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SMILOVICE. Jan Neckař Dana Chromíková. B2 - CONCEPT. EXPECTED LOSS. Basel II concept differs two types of loss:. UNEXPECTED LOSS. LOSSES IN TIME. Frequency. VALUE AT RISK. Extreme loss. Unexpected loss. Expected loss. B2 - CONCEPT. BASEL II CONCEPT – distribution of the losses.
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SMILOVICE Jan Neckař Dana Chromíková
B2 - CONCEPT EXPECTED LOSS Basel II concept differs two types of loss: UNEXPECTED LOSS LOSSES IN TIME Frequency
VALUE AT RISK Extreme loss Unexpected loss Expected loss B2 - CONCEPT BASEL II CONCEPT – distribution of the losses Creation of Provisions - Covered by SRC CAPITAL RESERVES MAINTENANCE STRESS TESTING FREQUENCY Probability 99,9% Probability 0,1% LOSS
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
B2 - CONCEPT UNEXPECTED LOSS – CAPITAL REQUIREMENT & Tier1 ≥ Tier2 Tier1 + Tier2 ≥ 8% * Σ RW * EAD 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
STRESS-TESTING Behavior under stress is not easy to predict
STRESS-TESTING LOSSES IN TIME Frequency
STRESS-TESTING STRESSED CHARACTERISTICS STRESS-TESTING MODELS STRESS SCENARIOS ECONOMETRIC MODEL
STRESS-TESTING ECONOMETRIC MODEL STRESS-TESTING SCENARIOS & 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. • GDP • unemployment • interest rates • inflation / deflation • price of oil • … • baseline • depression • deep depression • high inflation • …
STRESS-TESTING extremebut realistic events STRESS-TESTING MODELS Stress testing = a way how to measure risk of Modeled via scenarios for macroeconomics characteristics We assume that portfolio depends on macroeconomic situation and we need to find relation between stressed variable (PD, LGD, CCF) and macroeconomic characteristics: Example for stressing PD: PDt = f (Mt1) t ≥ t1,f (Mt1) function of macroeconomic characteristics Logistic regression Two type ofmodels: Factor model based on Merton’s model
STRESS-TESTING STRESS-TESTING MODELS Logistic regression 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
STRESS-TESTING STRESS-TESTING MODELS Factor model based on Merton’s model Where is logarithmic change of client’s asset is systematic factor is specific factor
STRESS-TESTING STRESS-TESTING MODELS Factor model based on Merton’s model 1 in case of default 0 in case of non-default Probability of default
STRESS-TESTING STRESS-TESTING MODELS Factor model based on Merton’s model Conditional probability of default: Likelihood function derivated from binomial distribution of default rate:
