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using R frauds, robberies, liabilities, ...) Two complementary - - PowerPoint PPT Presentation

Apr 16, 2023 208 likes •270 views

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:

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SLIDE 1

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Statistical approach to

  • perational risk measurement

using R

Roberto Ugoccioni

Sanpaolo IMI Group

Torino, Italy

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

OR: Failures of normal processes (mistakes,

frauds, robberies, liabilities, ...)

Two complementary approaches:

historical data (backward-looking) scenario analysis (forward-looking)

Actuarial method: compose

Frequency distribution Severity distribution

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 3/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Why R and how

Why use R?

no best-practice in the field, few existing tools powerful, complete language flexible framework

How R is used at Sanpaolo IMI:

methodological research application prototyping production environment

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 4/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Historical loss data analysis

For each risk class (i.i.d.):

Fit distributions (maximum likelihood) to internal

and external data

Choose best fits (GOF tests) Compose internal/external distributions Use FFT to compute 1-year period aggregate,

including insurance effects

Measure rank correlations between risk

classes in the data

Aggregate classes using copulas

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SLIDE 2

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 5/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example loss data analysis

  • Fit distributions

(maximum likelihood) to internal and external data

  • Choose best fits (GOF

tests)

  • Compose internal/external

distributions

  • Use FFT to compute 1-

year period aggregate, including insurance effects

Dati interni

perdita (scala arbitraria) Probabilità (%)

1 10 50 90 99 99.9 99.97 99.99 99.997 99.999 1 10 100 1000 10000 gpd lnorm A lnorm B

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 6/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example loss data analysis

  • Fit distributions

(maximum likelihood) to internal and external data

  • Choose best fits (GOF

tests)

  • Compose internal/external

distributions

  • Use FFT to compute 1-

year period aggregate, including insurance effects

Dati interni

perdita (scala arbitraria) Probabilità (%)

1 10 50 90 99 99.9 99.97 99.99 99.997 99.999 1 10 100 1000 10000 gpd lnorm A lnorm B

chisquare KS AD SCvM SBC rank 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 ln.A 0.2199431 0.2291122 0.3275139 0.3912281 -14138.940 3.0

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 7/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example loss data analysis

  • Fit distributions

(maximum likelihood) to internal and external data

  • Choose best fits (GOF

tests)

  • Compose internal/external

distributions

  • Use FFT to compute 1-

year period aggregate, including insurance effects

Composizione

perdita (scala arbitraria) Probabilità (%)

1 10 50 90 99 99.9 99.97 99.99 99.997 99.999 99.9999 1 100 10000 full mixture internal fit Italian fit

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 8/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example loss data analysis

  • Fit distributions

(maximum likelihood) to internal and external data

  • Choose best fits (GOF

tests)

  • Compose internal/external

distributions

  • Use FFT to compute 1-

year period aggregate, including insurance effects

Aggregate loss

Perdita (scala arbitraria) Probabilità (%)

0.01 0.1 1 10 50 90 99 99.9 99.97 99.99 99.997 99.999 5 10 20 50 100 200 500 1000 2000 5000 senza assicurazione con assicurazione

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SLIDE 3

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 9/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Scenario analysis

Interview local management For each event type

Ask average frequency Ask average loss Ask “worst case” loss (99% quantile)

Use ranges to guide these answers

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 10/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Preparing scenario analysis

Prepare the answer ranges:

fix frequency classes determine three possible values for the 1-year

aggregate unexpected loss (UL+ EL= 99.9% quantile)

for each mean frequency, determine points with

same UL

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

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example scenario construction

  • fix frequency classes
  • determine three

possible values for the 1-year aggregate unexpected loss

  • for each mean

frequency, determine points with same UL

  • determine mean loss

ranges

  • for each mean loss

range, determine worst-case ranges by instersecting with iso-UL curves

lognormal - lambda=1

severity quantile 99.9% mean severity

0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M 0M 0.01M 0.02M 0.03M 0.04M 0.05M

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 12/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example scenario construction

  • fix frequency classes
  • determine three

possible values for the 1-year aggregate unexpected loss

  • for each frequency

class, determine curves with same UL

  • determine mean loss

ranges

  • for each mean loss

range, determine worst-case ranges by instersecting with iso-UL curves

lognormal - lambda=1

severity quantile 99.9% mean severity

0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M 0M 0.01M 0.02M 0.03M 0.04M 0.05M

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SLIDE 4

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 13/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

Example scenario construction

  • fix frequency classes
  • determine three

possible values for the 1-year aggregate unexpected loss

  • for each frequency

class, determine curves with same UL

  • determine mean loss

ranges

  • for each mean loss

range, determine worst-case ranges by instersecting with iso-UL curves

lognormal - lambda=1

severity quantile 99.9% mean severity

0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M 0M 0.01M 0.02M 0.03M 0.04M 0.05M

Statistical approach to operational risk... UseR! 2006 Roberto Ugoccioni (SanpaoloIMI) 14/15

ORM UNI T di GRUPPO ORM UNI T di GRUPPO

lognormal - lambda=1

severity quantile 99.9% mean severity

0M 0.02M 0.04M 0.06M 0.08M 0.1M 0.12M 0.14M 0M 0.01M 0.02M 0.03M 0.04M 0.05M

Example scenario construction

UL range: 44,005.20 93,386.79 Results: EL : mean 8,868 stddev 1,287 UL : mean 67,295 stddev 11,909 VaR: mean 76,085 stddev 12,436 rating (%): A B C D 3.4 93.2 3.4 0.0

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 (> 107 points)