Yue by qingyunliuliu

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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 University
  Sixth International Longevity Risk and
  Capital Markets Solutions Conference
                                           1
Summary
Motivation
Data Description
Empirical Analyses
Mortality Improvement
Discussions

                         2
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.


                                              3
The Life Expectancy of U.S. and Taiwan




                                         4
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.


                                                5
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).
                                               6
                                               Time Series Plot of Ratio of having Insurance Coverage

                                  2.0
Ratio of having Insurance Cover




                                  1.5



                                  1.0



                                  0.5



                                  0.0

                                        1960          1970         1980          1990         2000      2010
                                                                          Year


                                                                                                          7
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.                                                8
  Life Insurance in Taiwan (1972~2008)

  Type       No. of Policy       %

Term Life      4,268,921        8.4%

Endowment     24,132,752       47.3%

Whole Life    22,610,097       44.3%


                                         9
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)

                                               10
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 option
We 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     11
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

                                                12
Mortality rates are smaller for Principal Repayment (50%
and 80% for Term Life and Whole Life)                  13
            Table 4. Summary of Company Size
               Company
   Gender                Term Life   Endowment   Whole Life
                 Size
                Large
                         1,584,231 11,352,337     9,560,227
               Company
    Male
                Middle
                           239,357     654,538    1,721,926
               Company

                Large
                         2,165,901 10,952,936     9,160,791
               Company
   Female
                Middle
                           223,935     712,346    1,745,610
               Company

The middle companies have more on Whole life (about 65.6%)
while the large companies have more on Endowment (50%).  14
The large size companies have higher mortality rates.

                                                        15
Higher benefit amounts do not indicate smaller mortality
rates (e.g., Term Life). Mortality rates for those with
health exam are generally smaller.                         16
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!
                                                 17
Mortality Improvement
 We will use the Taiwan experience data on
  the Lee-Carter Model, to explore the
  mortality risk.

              ln  mx,t    x   x t   x,t
 x describes the average age-specific mortality,
 t represents the general mortality level, and the
decline in mortality at age x is captured by  x .
                                                     18
The mortality improvement over time  t behave quite
different for the population and experience data.      19
The differences of population and experience data in
improvement rates are larger for younger age groups.   20
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
                                               21
22
Table 5. Percentages of Over-estimate in Whole Life

    Issue Age        20      30      40      50

           Male     54.6%   47.0%   39.4%   31.7%
  2002
  TSO      Female   90.6%   86.7%   81.6%   75.1%

           Male     54.1%   46.6%   38.5%   30.1%
 9th TPL
           Female   90.6%   86.8%   81.7%   75.2%


                                                    23
Table 6. Percentages of Under-estimate in Annuity (Male)

 Deferred period/Age    20      30       40       50
               0       8.2%    9.5%    10.9%     12.0%
  2002
              10       26.7%   27.9%   29.3%     30.6%
 Annuity
              20       33.3%   36.6%   41.6%     49.8%
               0       10.9%   13.4%   16.1%     18.8%
  9th TPL     10       35.1%   38.4%   42.1%     46.9%
              20       44.4%   51.2%   61.3%     77.9%

                                                       24
Underestimate of Endowment Policy (2002 TSO vs. Experience)
                                                        25
Underestimate of Endowment Policy (9th TPL vs. Experience)
                                                        26
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.
                                            27
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.
                                                 28
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).
                                                29
Thank you
  for your attention!



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