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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LCP is part of the Alexander Forbes Group, a leading independent provider of financial and risk services. Lane Clark & Peacock LLP is a limited liability partnership registered in England and Wales with registered number OC301436. LCP is a registered trademark in the UK (Regd. TM No 2315442) and in the EU (Regd. TM No 002935583). All partners are members of Lane Clark & Peacock LLP. A list of members’ names is available for inspection at 95 Wigmore Street, London, W1U 1DQ, the firm’s principal place of business and registered office. The firm is regulated by the Institute and Faculty of Actuaries in respect of a range of investment business activities. Locations in London, Winchester, Belgium, Switzerland, the Netherlands, Ireland and the UAE.

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