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ΣT will be in the form of
ΣT = F>F +
σ21 0
0 σ22
, (34)
which implies heteroskedasticity in time series dimension. This suggests that the time het-eroskedasticity is crucial to multi-population mortality model. On the cross-sectional dimen-sion, the joint idiosyncratic covariance is a direct sum of individual idiosyncratic covariances, which will be heteroskedastic unless all mortality rates from each population have the same variance. This could happen when the populations have distinct structure due to varying so-cioeconomic condition. We conjecture that the impact would be less visible if the populations were chosen from the same country. After all, the timing and size of mortality improvement could be very different across countries, and we cannot capture these features without modeling the idiosyncratic heteroskedasticity.
The appeal of modeling idiosyncratic covariance can be demonstrated in multi-population approximate factor model. As previously noted, the common component of POET model is estimated with PCA, therefore their fitted value to mortality data is the same hence LC and POET model have exactly the same ER ratio. In Table 3 we can see that the log-likelihood value of POET model is almost twice as much of the LC when incorporating the full idiosyncratic covariance estimation. Even with APCA and HFA model the increase in both log-likelihood and BIC is substantial. As we increase the number of factor, the contribution of idiosyncratic covariance to goodness-of-fit becomes smaller, but still large in the case of 2-factor models.
Compared to the augmented common factor model, the 2-factor models perform better in both log-likelihood value and BIC except the LC model. The fact that log-likelihood value of LC model is very close to, but not greater the augmented common factor model may suggest that the estimation of idiosyncratic covariance might be more important than the interrelation of the different population. Overall, our result suggested that the APCA, HFA, and POET not only suitable in single population, but in multi-population modeling as well.
5.4 Forecast comparison
In this section we carry out a simple but rigorous statistical test of forecast accuracy for the competing models. After all, model that fits the best does not necessarily forecast the best.
Diebold and Mariano (1995) developed a test of equal predictive accuracy, that is, test whether
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two forecasts is equally accurate.13 The test statistic of Diebold-Mariano is defined as
D = d¯
pVar( ¯d) ∼ N (0, 1), d =¯ 1 T
T
X
t=1
g(ˆx1t) − g(ˆx2t) (35)
where x1t and x2t is the time-t forecast of model 1 and 2, and g(·) is a loss function. We use the heteroskedasticity and autocorrelation consistent (HAC) estimate for the long-run standard error of ¯d. We also correct the small sample bias by D0 =
qT +1−2h+h(h−1)
T so that D0 follows Student’s t with degree of freedom T − 1.
One of the great features about Diebold-Mariano test is its flexibility; the test is based on a user-defined loss function, which can be very helpful when the subject under comparison is a multivariate forecast. In our case, we choose the loss function to be the negative predictive log-likelihood value, that is, g(·) = −L(X; µf c, Σf c), where forecast mean µf c and Σf c is the forecast covariance, both generated from the model forecast. The forecast covariance of factor model remains to be the sum of a common component and an idiosyncratic covariance matrix.
But since the factor Kt has its own dynamic now, the common component shall include the covariance of the factor forecast. Specifically, for an h-step ahead forecast of mortality rate matrix at time t, the forecast mean ˆMt+h is
Mˆt+h = Ax+ BxKˆt+h, (36)
where ˆKt+his the h-step ahead forecast of the factors. Previous researches suggested, based on the shape of the estimated factor and other criterion such as biological reasonableness14, that first factor represents the mortality trend, and empirically it is very likely to have a unit root.
The second factor and beyond is assumed to be a stationary process (if it does not possess an unit root) for biological reasonableness of the mortality curve. We follow their advice and assume the first factor k1t in the approximate factor model is a random walk with drift process, i.e.
an ARIMA(0,1,0) process. The second factor k2t is assumed to be AR(1) since the empirical estimate of second factor often show autoregressive behavior, and it is used in many other mortality model as well such as Lee and Carter (1992), Plat (2009), O’Hare and Li (2012) and Li and Hardy (2011).
Let us consider a 2-factor model for example. The mortality rate at time t in the state-space
‧
The h-step ahead forecast mean of Mt is
Mˆt+h|t = Ax+ BxKˆt+h,
and the forecast covariance is
Σ(t + h|t) = Σc(t + h|t) + Σu(t + h|t)
= Bcov( ˆKt+h|t)B>+ cov(εtε>t).
(39)
To carry out the Diebold-Mariano test, we split our data into two separate periods, 1933 – 1970 and 1971 – 2009. We use the former as the in-the-sample period and perform a rolling win-dow forecast to the latter pseudo out-of-sample period. We avoid the nested model comparison and compute the test statistic with canonical 1-step ahead forecast.
Table 5 reports the Diebold-Mariano test statistics. The tests reject the null of equal ac-curacy at 1% level when comparing to the single population model, which is as expected.15 The test also rejects the null at 1% level when comparing to the augmented common factor model, which actually surprises us because the results from the previous section indicate that the augmented common factor model fits the sample relatively well.
6 Conclusion
Mortality rate, like interest rate, is commonly involved in many economic activities. Despite its importance, we cannot observe the mortality any faster; the tremendous effort needed in the data processing is not helping either. The limitation of observing mortality data shackled our ability to estimate a large multi-population mortality model. We introduce a modern factor model that suits the nature of mortality data really well. The approximate factor model capitalizes on the abundance of cross-sectional data to estimate the true mortality trend factor
15The critical values at significant level 5% and 1% is -1.69 and -2.43, respectively.
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among populations.
Not only is the mortality rate observation scarce in time, it is also heteroskedastic and cor-related. Even after the common factor explained a major portion of variation, idiosyncratic mortality rate are still heteroskedastic and correlated as can be seen from the benchmark case in Section 2.7. The approximate factor model allows for the correlation and heteroskedasticity in idiosyncratic mortality rates. We introduce three approaches based on the nature of het-eroskedasticity and correlation to incorporate them into the mortality model. As a result, the approximate model produces the analytical tractable covariance matrix for the mortality rates, making the risk management for large population or multiple population very easy.
We analyze these approaches in the context of both single population and multi-population.
Specifically, we compare the approximate factor model to each other and the standard Lee-Carter model that did not take conditional heteroskedasticity and conditional correlation into account. The attempt to model the conditional heteroskedasticity and correlation is an effort made to explain the higher order variation in a parsimonious way. The advantage is evident. We carry out a study using 45 populations to illustrate the empirical performance in fitting all kinds of different population around the globe. The empirical evidences overwhelmingly show that the approximate factor model is preferred in all 45 populations. By considering heteroskedasticity and correlation, the fitting performance in an uniform way. The result suggested that leaving the conditional heteroskedasticity and correlation unattended is unwise. We compare the log-likelihood and BIC, both support the approximate factor model as a better model in describing the data. APCA performs well because its ability to capture the conditional heteroskedasticity in age while remain relatively parsimonious.
Another theoretical advantage of approximate factor model is the ability to find the true pervasive factor when the number of mortality rate tends to infinity. This N → ∞ property turn the disadvantage of traditional factor analysis into an advantage. We examine the case of the multi-population mortality model, which the number of mortality rates of our concern are usually large and much greater than the number of observation T . When compare to other multi-population mortality models, the advantage of approximate factor model is that it allows us to estimate the joint covariance matrix, with no limitation on the size (number of the variable) of model. On the contrary, the previous multi-population mortality models is either designed to
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particularly suited for the multivariate environment.
The empirical performance in the multi-population context also favors the approximate factor model. Specifically, the HFA model is preferred in the multi-population setting. We conjecture that the heteroskedasticity is naturally introduced to the multi-population model because the population drawn from different countries is unlikely to have the same variance.
Even if they are homoscedastic within the population, which already seems not the case in our example, the multi-population could still be heteroskedastic in both time and cross-section dimension. This support the result that the HFA model outperforms other models in both fitting and forecasting.
Finally, our intention is not meant to challenge the existing mortality model. Rather, we hope that the result of this paper can be used to support the application of factor model in mortality rate modeling. The approximate factor model can be used to refine the estimation of the existing factor model, like an upgrade module that enhance the performance of a proven and reliable machinery.
