Driver-based dependencies in capital modelling Charl Cronje and Paul O’Connor 1 October 2014
Driver-based dependencies in capital modelling
Charl Cronje and Paul O’Connor 1 October 2014
Meet the team
Charl Cronje Partner
Paul O’Connor Consultant
Agenda
Copula process and issues What is a dependency scenario generator (DSG)? Uses of a DSG Lessons learned Next steps
Copula process and issues
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Dependency
LoB A premium risk
LoB B premium risk
Limited data A simple dependency problem
Copula
Copula process and issues Current understanding
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Inputs required: Which copula family?
What parameter values?
Issues: Do I understand the dependency structure well enough? How can I parameterise given only sparse data? Can I easily explain my dependency structure? How should I validate my choices? Am I constrained by:
current regulatory expectations (eg tail-dependency)? available copulas: how do I cope with cases where body differs from tail?
Positives: Standard market approach Regulatory acceptability Quick and inexpensive
What is a DSG?
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What is a DSG? Introducing the concept
“Dependency Scenario Generator”
– Driver-based dependency model (external to the internal model)
– Outputs (“pseudo-data”) used as an input into other processes – eg copula calibration, copula validation, MI
– Based on understanding of business processes and risks held
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Definition What do we mean by a driver approach?
D
X Y
“Induced” dependency
𝐿𝐿𝐿 𝑓𝑋 𝑥|𝜃𝑋 𝑏𝐿 𝑃𝑃𝑃 𝑜𝑓 𝑋, 𝑓𝐷 𝑑|𝜃𝐷 𝑏𝐿 𝑃𝑃𝑃 𝑜𝑓 𝑃
We say that
D is a driver of X If
∃ 𝑓𝑓𝑓𝑓𝐿𝑓𝑜𝑓 ℎ𝑋 such that
𝜃𝑋 = ℎ𝑋 (𝑑)
We call ℎ𝑋 a “linking function”
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Definitions Some existing usage from the market
Catastrophe models
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LCP example model A driver approach to insurance risk
Insurance risk (Reserve / UW)
Shock Claims inflation
Claims frequency Workload strain
Underwriting cycle
Model design (showing one line of business only):
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LCP example model A driver approach to insurance risk
Some independent outputs - reserve risk across two lines of business
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LCP example model A driver approach to insurance risk
Two lines of business – no legal shock
Reserve risk A Reserve risk B
Claims inflation
Claims frequency Workload strain
Underwriting cycle
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LCP example model A driver approach to insurance risk
Common drivers: claims inflation, claims frequency, workload strain, UW cycle
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LCP example model A driver approach to insurance risk
Adding in legal shock on claims frequency
Reserve risk A Reserve risk B
Claims inflation
Claims frequency Workload strain
Underwriting cycle
Shock
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LCP example model A driver approach to insurance risk
Adding in legal shock on claims frequency
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Uses of a DSG
DSGs to support existing model Putting “pseudo-data” to use
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Driver-based Dependency Scenario Generator
Separate from existing model
Built with input of key individuals from business
Focused on most material dependencies
Produces arbitrarily large set of outputs (“pseudo-data”)
But how do we use it?
Direct implementation of a DSG A driver-based internal model?
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Inputs required
Choice of drivers and their distributions
Choice of links between modelled variables and drivers
Positives Very flexible with regard to output “shapes” Some drivers easily observed (can parameterise objectively) Remaining drivers can be explicitly stress-tested More easily communicated to management Parameterised with understanding of business Freed of constraints associated with copula modelling More realistic? Issues Perceived increase in model complexity Costs of shifting from market norm Addressing non-modelled drivers Costs of rebuilding if built into existing models (model change) Conclusions Useful, but may be too big a leap for some… so what can we do?
Design and build Select Copula from
implementable options
DSGs to support existing model “Pseudo-data” as a validation tool – option 1
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Choose Copula type
Parameterise
Validation process Identify key underlying
scenarios
Build DSG for main drivers
Generate pseudo-data
Fit copula for comparison
Parameterisation Expert Judgement
Historical data
Remove non-desirable features / fill in gaps
Sense check
Dependency scenario generator
Fit Copula Validate
DSGs to support existing model “Pseudo-data” as a validation tool – option 2
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Internal model (with existing dependency
structure)
Internal model outputs
Validation process Identify key underlying scenarios
Build DSG for main drivers
Generate pseudo-data
Use pseudo-data to resample from IM outputs and compare results
Dependency scenario generator
Resampled internal model
outputs Validate
Expert judgement
DSGs to support existing model “Pseudo-data” as a parameterisation tool
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Fit copula
Validation activity Review for missing key drivers
Sensitivity testing
Compare with historical correlation
Historical data Apply expert judgement
Identify non-desirable features
Sense-check
Dependency Scenario
Generator
Identify key drivers
Review and refine DSG
“Pseudo-data”
Validation: lessons learned
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Validation: lessons learned DSG work to date
Validation: lessons learned Common themes
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In real-life cases we have seen, T-copulas cannot simultaneously achieve the 1-in-200 and “body” percentiles implied by company views
Validation: lessons learned A new benchmark
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Validation: lessons learned A new benchmark
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Dependency assumptions are a known weakness for current model use
Many companies already make explicit adjustments to outputs to account for suspected weaknesses in dependency assumptions
The DSG now provides a benchmark distribution for more informed adjustments prior to model use
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Validation: lessons learned DSG work to date
Challenges – Simplicity is key
– If you want to parameterise credibly – If you want a manageable model
– Non-modelled volatility HAS to be considered Positives
– Building a driver model teaches you a LOT about that system – Others have been exploring these ideas – Its doable!
Next steps
Take the first steps towards building a DSG
– Gather individuals in your business best placed to identify drivers of dependency
– Discuss those drivers as a group, and try to come to a communal view of – The 3-5 most important dependency drivers underlying the business – The ways in which those drivers impact the business
– Start thinking about how you might build a model for these drivers
– Cycles, shocks, indices etc – Plausible parameters – Back-testing
Next steps Some actions for you
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Scope
This document is a visual aid to complement an oral presentation and does not constitute our written professional advice.
Written advice about any matters discussed should always be sought in order to clarify the data relied upon, assumptions, conclusions and recommendations.
This generic presentation should not be relied upon for detailed advice or taken as an authoritative statement of the law.
If you would like any assistance or further information, please contact the partner who normally advises you.
While this document does not represent our advice, nevertheless it should not be passed to any third party without our formal written agreement.
© Lane Clark & Peacock LLP 2014
Driver-based dependencies in capital modelling
Charl Cronje and Paul O’Connor 1 October 2014