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Risk Pricing Linkages between Financial and Insurance Markets

Risk Pricing Linkages between Financial and Insurance Markets. John Daniel Pollner, World Bank Presented at World Bank conference on “Financing the Risks of Natural Disasters,” Washington, DC, June 2-3 2003. Volatility, Variance & Risk.

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Risk Pricing Linkages between Financial and Insurance Markets

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  1. Risk Pricing Linkages between Financial and Insurance Markets John Daniel Pollner, World Bank Presented at World Bank conference on “Financing the Risks of Natural Disasters,” Washington, DC, June 2-3 2003

  2. Volatility, Variance & Risk • Risk in Securities is measured as volatility in terms of variance or standard deviation of the price: σ

  3. Variance and Pricing High Variance in a Price Series adds a Premium To the Expected Value

  4. σ (sigma) reflects uncertainty • For financial markets, the sigma of a security therefore, reflects its riskiness and thus price

  5. Bond Market Risk Another Measure of Risk is the probability of default based on a historical record of experience • Risk = Default Probability, p(D) • Bond yield = risk free rate (eg. 5%) + p(D) (eg. 4% or spread over risk free rate) = 5% + 4% = 9% bond yield

  6. Pricing Natural Disaster Risk • Using probability: • Example: annual probability of a Class 4 Hurricane: • p (Class 4) = 1%

  7. Uncertainty of the Probability • Since Natural Disasters are rare, the sigma (σ) of the statistical distribution is much higher. • Therefore the uncertainty premium will also be high. • If the probability was 1%, the sigma might be as high as 3% around the 1% probability mean.

  8. Pricing a Catastrophe Bond • A bond based on a catastrophe event would thus be priced: • Prob. = 1% + sigma = 3% • Plus risk free rate = 5% • = Bond rate = 9% • 9% earned if no disaster. • Bond principal goes to holder if a disaster occurs (default)

  9. Insurance & Reinsurance Pricing • Criteria 1: ROE (20%) • Criteria 2: actuarial pricing + admin. costs + brokerage costs + reinsurance costs + profit margin = p(D) + σ + A + B + R + P • Criteria 3: XL Layer: p(D) + σ + profit

  10. Structures for Government Risk Loss Coverage Structure • Cat bond for creditworthy governments, reinsurance for others using parametric triggers • Credit can reduce cost Contingent Credit Layer Reinsurance Layer or Catastrophe Bond Layer Retention Layer $ Loss

  11. Credit As a Form of Insurance? • Credit: P + I annuitized, e.g.: 20% • Reinsurance: 4% prem • Probability: 1% • E(C) = 1% x (20%) + 99%(0) = 0.2% < 4% • Even adding sigma factor, l.t. cost still less

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