Orfival GPMS

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Risk ManagementLiability Driven Investment
Philippe Grégoire
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Agenda

• Risk
• Case study life insurance
• Modelling
• Results

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Introduction

• Risk is an exposure to uncertainty
• What are the risk drivers
• Market prices
• Customer behavior
• Modelling
• Risk factors dynamics
• Pricing models
• Risk measures
• Total risk Duration gap, VaR, Volatility,
• Systematic risk beta,
• Specific risk tracking error,

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Example
Calibration initial Yield curve Volatility Term
structure
Calibration Market Risk Premium Volatility
Hull and White Model
Stock Index
Risk free curve
Risk free curve
Index Return
Buy back Prepayment
Sectorial Indexes Asset Prices
Incentives
Sectorial/Asset beta
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Risk factor modelling

• Diffusion process
• a(t) is a drift that can fluctuate
• b(t) is a volatility term
• dz is a brownian motion

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Monte-Carlo Simulation

• Example diffusion process for Index prices
• R is the expected return risk free market
  risk premium
• s is the market volatility
• e is a random number N(0,1)

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Monte-Carlo SimulationExample stock index
Random number N(0,s)
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Interest Rate Dynamics

• Hull and White process
• Interest rates mean revert towards the forward
  rates level and slope q(t)
• Interest rate volatility is calibrated on caplet
  volatilities
• Average interest rate path is equal to the
  forward yield curve
• The model gives the entire yield curve at each
  future date t.

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Interest rates path
Forward rates
s 1.088 annuelle
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Spread LT / ST
Long Term rate
Short term rate
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Stock Index Dynamics

• Black Scholes Model
• Capital Asset Pricing Model
• sI is the volatility of the risk premium

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Case study Life insurance
Mortality risk
Interest rate risk
Buy back
Market or systematic risk
Interest rate risk
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Risk measure VaR (Gap)

• Gap measures the liabilities coverage under
  different scenarios
• Future Gap values depends on
• Assets
• Asset prices fluctuate
• Reinvestment rates are uncertain
• Liabilities
• Effective mortality rate maybe different from
  expected rate (Unexpected Loss)
• Insurance customers have the option to buy back
  their contract (similar to prepayment rate)
• VaR (Gap) is the maximum loss due to asset
  coverage for an horizon and a confidence level

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Case Study GPMS

• Assets
• Cash Flows Mapping
• Bonds redemptions and coupons
• Dividends
• Strategic allocation

• Liabilities
• Cash Flows Mapping
• Life or pension payments
• Payments in case of death
• Buy back

Asset Liability simulation Both cash-flows
enter the simulation
Future Gap value distribution VaR (Gap)
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Gap Distribution

• Simulation of 10,000 paths for risk factors. For
  each path, future asset value and liability
  payment are estimated. Gap (Asset Liability) is
  calculated at maturity.

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Cumulated distribution of Gap
Strategic allocation 60 equities, 40 Bonds
Strategic allocation 40 equities, 60 Bonds
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Sensitivity analysis

• Measures the impact of a parameter change on risk
• Example
• Market volatility increases by 5
• Parallel shift in the initial yield curve
• Change in strategic asset allocation
• Case study

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Summary

• Indentification of the risk drivers for assets
  and liabilities
• Economic risk (interest rates, stock indexes,)
• Customer behavior risk (prepayment, buy back,)
• Statistical risk (mortality,)
• Regulatory risk
• Modelling risk factors dynamic and pricing
• Risk Measures VaR (Gap)
• Sensitivity analysis