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Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 2/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO Operational risk measurement Statistical approach to operational risk measurement OR:

  1. Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 2/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO Operational risk measurement Statistical approach to operational risk measurement � OR: Failures of normal processes (mistakes, using R frauds, robberies, liabilities, ...) � Two complementary approaches: � historical data (backward-looking) � scenario analysis (forward-looking) Roberto Ugoccioni � Actuarial method: compose Sanpaolo IMI Group Torino, Italy � Frequency distribution � Severity distribution ORM UNI T di GRUPPO ORM UNI T di GRUPPO Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 3/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 4/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Why R and how Historical loss data analysis � For each risk class (i.i.d.): � Why use R ? � Fit distributions (maximum likelihood) to internal � no best-practice in the field, few existing tools and external data � powerful, complete language � Choose best fits (GOF tests) � flexible framework � Compose internal/external distributions � How R is used at Sanpaolo IMI: � Use FFT to compute 1-year period aggregate, including insurance effects � methodological research � Measure rank correlations between risk � application prototyping classes in the data � production environment � Aggregate classes using copulas

  2. Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 5/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 6/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Example loss data analysis Example loss data analysis Dati interni Dati interni � Fit distributions � Fit distributions 99.999 99.999 (maximum likelihood) to (maximum likelihood) to 99.997 99.997 99.99 99.99 internal and external data internal and external data 99.97 99.97 99.9 99.9 Choose best fits (GOF Choose best fits (GOF � � 99 99 tests) tests) Probabilità (%) Probabilità (%) � Compose internal/external � Compose internal/external 90 90 distributions distributions � Use FFT to compute 1- � Use FFT to compute 1- 50 50 year period aggregate, year period aggregate, including insurance effects including insurance effects 10 10 gpd gpd lnorm A lnorm A chisquare KS AD SCvM SBC rank lnorm B lnorm B 1 1 gpd 0.3517447 0.8666720 0.9756209 0.9548710 -2006.659 1.2 ln.B 0.5970360 0.7966336 0.6693486 0.5158578 -2009.520 1.8 1 10 100 1000 10000 1 10 100 1000 10000 ln.A 0.2199431 0.2291122 0.3275139 0.3912281 -14138.940 3.0 perdita (scala arbitraria) perdita (scala arbitraria) Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 7/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 8/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Example loss data analysis Example loss data analysis Composizione Aggregate loss Fit distributions Fit distributions � � 99.999 (maximum likelihood) to (maximum likelihood) to 99.997 99.9999 99.99 internal and external data internal and external data 99.97 99.999 99.997 99.9 99.99 Choose best fits (GOF Choose best fits (GOF � � 99.97 99 99.9 tests) tests) Probabilità (%) 99 Probabilità (%) 90 � Compose internal/external � Compose internal/external distributions distributions 90 50 � Use FFT to compute 1- � Use FFT to compute 1- 50 year period aggregate, year period aggregate, 10 including insurance effects including insurance effects 1 10 full mixture 0.1 internal fit senza assicurazione Italian fit con assicurazione 1 0.01 1 100 10000 5 10 20 50 100 200 500 1000 2000 5000 perdita (scala arbitraria) Perdita (scala arbitraria)

  3. Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 9/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 10/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Scenario analysis Preparing scenario analysis � Prepare the answer ranges: � Interview local management � fix frequency classes � For each event type � determine three possible values for the 1-year � Ask average frequency aggregate unexpected loss (UL+ EL= 99.9% � Ask average loss quantile) � Ask “worst case” loss (99% quantile) � for each mean frequency, determine points with same UL � Use ranges to guide these answers � determine mean loss ranges � for each mean loss range, determine worst-case ranges by instersecting with iso-UL curves Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 11/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 12/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Example scenario construction Example scenario construction lognormal - lambda=1 lognormal - lambda=1 fix frequency classes fix frequency classes � � 0.05M 0.05M � determine three � determine three possible values for possible values for the 1-year aggregate the 1-year aggregate 0.04M 0.04M unexpected loss unexpected loss mean severity mean severity for each mean for each frequency � � 0.03M 0.03M frequency, determine class, determine points with same UL curves with same UL 0.02M 0.02M determine mean loss determine mean loss � � ranges ranges for each mean loss 0.01M for each mean loss 0.01M � � range, determine range, determine worst-case ranges by worst-case ranges by 0M 0M instersecting with instersecting with iso-UL curves 0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M iso-UL curves 0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M severity quantile 99.9% severity quantile 99.9%

  4. Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 13/15 Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 14/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO ORM UNI T di GRUPPO Example scenario construction Example scenario construction lognormal - lambda=1 lognormal - lambda=1 fix frequency classes � UL range: 0.05M 0.05M � determine three 44,005.20 93,386.79 possible values for the 1-year aggregate 0.04M 0.04M Results: unexpected loss EL : mean 8,868 mean severity mean severity for each frequency � stddev 1,287 0.03M 0.03M class, determine UL : mean 67,295 curves with same UL stddev 11,909 0.02M 0.02M VaR: mean 76,085 � determine mean loss stddev 12,436 ranges for each mean loss 0.01M 0.01M � rating (%): range, determine A B C D worst-case ranges by 0M 0M 3.4 93.2 3.4 0.0 instersecting with iso-UL curves 0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M 0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M severity quantile 99.9% severity quantile 99.9% Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 15/15 ORM UNI T di GRUPPO ORM UNI T di GRUPPO Conclusions � How did R perform? � methodological research and application prototyping: flexible tool, powerful language; library of tools developed � production environment: needs ad hoc GUI, has little support for compilation on mainframe architectures (e.g. HPUX) � memory/performance saturation limit hit when needing to handle very large amounts of data (> 10 7 points)

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