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Figure 1: Lee-Carter factor and loading estimate: USA, 1933–2010
●●●●
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Figure 2: Idiosyncratic variance in the cross-section dimension
●
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Figure 3: Idiosyncratic variance in the time series dimension
●
1933 1940 1947 1954 1961 1968 1975 1982 1989 1996 2003 2010
Year
Time Series Idiosyncratic Variance
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Figure 4: Sample correlation of 1-factor LC errors for USA
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Age
Age
Correlation [−1,−0.75]
(−0.75,−0.5]
(−0.5,−0.25]
(−0.25,−0.001]
(−0.001,0.001]
(0.001,0.25]
(0.25,0.5]
(0.5,0.75]
(0.75,1]
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Figure 5: Estimate of idiosyncratic correlation by POET
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Age
Age
Correlation [−1,−0.75]
(−0.75,−0.5]
(−0.5,−0.25]
(−0.25,−0.001]
(−0.001,0.001]
(0.001,0.25]
(0.25,0.5]
(0.5,0.75]
(0.75,1]
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Population LC APCA HFA POET Span # of factor
Australia 3722.90 (4) 4476.49 (2) 4454.61 (3) 7202.01 (1) 1921-2009 1
Austria 1429.62 (4) 4318.90 (3) 4336.62 (2) 5937.52 (1) 1947-2010 1
Bulgaria 2157.40 (4) 2910.60 (2) 2875.47 (3) 4519.28 (1) 1947-2010 1
Belarus 2722.60 (4) 3971.98 (3) 4021.42 (2) 5092.19 (1) 1959-2010 1
Canada 5948.59 (4) 6785.18 (2) 6776.64 (3) 7346.27 (1) 1921-2009 1
Switzerland -266.46 (4) 5982.18 (2) 5980.72 (3) 12746.97 (1) 1876-2011 1
Chile 1191.44 (4) 1606.26 (2) 1605.09 (3) 1967.80 (1) 1992-2005 1
Czech Republic 2404.83 (4) 4120.17 (2) 4087.86 (3) 6836.73 (1) 1950-2011 1
East Germany 2413.34 (4) 4156.90 (2) 4121.77 (3) 5624.24 (1) 1956-2011 1
Germany 2766.45 (4) 3327.53 (2) 3327.25 (3) 3847.22 (1) 1990-2011 1
West Germany 5771.91 (4) 6991.95 (2) 6982.74 (3) 8414.48 (1) 1956-2011 1
Denmark 377.87 (4) 7356.37 (2) 7350.98 (3) 13633.17 (1) 1835-2011 1
Spain 4010.53 (4) 5342.22 (2) 5340.38 (3) 6017.10 (1) 1908-2009 1
Estonia -2049.88 (4) 466.89 (2) 435.21 (3) 2290.22 (1) 1959-2011 1
Finland -5277.78 (4) 252.97 (2) 226.75 (3) 2091.69 (1) 1878-2009 1
France, Civ. Pop. 6803.07 (4) 8805.56 (2) 8778.06 (3) 12426.50 (1) 1816-2010 1 France, Total Pop. 2981.57 (4) 7204.83 (2) 7154.64 (3) 11410.26 (1) 1816-2010 1
Northern Ireland -2338.58 (4) 525.52 (2) 479.42 (3) 3946.61 (1) 1922-2011 1
United Kingdom 4146.75 (4) 5291.15 (2) 5244.59 (3) 5845.25 (1) 1922-2011 1
Scotland 822.44 (4) 4250.56 (2) 4241.87 (3) 4752.11 (1) 1855-2011 1
England and Wales, Civ. Nat. Pop. 7677.39 (4) 8641.34 (2) 8616.34 (3) 8956.49 (1) 1841-2011 1 England and Wales, Total Pop. 3963.33 (4) 6454.10 (2) 6445.19 (3) 6482.19 (1) 1841-2011 1
Hungary 1181.49 (4) 2502.87 (2) 2413.85 (3) 4476.73 (1) 1950-2009 1
Ireland -118.61 (4) 2112.57 (2) 2079.51 (3) 3407.75 (1) 1950-2009 1
Iceland -14812.88 (4) -11541.62 (2) -11551.39 (3) -2173.21 (1) 1838-2010 1
Israel, Total Pop. 1022.17 (4) 1892.96 (2) 1891.08 (3) 2583.82 (1) 1983-2009 1
Italy 2020.73 (4) 4965.77 (3) 4977.91 (2) 6154.80 (1) 1872-2009 1
Japan 4622.30 (4) 5534.53 (3) 5556.24 (2) 5792.15 (1) 1947-2009 1
