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A Study of Incidence Experience for Taiwan Life Insurance

Jack C. Yue and Hong-Chih Huang 2010/09/10

National Chengchi UniversitySixth International Longevity Risk and

Capital Markets Solutions Conference

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Summary

MotivationData DescriptionEmpirical AnalysesMortality ImprovementDiscussions

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Prolonging Life Expectancy

The life expectancy of people in Taiwan has increased significantly since the end of World War II, and becomes even more noticeable after the National Health Insurance (NHI) was enforced in 1995.

Now the life expectancies in Taiwan have surpassed those in the U.S.

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The Life Expectancy of U.S. and Taiwan

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Study Objective

Two reasons contribute to the difficulty of ratemaking for Taiwan insurance companies.

Population size & Rapid improvement

We will use the experience data from Taiwan life insurance companies to explore if there are factors affecting the mortality rates.

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Insurance Market in Taiwan (I)

Comparing to the developed countries, the history of life insurance in Taiwan is relatively short but the growth rate is fast.

On average, every Taiwan people owned 1/4 policy in 1989, 1/2 policy in 1994, and one policy in 1999.

Taiwan population is 23 millions in 2009. This indicates that the sizes of exposures were small before 1990 (less than 20 years of data).

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Time Series Plot of Ratio of having Insurance Coverage

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Insurance Market in Taiwan (II)

On average, every Taiwan people owns at least two life insurance policies since 2008, but about 1/3 populations in Taiwan never purchase any life insurance products.

(http://www.iiroc.org.tw/report_test/1010/PDF1010_2009.pdf)

It is unknown whether the population of purchasing insurance products would have similar mortality profiles as those do not purchase.

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Type No. of Policy %

Term Life 4,268,921 8.4%

Endowment 24,132,752 47.3%

Whole Life 22,610,097 44.3%

Life Insurance in Taiwan (1972~2008)

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Data Description (I)

Incidence data are from Taiwan Life insurance companies, for the years 1972~2008 (27 years) collected via Taiwan Insurance Institute (TII).

Major factors include:

age, gender (2), Policy type (3),

health exam (2), principal repayment (2), benefit amount, & insurance company size (3)

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Data Description (II)

The option of returning principal is one major attribute in many Taiwan life insurance products.

about 50% of WL and TL are with this optionWe separate 28 life insurance companies into

three groups (small, middle, & large) according to the number of policies.

small (9): # policy 100,000, < 2% share

middle (10): 10% share

large (9): # policy 400,000, 90% share

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Empirical Mortality Rates

The mortality rates of term life, endowment, and whole life policies are very similar.

There are differences with respect to

principal repayment

insurance company size

health exam

benefit amount

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Mortality rates are smaller for Principal Repayment (50% and 80% for Term Life and Whole Life)

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GenderCompany

SizeTerm Life Endowment Whole Life

Male

Large Company

1,584,231 11,352,337 9,560,227

Middle Company

239,357 654,538 1,721,926

Female

Large Company

2,165,901 10,952,936 9,160,791

Middle Company

223,935 712,346 1,745,610

Table 4. Summary of Company Size

The middle companies have more on Whole life (about 65.6%) while the large companies have more on Endowment (50%).

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The large size companies have higher mortality rates.

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Higher benefit amounts do not indicate smaller mortality rates (e.g., Term Life). Mortality rates for those with health exam are generally smaller.

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Summary of Empirical Analysis

The mortality rates from the experience data show some interesting results. we found that Repayment of Principal, Company Size, Health Exam, and Benefit Amount are highly correlated to the mortality risk.

Taiwan insurance companies should pay more attention to pricing the life insurance products. Using a single experience life table (TSO) won’t be appropriate!

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Mortality Improvement

We will use the Taiwan experience data on the Lee-Carter Model, to explore the mortality risk.

describes the average age-specific mortality, represents the general mortality level, and the

decline in mortality at age x is captured by .

, ,ln x t x x t x tm

x

t

x

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The mortality improvement over time behave quite different for the population and experience data.

t

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The differences of population and experience data in improvement rates are larger for younger age groups.

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Evaluate the Insurance Products We will use the experience data, applying the

Lee-Carter model, to evaluate the pricing insurance products.

Compare the pure premiums of whole life, annuity, and endowment

Compare with the results from 2002 TSO, 2002 Annuity Table, and 9th Taiwan Period Life Table (9th TPL, 1999-2001 Taiwan Complete Life Table)

Interest rate 3% & ultimate age is 100 year-old

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Issue Age 20 30 40 50

2002TSO

Male 54.6% 47.0% 39.4% 31.7%

Female 90.6% 86.7% 81.6% 75.1%

9th TPL

Male 54.1% 46.6% 38.5% 30.1%

Female 90.6% 86.8% 81.7% 75.2%

Table 5. Percentages of Over-estimate in Whole Life

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Table 6. Percentages of Under-estimate in Annuity (Male)

Deferred period/Age 20 30 40 50

2002Annuity

0 8.2% 9.5% 10.9% 12.0%

10 26.7% 27.9% 29.3% 30.6%

20 33.3% 36.6% 41.6% 49.8%

9th TPL

0 10.9% 13.4% 16.1% 18.8%

10 35.1% 38.4% 42.1% 46.9%

20 44.4% 51.2% 61.3% 77.9%

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Underestimate of Endowment Policy (2002 TSO vs. Experience)

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Underestimate of Endowment Policy (9th TPL vs. Experience)

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Summary of Premium Analysis

The Mortality rates from the experience data are much lower than the life tables used.

Pure premiums of life insurance products are over-estimated (more obvious for the female).

Pure premiums of annuity products are under-estimated (more obvious for the female).

Insurance companies are possible to be in deficit (more than 30%) by issuing the endowment policies.

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Conclusion and Discussions

The consumer’s behaviors in Taiwan might be different from those in other countries (need to be careful about introducing new products).

The principal repayment is an important factor, as well as benefit amount & health exam.

The experience and population data in Taiwan have different mortality improvement rates.

Using the population data to construct experience life table is feasible, but needs to be careful at the younger age groups.

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Suggestions

The experience data in Taiwan are not fully explored and used.

Further study of mortality-related risk factors is recommended, and the premium calculation should include these factors.

Insurance companies should build their own experience tables, instead of relying on the same experience tables (e.g., 2002 TSO and 2002 Annuity Table).

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Thank you for your attention!