Risk Pricing Linkages between Financial and Insurance Markets

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
• s

3
Variance and Pricing
High Variance in a Price Series adds a Premium To
the Expected Value
4
s (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 (s)
  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) s A B R P
• Criteria 3 XL Layer p(D) s profit

10
Structures for Government Risk

• Cat bond for creditworthy governments,
  reinsurance for others using parametric triggers
• Credit can reduce cost

Loss Coverage Structure
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 lt 4
• Even adding sigma factor, l.t. cost still less