Lithuania 1003.20 (4) 2395.39 (3) 2414.24 (2) 3874.91 (1) 1959-2011 1
Luxembourg -5217.80 (4) -2508.73 (2) -2516.71 (3) -1383.10 (1) 1960-2009 1
Latvia 364.60 (4) 1436.35 (2) 1413.45 (3) 3984.27 (1) 1959-2011 1
Netherlands 2124.68 (4) 8960.99 (2) 8945.04 (3) 13684.07 (1) 1850-2009 1
Norway 3302.39 (4) 6890.87 (2) 6890.72 (3) 13187.66 (1) 1846-2009 1
New Zealand – Maori -6911.35 (4) -5411.19 (2) -5413.85 (3) -3767.27 (1) 1948-2008 1 New Zealand – Non-Maori -1806.27 (4) 917.21 (2) 893.03 (3) 2202.67 (1) 1901-2008 1
New Zealand 740.26 (4) 2774.04 (3) 2785.28 (2) 4025.58 (1) 1948-2008 1
Poland 4087.98 (4) 4851.51 (2) 4837.02 (3) 7253.35 (1) 1958-2009 1
Portugal 1939.93 (4) 4005.40 (2) 4004.67 (3) 6088.25 (1) 1940-2009 1
Russia 4255.35 (4) 5447.10 (3) 5496.39 (2) 7154.06 (1) 1959-2010 1
Slovakia 360.54 (4) 2572.13 (2) 2571.80 (3) 5072.72 (1) 1950-2009 1
Slovenia -1523.43 (4) 835.22 (2) 823.40 (3) 1433.79 (1) 1983-2009 1
Sweden -1010.86 (4) 7126.48 (2) 7111.98 (3) 17021.30 (1) 1751-2011 1
Taiwan 2783.53 (4) 3973.29 (2) 3965.49 (3) 4916.92 (1) 1970-2010 1
Ukraine 4734.86 (4) 5705.67 (3) 5717.67 (2) 7143.49 (1) 1959-2009 1
The United States of America 7876.67 (4) 8754.48 (3) 8762.51 (2) 11658.99 (1) 1933-2010 1
Average Rank 4.00 2.33 2.67 1.00
Table 1: The log-likelihood value of 1 factor model of LC, APCA, HFA, and POET. The number in parentheses indicates the ranking of accuracy in ascending order; 1 = most accurate and 4 = least accurate. The population is alphabetically ordered using the codename in Human Mortality Database. We use age 0 - 100 mortality rate for all populations. The number of factor is estimated using Bai and Ng (2002)’s IC1 and IC2. We choose the maximum number of factor estimated by IC1 and IC2.
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Population Code LC APCA HFA POET Span # of factor
Australia -5725.19 (3) -6312.89 (1) -5458.90 (4) -6312.01 (2) 1921-2009 1
Austria -1420.30 (4) -6312.70 (2) -5786.60 (3) -6323.57 (1) 1947-2010 1
Bulgaria -2875.86 (3) -3496.10 (1) -2864.30 (4) -3494.81 (2) 1947-2010 1
Belarus -4143.12 (4) -5776.67 (1) -5430.09 (3) -5680.89 (2) 1959-2010 1
Canada -10176.58 (3) -10930.28 (2) -10102.95 (4) -10931.60 (1) 1921-2009 1
Switzerland 2781.48 (4) -8753.49 (2) -7454.79 (3) -8756.90 (1) 1876-2011 1
Chile -1555.90 (3) -1652.87 (2) -1548.97 (4) -1671.07 (1) 1992-2005 1
Czech Republic -3393.41 (4) -5941.12 (1) -5334.48 (3) -5915.31 (2) 1950-2011 1
East Germany -3478.76 (4) -6093.19 (2) -5539.08 (3) -6130.21 (1) 1956-2011 1
Germany -4592.76 (4) -4936.60 (2) -4766.49 (3) -4956.44 (1) 1990-2011 1
West Germany -10195.90 (4) -11763.29 (2) -11261.02 (3) -11844.20 (1) 1956-2011 1
Denmark 1956.44 (3) -11011.64 (1) -9267.80 (2) 6705.21 (4) 1835-2011 1
Spain -6154.56 (4) -7884.68 (2) -6938.53 (3) -7887.15 (1) 1908-2009 1
Estonia 5413.32 (4) 1246.92 (2) 1765.30 (3) 1231.27 (1) 1959-2011 1
Finland 12759.07 (4) 2656.87 (1) 3963.04 (2) 11501.94 (3) 1878-2009 1
France, Civ. Pop. -10689.15 (4) -13695.43 (2) -11712.24 (3) -23446.47 (1) 1816-2010 1 France, Total Pop. -3046.14 (4) -10493.97 (1) -8465.41 (3) -10473.30 (2) 1816-2010 1
Northern Ireland 6409.00 (4) 1601.40 (1) 2513.95 (3) 1613.36 (2) 1922-2011 1
