JJ Mois Année SMILOVICE Jan Neckař Dana Chromíková

Scoring Unit (SCOR)2April 2008 Basel II concept differs two types of loss: Frequency UNEXPECTED LOSS EXPECTED LOSS B2 - CONCEPT LOSSES IN TIME

Scoring Unit (SCOR)3April 2008 Probability 0,1% Probability 99,9% Creation of Provisions - Covered by SRC CAPITAL RESERVES MAINTENANCE STRESS TESTING BASEL II CONCEPT – distribution of the losses VALUE AT RISK LOSS FREQUENCY B2 - CONCEPT

Scoring Unit (SCOR)4April 2008 B2 - CONCEPT EXPECTED LOSS EL = PD * LGD * EAD PD – probability of default - estimation of probability then client is longer than 90 days delayed with payments, insolvency, … LGD – loss given default - estimation of the resulting economic loss after the recovery process - conditional estimation in case of client is in default EAD – exposure at default - conditional estimation of exposures in case of client is in default - average drawing at default is higher than outside default EL = PD*E(loss|default) + (1-PD)*E(loss|nedefault) = PD * LGD * EAD

Scoring Unit (SCOR)5April 2008 N(x) – distribution function of normalized normal distribution of random quantity G(x) – inversion function to distribution function of normalized normal distribution Scaling factor – according to direction of ČNB is equal to 1,06 Maturity (M) – Average maturity of the expected cash-flows (repayments) Factor of maturity Correlation factor R for retail exposures (excl. Mortgages = 0,15, qualifying revolving = 0,04): Correlation factor for non-retail exposures: S – Annual sales for the consolidated group (million EUR) B2 - CONCEPT UNEXPECTED LOSS – CAPITAL REQUIREMENT Tier1 + Tier2 ≥ 8% * Σ RW * EAD Tier1 ≥ Tier2 &

Scoring Unit (SCOR)6April 2008 B2 - CONCEPT UNEXPECTED LOSS – CAPITAL REQUIREMENT

Scoring Unit (SCOR)7April 2008 Behavior under stress is not easy to predict STRESS-TESTING

Scoring Unit (SCOR)8April 2008 Frequency LOSSES IN TIME STRESS-TESTING

Scoring Unit (SCOR)9April 2008 STRESS-TESTING ECONOMETRIC MODEL STRESS SCENARIOS STRESS-TESTING MODELS STRESSED CHARACTERISTICS

Scoring Unit (SCOR)10April 2008 Econometric model predicts the macroeconomic characteristic as: These models have usually 50 – 100 formulas and above 200 parameters There are several various of predictions, called as scenarios: The most probable scenario is selected for development of the model. STRESS-TESTING  GDP  unemployment  interest rates  inflation / deflation  price of oil  …  baseline  depression  deep depression  high inflation  … ECONOMETRIC MODEL STRESS-TESTING SCENARIOS &

Scoring Unit (SCOR)11April 2008 STRESS-TESTING MODELS Stress testing = a way how to measure risk of Modeled via scenarios for macroeconomics characteristics extreme but realistic events Two type of models : Logistic regression Factor model based on Merton’s model We assume that portfolio depends on macroeconomic situation and we need to find relation between stressed variable (PD, LGD, CCF) and macroeconomic characteristics: PDt = f (Mt1) t ≥ t1, f (Mt1) function of macroeconomic characteristics Example for stressing PD:

Scoring Unit (SCOR)12April 2008 STRESS-TESTING MODELS Y is explained variable (indicator of default), EY is probability of default is vector of explanatory variables (macro-economic indicators). Main advantages of this model: Basic statistical model used for modelling 0-1 variable with good mathematical properties Logistic regression

Scoring Unit (SCOR)13April 2008 STRESS-TESTING MODELS Factor model based on Merton’s model Where is logarithmic change of client’s asset is systematic factor is specific factor

Scoring Unit (SCOR)14April 2008 STRESS-TESTING MODELS Factor model based on Merton’s model 1 in case of default 0 in case of non-default Probability of default

Scoring Unit (SCOR)15April 2008 STRESS-TESTING MODELS Conditional probability of default: Factor model based on Merton’s model Likelihood function derivated from binomial distribution of default rate: