaults are independent and identically distributed (i.i.d.) as a Bernoulli
—>ignores default correlation
—>Moody’s table is based on historical data
Explain how we can use Credit Spreads for estimating PDs:
Difference between yield of corporate bonds and treasury rates (credit spread) incorporate market expectations about probability of default of the issuer (compensate expected loss)
Explain the difference btw real world & risk-neutral default probabilities:
Name two fundamental classes of Credit Risk Models:
1. Structural or asset value models (Merton-like), threshold or latent variable models: based on definition of a stochastic model for firm’s evolution
2. Reduced form models: directly modeled default process; PD depends on economic variables
What is Merton’s Model, what is it used for, and what does it provide?
it’s a Credit Risk Model
it analyzes the structure of a company
it provides PD, market value of debt and the spread
What are the assumptions of Merton’s model?
Assumptions:
Market is frictionless
Investors are price takers
No arbitrage
Value of assets of a company follow a GBM, lognormally distributed
Risk of shareholders limited to their shares
No bankruptcy costs
How does Mertons Model work?
How does the value of a company assets result in an option for the shareholders?
the shareholder have a put:
Shareholders:
- Hold an option to sell in the company at a strike price
- They have the right to sell the company to the bondholders in the event of default
Bondholders / Money lenders are the writer of the put option
What are the results from the Merton’s model? Provide the formulas for:
market value of debt
spread
PD
What are advantages and disadvantages of Merton’s model?
Beside of Merton’s model as a Structural Approach for Credit Risk Models, we also have Reduced form models. Explain the Reduced form Model:
Studies dynamics of defaults regardless of company structure
Default as exogeneous event described by the first jump in a Poisson process, incorporating the default intensity
Price of a risky bond with : risk-free price times probability of survival until maturity
What are Asymptotic Single Risk factors?
- One factor Merton type model with central role in the Basel framework
- Allows to derive analytically the VaR and economic capital under assumpions:
o Merton type model
o Unique systemic risk factor
o Infinity granular portfolio (large number of small loans)
o Dependence described by the Gaussian copula
What are Credit Portfolio models? What kind of simplifications do we assume for Bernoulli Models?
Model to measure Credit Risk of Credit Portfolios. Different to the Credit Risk due to the dependence structure among the assets.
Explain the Scope of Vasicek Portfolio Model and its assumptions:
Shows the relevance of the dependence structure among assets in the estimation of credit risk for portfolios of assets.
company defaults at T, if value of assets falls below value of the bonds —> can’t repay debt
individual loan default probabilities are correlated —> for very large portfolios the limiting form of loss distribution is not Gaussian!
Values of individual assets are described by a GBM
What are the results of the Vasicek Portfolio Model?
N^-1: inverse normal cdf
What are copula functions? What is the Use and how do they work?
Characterize dependence for continuous multivariate distributions
Uses:
Improve reliability of credit risk models
Pricing of credit derivatives (e.g.: CDOs)
How?
Helps isolating marginal probabilities (e.g.: time to default) of a pair of variables that are enmeshed in a more complex multivariate system
—> describes dependence structure between variables by combining the marginals
—> only 1 univariate marginal distribution —> less observations needed
Last changeda year ago