United Kingdom -6561.67 (4) -7929.85 (2) -7016.40 (3) -7931.60 (1) 1922-2011 1
Scotland 840.67 (4) -5038.76 (1) -3502.99 (2) -2325.12 (3) 1855-2011 1
England and Wales, Civ. Nat. Pop. -12710.70 (3) -13653.16 (2) -11934.75 (4) -21907.81 (1) 1841-2011 1 England and Wales, Total Pop. -5282.57 (4) -9278.69 (1) -7592.44 (3) -9275.14 (2) 1841-2011 1
Hungary -969.47 (4) -2732.57 (1) -2031.96 (3) -2727.14 (2) 1950-2009 1
Ireland 1630.74 (4) -1951.98 (2) -1363.29 (3) -1992.98 (1) 1950-2009 1
Iceland 32292.53 (3) 26736.62 (1) 28446.10 (2) 36642.94 (4) 1838-2010 1
Israel, Total Pop. -1039.65 (4) -1982.23 (2) -1764.86 (3) -2106.33 (1) 1983-2009 1
Italy -1770.37 (3) -6696.67 (1) -5404.11 (2) 5702.07 (4) 1872-2009 1
Japan -7817.01 (4) -8756.89 (2) -8248.52 (3) -8761.45 (1) 1947-2009 1
Lithuania -692.82 (4) -2610.09 (1) -2192.76 (3) -2499.14 (2) 1959-2011 1
Luxembourg 11714.68 (4) 7157.77 (1) 7600.10 (3) 7183.66 (2) 1960-2009 1
Latvia 584.37 (4) -692.00 (1) -191.17 (3) -635.40 (2) 1959-2011 1
Netherlands -1729.87 (4) -14423.78 (2) -12841.44 (3) -14425.84 (1) 1850-2009 1
Norway -4040.01 (3) -10235.76 (1) -8642.21 (2) 3268.44 (4) 1846-2009 1
New Zealand – Maori 15227.58 (4) 13108.59 (1) 13646.19 (3) 13183.18 (2) 1948-2008 1 New Zealand – Non-Maori 5546.36 (3) 1038.43 (1) 2090.90 (2) 27984.43 (4) 1901-2008 1
New Zealand -75.63 (4) -3261.86 (1) -2752.06 (3) -3256.87 (2) 1948-2008 1
Poland -6873.88 (4) -7535.73 (1) -7061.30 (3) -7527.95 (2) 1958-2009 1
Portugal -2373.05 (4) -5608.76 (2) -4986.85 (3) -5612.91 (1) 1940-2009 1
Russia -7208.61 (4) -8726.92 (2) -8380.04 (3) -8767.31 (1) 1959-2010 1
Slovakia 672.44 (4) -2871.10 (2) -2347.87 (3) -2871.75 (1) 1950-2009 1
Slovenia 4051.55 (4) 133.26 (1) 370.50 (3) 298.59 (2) 1983-2009 1
Sweden 5696.56 (4) -9549.97 (1) -6864.09 (2) -2832.88 (3) 1751-2011 1
Taiwan -4392.71 (4) -5931.04 (2) -5573.95 (3) -5994.55 (1) 1970-2010 1
Ukraine -8179.13 (4) -9257.52 (2) -8845.62 (3) -9361.92 (1) 1959-2009 1
The United States of America -14156.36 (4) -15005.82 (2) -14322.08 (3) -15139.70 (1) 1933-2010 1
Average Rank 3.78 1.49 2.93 1.80
Table 2: BIC of 1 factor model of LC, APCA, HFA, and POET. The number in parentheses indicates the ranking of accuracy in ascending order; 1 = most favorable and 4 = least favorable.
The population is alphabetically ordered using the codename in Human Mortality Database.
We use age 0 - 100 mortality rate for all populations. The number of factor is estimated using Bai and Ng (2002)’s IC1 and IC2. We choose the maximum number of factor estimated by IC1 and IC2.
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Multi-population models Single population models
Model LC APCA HFA POET ACM Indiv. LC M9 M10
LL 14217 23609 23926 23908 27420 19646 17514 20989
# of parameter 581 1086 1163 1491 1061 885 1160 1160
BIC -22294 -35741 -35561 -32059 -43628 -29939 -22768 -29720 ER ratio (%) 90.26 89.72 90.21 90.26 94.56 92.31 91.35 92.75 Table 3: log-likelihood value and BIC for 1-factor approximate factor models, augment common factor model, and single population models. We use age 0 –100 mortality rates for all five populations containing USA, UK, Spain, France, and Italy. The ER ratio is defined as 1 − P
i,x,tε(i)x,t2/P
i,x,t(m(i)x,t− a(i)x,t)2.
