**Kristen La Picque**

Guillia Bardoni

Valentin Jouvenot

Guillia Bardoni

Valentin Jouvenot

**Presented by :**

**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

130

100

Default threshold: 100

Expected return (mu): 5%

Volatility (mu): 20 %

ln (130/100) = 26%

134

29,2%

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

Part II

"Hold 8% of the Risk Weighted Assets (RWA)"

Sum of individual Risks

x Exposure size (ei)

Weigth (ei)

Probability of default: Overview

FIRM VALUE

TIME

Vo

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 ?

Part III

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

Expected loss

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

MIXTURE MODELS

The majority of threshold models can be represented as Bernoulli mixture models.

TRESHOLD 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

Giulia Bardoni

Valentin Jouvenot

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