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Credit Risk Management
Transcript of Credit Risk Management
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Credit Risk Management
B A S E L II
According to the book of A. J. McNeil | R. Frey | P. Embrechts
"Quantitative Risk Management - Concepts, Techniques & Tools" | Chapter 8 | Credit Risk Management, 327 - 381
Firm value of asset : 130
Default threshold: 100
Expected return (mu): 5%
Volatility (mu): 20 %
ln (130/100) = 26%
r = 5 %
Sigma = 20 %
29,2% / 20%
=1,46 standard deviation
Numerator = 29,2%
Denominator = 20%
d2 = 1,462
PD = N(-d2) = 7,19%
EDF(KMV) > N(d2)
MODEL THEORETIC ASPECTS OF BASEL II
"Hold 8% of the Risk Weighted Assets (RWA)"
Sum of individual Risks
x Exposure size (ei)
Probability of default: Overview
The process (Vt) follows a diffusion model:
Geometric Brownian Motion
It implies that :
And in particular :
So the Default probability :
How measure Probability to default ?
It is often possible to transform a latent variable model to obtain an equivalent Bernoulli mixture model with factor structure. This is useful in
Monte Carlo simulation
, since Bernoulli mixture models are generally easier to simulate than latent variable models.
Conditional expected loss = Var
- LGD x PD
The RWA of a portfolio is given by the sum of thr RWA of the individual risks in the portfolio
Merton Model & KMV Approach
Consider the Black-Scholes model:
NEW BASEL II
KMV vs CREDIT METRICS
The default risk of an obligor is assumed to depend on a set of common economic factors, which are also modelled stochastically.
Defaults of individual firms are assumed to be independent
The majority of threshold models can be represented as Bernoulli mixture models.
Credit risk is the risk that the value of a portfolio changes due to unexpected changes in the credit quality of the issuers.
1. WHAT IS CREDIT RISK?
Bernoulli mixture models lend to Monte Carlo risk studies
Mixture models are more convenient for statistical purposes.
Behaviour of Bernoulli= Behaviour of the distribution of the common economic factors
ADVANTAGES OF BERNOULLI
The key quantity of interest in the KMV model is the so-called expected default frequency (EDF): this is simply the probability (under the probability measure P) that a given firm will default within one year as estimated using the KMV methodology.
THE KMV MODEL
Alexander J. McNeil, Rudiger Frey and Paul Embrechts
Kristen La Picque
CREDIT RISK MANAGEMENT
CreditMetrics (developed by JPMorgan and the RiskMetrics Group).
The default probability of a given firm is determined from an analysis of credit migration.
CREDIT MIGRATION MODEL
1) Lack of public information and data
2) Skewed loss distributions
3) Dependence structure of the default events
CREDIT RISK CHALLENGES
Under the new framework a bank is required to hold 8% of the so-called risk-weighted assets (RWA) of its credit portfolio as risk capital.
The risk weight is determined by:
simpler standardized approach
internal-ratings-based (IRB) approach
RISK WEIGHTED ASSETS