Using Stochastic Models in Risk and Capital Management in Life Assurance
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Using Stochastic Models in Risk and Capital Management in Life Assurance Tuesday 5 th April 2005 Craig Turnbull. Agenda. Introduction: Developments in the use of (internal) stochastic models in life assurance Why now? Who wants it? How does it work? What questions is it used to answer?

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Using Stochastic Models in Risk and Capital Management in Life Assurance Tuesday 5th April 2005 Craig Turnbull


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Agenda Life Assurance

  • Introduction: Developments in the use of (internal) stochastic models in life assurance

    • Why now? Who wants it?

    • How does it work?

    • What questions is it used to answer?

  • Assessing Risk-Based Capital for With-Profits Business

    • Quantifying risks and their interaction

  • Using Models as a Capital Management Tool

    • Identifying and appraising candidate solutions

  • Questions and Answers


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Introduction: Life AssuranceDevelopments in the use of (internal) stochastic models in life assurance


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What Developments? Life Assurance

  • Global life assurance industry developing large-scale internal stochastic asset-liability models

    • Sophisticated arbitrage-free multi-asset models

    • Complex liability models

      • Dynamic management rules, ‘000s model points, etc

  • Particularly in UK life industry and the top 20 multinational insurance groups


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Why Now? Life Assurance

  • Regulatory compulsion (UK only)

  • Greater appreciation of risks in guarantees in life & pensions business

  • Less capital / risk appetite than 5 years ago

  • Appreciation that life / pensions ALM falling behind banking industry

  • Technology

    • Cheaper, faster


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Who Wants It? Life Assurance

  • Regulators

    • FSA

      • Market-consistent guarantee costs (RBS / Pillar 1)

      • Risk-based capital assessment (ICA / Pillar 2)

    • Stochastic modelling approach required in US and Canada

    • Will other regulators follow FSA regime?

  • Accountants

    • IAS, FRS 27 (FRS 17)

    • European Embedded Value

  • Credit rating agencies

    • Risk-based capital adequacy

    • Calculation and communication

  • Internal management

    • Economic capital allocation and performance measurement

    • Risk / capital management

    • Product design / pricing


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What can it deliver? Life Assurance

  • Quantification of costs, risks and capital requirements

    • Relative size of drivers

    • Risk dynamics

      • Diversification, interaction, non-linearity

  • Identification and appraisal of candidate management solutions

    • Informing trade-offs


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Office - Specific Liability Features, Management Strategies Life Assurance

Model Office Software

Market-Consistent Balance Sheet /

Capital Assessment /

etc

(Market – Consistent) Economic Scenario Generator

Market Prices / Best-Estimates

How Does it Work?



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Approaches to measuring RBC Life Assurance

  • What approaches can be taken to assessing risk-based capital requirements for insurance liabilities?

    • Run-Off

      • Capital required to fund projected cashflow shortfalls with a specified level of confidence

    • Value-At-Risk

      • Capital required to fund a future market-consistent liability value with a specified level of confidence

        • Funding the cost of transferring market risk to market


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With-Profit Life AssuranceImplementation challenges

  • Run-Off

    • Estimating long-term asset return tails

      • Scarcity of relevant data

    • Projecting market-consistent balance sheet forward over multiple time horizons

      • Important if m-c balance sheet is a driver of decision rules


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With-Profit Life AssuranceImplementation challenges

  • VaR

    • Estimating 1-year asset return extreme tails

      • Conditional on recent market behaviour, option prices?

    • Nested simulations required (in theory!!)

    • Practical (approximate) implementation approaches



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Implied Equity Falls Life Assurance


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Individual Capital Assessment Life Assurance

  • Predominantly VaR-style definitions used currently

    • Capital required to produce 99.5% confidence that realistic liabilities are funded after one year

    • Given the above difficulties, how is VaR being implemented for With-Profits?

