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Chapter 8 Insurance Pricing
Prof . Deepak Tandon IILM Gurgaon
Insurance Costs and fair premium
Premium received to cover the Expected Losses and administartive costs
Expected profit for compensation of cost for sale of coverage
Fair Insurance Premium = EL costs +Investment Income +Administrative costs + Fair Profit Loading
Points to be taken care
Insurance Companies want to make money or avoid losing money
Insurance buyer are looking for low premium and good quality of coverage
One or more insurers can predict differences in expected claim costs across the customers at a sufficiently low cost
Low Premiums = Cost Based Prices Risk Classification + Class Rate
Customers
Claims paid
Claims paid at 1 year $100 how much money needed for collection to pay
P+rP=P(1+r)=100 P(1+r)=100 100/(1+r)=P 2nd Year P(1+r)+ rP(1+r)=100 P+rP=100/1+r Divide again by 1+r P=100/(1+r)^2
DEPOSIT INSURANCE Method I: Equity Price
Experience Deposit insurance can be modeled as a
put option on the bank’s assets (Merton, 1977)
Input parameters: Volatility of equity returns Bank leverage (market value of equity over
debt) Degree of regulatory capital forbearance
Limited application: Need market valuation of the bank’s net
worth (listed banks in market-oriented countries)
Method II: Default Experience
Expected loss pricing
Expected loss=Expected default probability*Exposure*Loss given default
Expected loss = Size of the loss to the deposit insurer as percentage of insured deposits
Expected default probability = The bank’s estimated probability of default
Exposure = Amount of insured deposits Loss given default (LGD) = Loss to deposit
insurer as a percentage of the total defaulted exposure
Estimating LGD
Historical experience of deposit insurer
US FDIC’s historical loss rate equals 8% of bank assets
In developing countries, loss rates of 50 % and up are typical
Good indicators: loan concentration, business mix, structure of bank liabilities
Estimating Default Probability
Historical default probabilities Implied by historical losses of the deposit
insurer Implied by a bank’s credit ratings on
deposits Implied by a bank’s interest rates on
uninsured debt (e.g. interbank deposits, subordinated debt)
p=(y - rf )/(1+y), where p is probability of default on default risky debt, y is the yield on a zero-coupon default risk debt, and rf is the yield on a zero-coupon default risk-free debt (all with the same maturity)
Pricing Design Features
Ex-ante funding vs. ex-post funding Flat-rate premium vs. risk-based
premium Levy on total deposits vs. levy on insured
deposits Broad coverage vs. narrow coverage
Coverage limit Co-insurance Include or exclude foreign-currency deposits
Comparing Design Features
Design feature Coverage limit Co-insurance FX deposits Interbank deposits Funded Management Compulsory
membership Risk-based premium
3.2 times per capita GDP
28% of countries 68% of countries 26% of countries 87% of countries 51% of countries
public 87% of countries 41% of countries
Insurability
Insurability of a risk is greater if: Losses occur with a high degree of randomness Maximum possible loss is very limited Average loss amount upon occurrence is small Losses occur frequently Insurance premium is high Possibility of moral hazard is low Coverage of the risk is consistent with public
policy The law permits the cover
Insurance Coverage and Premia
Cost of deposit insurance can be dramatically reduced by reducing the coverage of insurance Reducing the coverage reduces (at least)
proportionally the deposit insurance cost Reduction in actuarially fair premium could
be larger if the reduction in the coverage reduces the asset risk of the bank
Since the per dollar premium is higher with higher asset risk, limiting the coverage has a larger impact on reducing the cost of deposit insurance in developing countries
Risk Diversification and Premia
Non-systemic risk can be diversified away by pooling assets of banks Potential for risk diversification is larger in:
larger countries; countries with many banks; countries with different types of banks (ceteris paribus)
Price of deposit insurance of a group of banks is lower than the weighted average of the price of deposit insurance for each individual bank
Case-study: Korea. Fair premium (% of deposits): 2.81%, if measured as weighted average of
individual premia 1.44%, if measured as a pool of assets
Risk Differentiation and Premia
Exclusion of risky banks can significantly reduce the cost of deposit insurance Unless some of these banks have great
diversification potential Case-study: Korea. Fair premium (% of
deposits): 1.44% (if measured as a pool of assets) – all
banks 1.28% (if measured as a pool of assets) –
excluding the three riskiest banks (in terms of equity volatility)
Is Deposit Insurance Underpriced?
For comparison purposes, estimated fair premiums should be expressed as a percentage of insured deposits
Estimated fair premiums are higher than actual premiums in many countries – even if estimated on the basis of conservative estimates On the basis of equity prices:
No capital forbearance: 5 out of 21 countries (24%) underpriced
With 3% capital forbearance: 9 out of 21 countries (43%) underpriced
On the basis of bank credit ratings: 8% loss rate: 5 out of 32 countries (16%) underpriced 50% loss rate: 22 out of 32 countries (69%) underpriced
Pricing the Adoption of Deposit Insurance: The
Case of Russia Alternative methods:
Compare with actual premiums and historical losses in other (comparable) countries
Estimate actuarially fair premium on the basis of the discussed methods
Take design features into account Estimates of fair premium for Russia are
higher than the proposed premium of 0.6% of deposits Default experience suggests a premium of about 4% Equity price experience suggests a premium
between about 2% and 4% (or even higher depending on the enforcement of capital rules)
Conclusions
Explicit deposit insurance should not be adopted in countries with weak institutional environment
Pricing deposit insurance as accurately as possible is important, but not easy
However, there are several methods that can help in estimating actuarially fair premiums
There exist several design features that can limit the cost of deposit insurance