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