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Estimation of the Loss Given Default LGD Retail Portfolio

Agenda. Concept Methodology of estimationResults (just for illustration)Margin of conservatismCostsConclusion. Introduction. LGD: one of the three parameters (PD, LGD, EAD) in IRB approach for retailUnexpected Loss and Minimum capital reserve required proportional to LGDPragmatic approachJu

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Estimation of the Loss Given Default LGD Retail Portfolio

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    1. Estimation of the Loss Given Default (LGD) – Retail Portfolio

    2. Agenda Concept Methodology of estimation Results (just for illustration) Margin of conservatism Costs Conclusion

    3. Introduction LGD: one of the three parameters (PD, LGD, EAD) in IRB approach for retail Unexpected Loss and Minimum capital reserve required proportional to LGD Pragmatic approach Just a calculation method Neither statistical segmentation nor model In the underlying Merton model of Basel 2 formulas, only E(LGD) is expected. An individual estimation of LGD is not required. Use of the historical data available For retail portfolio

    4. Definitions (DIRECTIVE 2006/48/EC, 14 June 2006, article 4) ‘loss’ means economic loss, including material discount effects, and material direct and indirect costs associated with collecting on the instrument; ‘loss given default (LGD)’ means the ratio of the loss on an exposure due to the default of a counterparty to the amount outstanding at default; Concept

    5. Calculation Basic loss : = EAD (exposure at default) – recoveries (all over the period of default) + increases of exposure (all over the period of default) Economic loss: add discount effects and costs (human resources…) Increases include drawing after default (not in the CCF parameter) costs Concept

    6. Calculation where j >=0, at default, j=0 : EAD = exposure at default C*j = increases of period j, converted to current value (at default) with rate r. R*j = recoveries of period j, converted to current value (at default) with rate r. cs indirect costs (% of exposure) – set, same for all exposures Concept

    7. Illustration on a theoretical case (overdraft on a bank account): Basic Loss = Exposure at default – recovery flow + increase flow = 300 – 200 + 30 = 130 Discount effects (rate: 15%) “Discounted” loss = EAD – converted to current value recovery flow + converted to current value increase flow = 300 – (200/1.15) + (30/1.15) = 300 – 174 + 26 = 152 Indirect costs : 10 € for mail, 3% of EAD Add a margin of conservatism if necessary Concept

    8. Illustration on real data: 1st example – mortgage, default in December 2004, loss in January 2005 Concept

    9. Illustration on real data : 2nd example – Mortgage, default in October 2003, last recovery in March 2004 Discount rate : 7.5% (1 year), or 0.6% (1 month) Concept

    10. Conversion to current value: choice of the rate Not detailed in Basel 2 Framework Choice of Group: real interest rate of the loan Coherence with IFRS Conversion with a monthly step Horizon Recovery observed on 10 years All recovery flows coming after 10 years are considered as lost Methodology

    11. Practical calculation – individual level Division in 10 years of recovery Year 0 = 12 months following default Year 1 = 13 to 24 months following default … Year 9 = 108 to 120 months following default Look at every period j, from 0 to 9 years, of Recovery flows, converted to current value (Rj*) Increase flows, converted to current value (Cj*) Amount still to recover at the beginning of period j (RRj*) At default, j=0 and RR0 = EAD After default RRj = RRj-1 – R*j-1 + C*j-1 marginal rate of recovery, on period j ?j = (R*j - C*j) / RRj-1 Calculation of a rate of no recovery at 10 years (Kaplan-Meier estimator) Methodology

    12. Aggregation of flows – Vintage matrix By category of product and by generation of default construction of matrix giving the dynamic of recoveries for each generation of default (A generation groups all loans or overdrafts in default at the same time, year, quarter or month) Still to recover Marginal rate LGD Methodology

    13. Truncated and censored data The oldest generations aren’t observed since default => left truncation The youngest generations are still in default and not closed => right censoring They take part to the calculation while they are observed Methodology

    14. Advantages of the method: All observations can take part to the estimation, including when data are censured or truncated Marginal rates can easily be “backtested” An estimation of LGD depending of age in default can be produced: After j periods in default: Segmentation By category of product, type of guarantee, age in default Not a statistical model Methodology

    15. Margin of conservatism Reasons of adding a margin of conservatism Lack of robustness (low numbers of data) Temporal volatility (changing in organization, big amounts…) Economic cycle (downturn LGD) Methods to treat these uncertainties Bootstrap 1000 random draws quantile : 95% Sampling (elimination of 5% of quarterly generations with the better marginal rate) Methodology

    16. Bootstrap Recent method (1979 - B. EFRON) based on data simulation Sampling with replacement, where sample size is the same as the original dataset. Each sample simulate new “stressed” data. Estimation of LGD on all these samples Distribution of empirical statistics, and quantiles giving a confidence interval. Methodology

    17. Additional margin For approximations done during estimation, intended for disappearing. They can lead to errors in estimation, that is why a margin is added to regulatory margin of conservatism. Examples of approximations identified: Entity bias (estimation on 10 regional banks among 25) Loss registered in commercial agency, not available in data Exact Basel default not available in historical data, approximation with other close notions Methodology

    18. Costs Costs entered: From litigation department 3 types of costs: Human resources (70%) Customers (25%) Regular costs (5%) Methodology: Average cost of litigation (by loan) Average exposure at default (by loan) Results (illustration for example)

    19. Results For confidential reasons, the results are changed… Big impact of indirect costs and margin of conservatism Results

    20. Illustration on theoretical data: Marginal Recovery Rate on 10 years - Mortgage Results

    21. Graphic illustration Results

    22. Results Results by age of default

    23. Conclusion Link with provisions For exposures in default (with PD = 100%), comparison between LGD and provisions, with impact on RWA For all exposures, comparison between LGD and provisions, with impact on capital Interactions with accounts department Link with economic capital Use of single factor models, like in Basel 2 framework LGD still an fundamental parameter May be adjusted (margin less conservative)

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