      • Unconditional asset modelling

      • Broadly two implementation approaches for VaR

        • Univariate

        • Multivariate


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ICA for With-Profits – Life AssuranceUnivariate Approach

  • Calculate 99.5th percentile events for each risk factor, and obtain capital requirements for each risk factor

  • Calculate total capital requirement by applying a correlation matrix to the capital requirements for each risk factor

  • This assumes:

    • Risks are linear

    • Risks do not interact


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ICA for With-Profits Life AssuranceMultivariate Approach

  • Estimate sensitivities of realistic balance sheet to each risk factor

  • Use these to project RBS to end-year (using stochastic asset model)

  • Read off 99.5th percentile discounted loss


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Illustrative Example Life Assurance

  • Liability is a 10-yr equity total return put option with strike at-the-spot

    • Interest rate of 5%

    • Volatility of 20%

    • Nominal of £1,644m

    • Current market value of put option of £100m

  • Assume assets backing guarantee cost are invested in equities

    • And any assets required in excess of guarantee cost are invested in cash


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RBC under Univariate approach: Life AssuranceRisk Contributions

  • 99.5th percentile equity return is -36%

    • Liability increases from 100 to 235

    • Assets fall from 100 to 64

    • Equity capital requirement is 163

      • [(235-100) – (100-64)]/ 1.05

  • 99.5th percentile rise in option-implied equity vol is 5%

    • Liabilities increase from 100 to 160

    • Assets do not change in value

    • Vol capital requirement is 57

  • 99.5th percentile interest rate fall is 1.5%

    • Liabilities increase from 100 to 157

    • Assets do not change in value

    • Interest rate capital requirement is 54


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RBC under Univariate approach: Life AssuranceAllowing for diversification

  • Sum of capital requirements is £274m

  • But this assumes perfect correlation

  • Assume correlations of:

    • -0.3 between equities / interest rates

    • -0.4 between equities / option-implied vol

    • +0.1 between interest rates / implied vol

  • Implies capital requirement of £185m

    • Diversification benefit of 32%


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RBC under Multivariate approach Life Assurance

  • Use a number of sensitivity tests:

    • 20% equity fall increases liabilities from 100 to 159

    • 40% equity fall increases liabilities from 100 to 259

    • 0.85% interest rate fall increases liabilities from 100 to 130

    • 2% option-implied interest rate rise increases liabilities from 100 to 124

    • Could use many more, e.g. 20% equity fall after 1% interest rate fall, etc…

  • Use ‘greeks’ to project liabilities in each 1-yr asset simulation





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RBC: Concluding Thoughts Life Assurance

  • Current implementations of the multivariate approach produce similar capital requirements to univariate approach

    • In example, capital requirements were £187m and £185m

  • But mulitvariate approach is inherently more flexible and transparent

    • Sophistication can be developed incrementally

    • More useful as a risk management tool (identifying and appraising candidate management solutions)


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Correlations: An Aside Life Assurance

  • Most life offices are exposed to falls in equities and falls in interest rates

    • (Also true for Defined Benefit pension funds)

  • Negative correlation assumption between equities and interest rates implies ‘natural hedge’

    • i.e. Big diversification benefit

  • What if we reduce equity / interest rate correlation?






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Appraising hedging solutions Life AssuranceMatching the risk exposures


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Appraising hedging solutions Life AssuranceEstimating economic capital

Neutralising equity exposure: reductions in ICA and RCM

Option strategy improves gamma and vega matches: significant reduction in ICA, no impact on RCM


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Monitoring and managing a hedging strategy Life Assurance

  • Liability risk exposures will change over time as financial markets move

  • Any hedge is unlikely to be static for long periods. The extent to which this is the case will depend on choice of hedging solution – e.g. how well matched is equity gamma?

  • Hedging performance can be regularly monitored (e.g. quarterly) and, when appropriate, re-balanced.

Impact of Interest Rate and Equity Market Interaction on Realistic Guarantee Cost

e.g. cash guarantee’s equity delta can double when the yield curve falls by 100bp.


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Concluding Thoughts Life Assurance

  • Changes in regulatory / accounting / rating agency regimes mean significant step towards convergence in various capital / value / profit measures

  • Reduces constraints to managing economic risks

  • New valuation tools allow capital market solutions to be more effective at mitigating market risks in life assurance business


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Questions and answers Life Assurance


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