Ekaterina Ovchinnikova Finance Academy under the Government of the Russian Federation Loss distribution approach to assessing operational risk State-of-the art methods and models for financial risk management September 14-17,2009

2 Risk Management Identify Assess Control Mitigate Quantitative assessment  BIA:  TSA:  AMA: the ORC estimate is found from bank’s internal model

3 Loss distribution approach F(frequency) – the number of risk events occurred during a set period S(severity) – the amount of operational loss resulting from a single event T(total risk) – the sum of F random variables S, i.e. total loss over the set period The computation is carried out simultaneously for several homogeneous groups with due account for dependencies OR capital estimate is calculated as Value-at-Risk – % quantile of the aggregate loss distribution T. Modeling is based on Monte-Carlo simulation

4 External fraud: Modeling (1)  Risk event – illegal obtention of a retail loan and/or deliberate default  The law for Severity is chosen using sample data. Data is collected via the everyday monitoring of mass media. Distribution is fitted by checking statistical hypotheses. Parameters are estimated by maximum likelihood method  Frequency follows binomial or Poisson law (this could be derived from the credit undewriting workflow). Parameters are set according to the peculiar features of the institution

5 External fraud: Frequency (1) P0P0 P1P1 P3P3 1-P 1 P2P2 1-P 2 1-P 3 P4P4 1-P 4 Fraud attemptApplication is accepted Application is processed Examined by Security Service Scoring P 0 – the probability of a fraud attempt; P i – the probability that fraud is recognized on the i-th check point; The probability of loss P = P 0 *(1–P 1 )*(1–P 2 )*(1–P 3 )*(1–P 4 ). Suppose we examine K applications during the set period of time. Then frequency is a binomially distributed random value with parameters K and P

6 External fraud: Frequency (2) p = P1*P2 – probability of loss; n – number of loans issued. Given n → ∞ and p<0.1 in a series of Bernoulli trials frequency is described by Poisson law witn λ=np 1-P 1 Loan is retuned Outstanding loan P1P1 P2P2 1-P 2 Honest borrower- credit risk Loan is not returned Deliberate default – operational risk

7 External fraud: Modeling (2)  Prediction horizon – 1 month, α = 99%  Amounts in terms of money are adjusted to correspond the CPI level in May 2008 (RUR)  Loss amount is considered without recovery  The calculation is carried out for an abstract credit institution TypenpLimits EXPEXP*811502,25% RUR AUTO28300,78%90 ths - 3 mio RUR IPT5090,36%300 ths- 30 mio RUR * including express loans, immediate needs loans and credit cards

8 Trial pattern (1)

9 Trial pattern (2)

10 Results (May 2008)

11 Results (Shortfall)  Disastrous loss estimate ES=E(T|T>VAR) exceeds VAR by 2.2%

Whу use EVT? 12 EVT cannot predict unpredictable. “But what EVT is doing is making the best use of whatever data you have about extreme phenomena” “Fat” tails EVT

What is EVT? Block maxima method Peaks over threshold method 13

14 Retail credit fraud: risk factors

15 Internal fraud losses

Choosing the threshold u 16 ME (u)=E(S-u|S>u)~

Parameter Estimation 17

Distribution of Excesses (S-u>s|S>u) GPD fit is №1 according to K-S test (33 other distributions checked) 18

Distribution of values below u 19 Heavy tailed as well

Challenges and Solutions ? X Y “Fat” tailsScarce DataDependencies EVT Bayesian Approach Copulae

The behavior of ML estimates 21 uExceedances ξβ ,00361, , ,00301, , ,00241, , ,00231, , ,00211, , ,00180, , ,00181, ,00

Software Enterprise-wide OR management: SAS Oprisk, Oracle Reveleus, RCS OpRisk Suite, Fermat OpRisk, Algo OpVar Russian vendors – Ultor, Zirvan Distribution fitting and Monte-Carlo Simulation Mathwave EasyFit 22

23 Thank You for Your Attention!

24 AMA Advantages  Based on real operational loss data and expert judgements provides more reliable measurement results;  Takes into account peculiar features of a particular bank, the profile of its operational risk exposure, control systems and efforts made to mitigate risk (insurance) ;  Encourages regular business process analysis and risk detection;  Suggests that bank would satisfy general, qualitative and quantitative standards (Basel-II);  Reduces OR capital requirements by virtue of efficient risk management and internal control mechanisms.

25 Consumer loan (EXP) EXP

26 Car loan (AVT) AVT

27 Mortgage (IPT) IPT

28 Comparison Type May 2008April 2007 npnp EXP811502,25%426672,7% AUTO28300,78%25000,6% IPT5090,36%3330,05% volumes n were evaluated as average performance over Top-30 retail banks in 2006 and 2007 respectively (we excluded Savings Bank of Russia data while calculating average for mortgages) estimates for probabilities p were obtained using data from mass media and expert judgement