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LC APCA HFA POET
LL 25200 36153 37330 36654
# of parameter 1161 1665 1742 2574 BIC -38131 -54709 -56250 -46105 ER ratio (%) 94.55 94.21 94.33 94.55
Table 4: log-likelihood value and BIC for 2-factor approximate factor models. We use age 0 – 100 mortality rates for all five populations containing USA, UK, Spain, France, and Italy. The ER ratio is defined as 1 −P
i,x,tε(i)x,t2/P
i,x,t(m(i)x,t− a(i)x,t)2.
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APCA 1f HFA 1f POET 1f APCA 2f HFA 2f POET 2f
vs M10 -6.24 -6.11 -5.32 -8.38 -8.34 -7.92
vs LC -8.34 -7.51 -5.33 -9.67 -9.49 -8.71
vs ACM -5.58 -4.46 -3.50 -11.30 -10.62 -10.20
Table 5: Diebold-Mariano test statistic for 1- and 2-factor approximate factor models. The robust standard error in the statistic were estimated using Newey-West HAC estimator. The null hypothesis of the test is H0 : E(g(Model 1 forecast)) = E(g(Model 2 forecast)), where is g is the negative predictive log-likelihood function. The statistic is corrected for small-sample bias hence follows Student’s t distribution. The critical values at significant level 5% and 1%
are -1.69 and -2.43, respectively. We use age 0 – 100 mortality rates for all five populations containing USA, UK, Spain, France, and Italy. We split the full sample to 1933–1970 and 1971 – 2009 and use latter as out-of-sample period. The rolling forecast was carried out with the fixed length of window of 38 years (1970 − 1933 + 1).
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Explaining the Yield Spread of Life Settlements
1 Introduction
Life settlement is relatively new but promising product in the secondary insurance market.1 It only appears on the radar in 2000, but the market volume (in terms of the death benefit) quickly grows from millions in 2000 to 5 billion in 2011 (Conning & Company, 2011). In particular, the market volume reaches its highest at 12 billion in 2007. As a new asset class, the increasing popularity of life settlement comes from the fact that it offers the diversification benefits to financial assets, as well as the high historical return (Gatzert, 2010; Braun, Gatzert, and Schmeiser, 2012). From the viewpoint of the supply side, it is an attractive tool for those retired policyholder who is cash poor but asset rich, as life settlement extracts cash from a valuable but illiquid asset. It stands to reason that life settlement market can be sustainable in near future.
In a hypothetical life settlement transaction, the policyholder sells their existing policy to an investor to extract immediate monetary value from the policy. Once a successful transaction is made, the policyholder then receives a payment, also known as the acquiring price. The acquiring price is usually greater than surrender value offered by life insurance company, so the policyholders are more willing to sell their policy on the life settlement market. On the other hand, the investor in the transaction assumes the obligation to pay future premiums and
1This chapter is based on a joint work with Ming-Hua Hsieh, Jing-Lung Peng, Jennifer L. Wang, and my advisor Chenghsien Tsai.
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becomes the beneficiary. The investment return depends on the lifetime of policyholder. One or multiple independent medical examiners provide an estimate on the life expectancy of the policyholder, which is used in the valuation of the policy.
This study investigates the expected yield spread determinants of life settlement. Under-standing of these determinants helps the investor and the policyholder to price them in a more transparent and unbiased fashion. The transparency could in turn facilitates more transactions, creating a more liquid market. From an academic point of view, the determinants of a traded asset have been an important research topic in the literature. Life settlement is essentially an insurance contract, therefore the crucial elements in the eyes of an actuary are the fundamen-tals. However, the financial risk factor that also affect the yield could be just as important as
This study investigates the expected yield spread determinants of life settlement. Under-standing of these determinants helps the investor and the policyholder to price them in a more transparent and unbiased fashion. The transparency could in turn facilitates more transactions, creating a more liquid market. From an academic point of view, the determinants of a traded asset have been an important research topic in the literature. Life settlement is essentially an insurance contract, therefore the crucial elements in the eyes of an actuary are the fundamen-tals. However, the financial risk factor that also affect the yield could be just as important as