Breakout Sessions' Abstract

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16 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

103 εμφανίσεις


Parallel Sessions



Panel A

Panel B

Panel C

Panel D

Panel E



Room D1

Room D2

Room D3

Meeting
Room 1

Meeting Room
6

Session
I

Fri 6
Sept
11:00
-
12:1
5

Reverse
M
ortgages

Mor
t
ality
-
linked
S
ecurities 1

Pensions
P
lans

Insurance
-
linked
S
ecurities
/

Personal
I
njury

Modelling 1

Session
II

Fri 6
Sept,
16:30
-
17:45

Mortality
-
linked
securities 2

Pension
S
ystems

Mortality
F
orecasting
1

Longevity R
isk

Modelling 2

Session
III

Sat 7
Sept,
08:20
-
10:00

Annuities

Mortality
F
orecasting 2

Modelling 3

Modelling 4




Parallel Session I
-

Panel A

-

Reverse mortgages

Session Chair


Deng Yinglu


"Reverse Mortgage Pricing and
Risk Analysis
Allowing for Idiosyncratic House
Price Risk and
Longevity Risk"

Adam Wenqiang Shao, Michael Sherris, Katja Hanewald

We analyse the combined impact of idiosyncratic house price risk and longevity risk on
the pricing and risk profile of reverse mortgage loans in a stochastic multi
-
period model.
The model

incorporates house characteristics and stochastic mortality projections
based on mortality improvements along the cohort direction. Our results show that
failing to account for idiosyncratic house price risk and cohort trends in mortality
improvements und
erestimates the risk underwritten by reverse mortgage providers.


"A Study on Pricing of the Reverse Mortgage with an Embedded Redeemable
Option: An analysis

based on China's market"

Bingzheng Chen, Yinglu Deng, Peng Qin


In this paper, we research the rev
erse mortgage with an embedded redeemable option.
Firstly, we propose a reverse mortgage pricing model with a dynamic interest rate and
dynamic housing price. Then, based on forecasts of future housing prices and interest
rates, we obtain the annuity amoun
t received by different age groups. We analyze the
effect of the embedded redemption option on different age groups. We also analyze the
sensitivity of a variety of exogenous factors on pricing of the reverse mortgage. The
results show that reverse mortgag
es can significantly improve the income level of the
elderly in China.


“Contributors to the Potential Demand for Reverse Mortgage in China

An
Empirical Investigation Based on a Questionnaire Survey of Residents in Beijing”

Bingzheng Chen, Yinglu Deng,
Xiaofei Liu, Lihong Zhang

Reverse mortgage has been used by several countries as an approach to solve the
aging problem and provide extra cash flow for the retirees. Our paper designs the
survey to investigate the demand for reverse mortgage in China. Thro
ugh the survey
and statistical analysis, we find the main contributors which affect the demand,
including the traditional concept, life style, insurance consumption, apartment value,
age, education level. Based on the empirical analysis, we propose the pol
icy for the
government agency and insurance industry on how to develop the reverse mortgage
products in China in the future.


Parallel S
ession I
-

Panel B

-

Mortality
-
linked securities 1

Session Chair


Ning Zhang


"Price Bounds of Mortality
-
Linked Securit
y in Incomplete Insurance Market"

Jeffrey Tzuhao Tsai, Yu Lieh Huang, Sharon S. Yang

This study discovers reasonable price bounds for mortality
-
linked securities when the
issuer has only a partial hedging ability. The price bounds are established by minimi
sing
the difference between the benchmark price and the replicating portfolio cost subject to
the gain
-
loss ratio. A framework with three insurance basis assets is constructed to
search for the price bounds for mortality
-
linked securities and take the Swis
s Re
mortality bond as an example. The price bounds would be valuable for setting bid
-
asked spreads and coupon premiums in the raising mortality securitization markets.


"Modelling Infectious Mortality Risk with Application to Mortality Security
Pricing"

Fen
-
Ying Chen, Hong
-
Chih Huang, Sharon S.Yang

Due to the serious disease event such as the flu in 1918, the mortality rates in a group
of nearby populations or worldwide may show a co
-
movement trend. In other word, a
large numbers of deaths may occur at th
e same time caused by this catastrophic event,
whereas we call it "infectious mortality risk" in this research.This research attempts to
model infectious mortality risk and investigate its effect in pricing mortality
-
linked
securities. Using the Swiss Re m
ortality bond as an example, we derive a closed
-
form
solution using Wang’s transform (2000) and the corresponding fair spread of the Swiss
Re bond is examined.


"Mortality Decomposition Model and its Application in the Grade
d

Longevity
Bond Building in Chi
na"

Ning Zhang, Wei Wang

Based on the idea of risk hierarchy, this paper introduces multi
-
scale analysis tech
n
ique
of signal processing to analyze and forecast Chin
ese mortality. The method is known as

Hilbert
-
Huang transform and Empirical Mode Decompositi
on showed its ability to deal
with longevity risk. Also it can be used to build the graded bond in which longevity risk
would be covered by central government, local government and markets separately.



Parallel session I
-

Panel C

-

Pensions P
lans

Session Chair

Jing Ai


"De
-
risking Defined Benefit Plans"

Yijia Lin,

Richard D MacMinn, Ruilin Tian

To identify an appropriate pension de
-
risking method, this paper proposes an
optimization model by minimizing expected total pension cost subject to a cond
itional
value at risk (CVaR) constraint on pension funding level. With this setup, we examine
three pension hedging strategies
---
longevity hedging, buy
-
in and buy
-
out with various
hedge costs, namely risk premium, search and information cost, underfunding
cost, and
cost of counter
-
party risk. Our numerical examples demonstrate that these hedge costs
significantly affect a plan's hedging decision. The hedge ratio (the total pension cost)
decreases (increases) with the transaction cost, the counter
-
party defa
ult probabil
ity
and the underfunding ratio.
Moreover, the buy
-
out underperforms the longevity hedging
and the buy
-
in for poorly
-
funded plans and the longevity hedging is less sensitive to the
default risk than the buy
-
in.


"The Analysis On

The Optimal Investment Return For Chinese Personal Pension
Account

In The View Of Longevity Risk"

Xiaoqian Yuan, Ning Zhang

In this paper, we paid attention to the investment return
and

its impacts on the personal
account, and described the relationship between the capital market
and

longevity risk in
the social pension system. We
use
d

stochastic simulation methods to simulate the
specific 1000 conditions of mortality improvement. The
re
placement rate

is calculated in
each case to obtain a more effective measure.
T
hen we

studied how to adjust the
investment

return
by the use of the interval estimation methods to achieve the ideal
balance of payments
.
Based on these results,
p
olicymakers ca
n

determine the yield
standard
of pension fund investment
that
should achieve according to the determined
target replacement rate level
.



"A New Approach to Pension Risk Management"

Jing Ai, Patrick L Brockett, Allen Jacobson

Pension plan sponsors have se
en the risks they take on for sponsoring these plans
manifest in the last several years. Determining the exact size of the risk exposure has
been a difficult task. In this paper we argue that strictly focusing on the size of the
unfunded liability does not

provide sufficient information regarding pension risk.
Borrowing an analytical framework from the life insurance & annuity industry, we
propose two approaches to measure pension sponsors’ assets at risk and thus provide
them a way to determine the amount
of risk they are holding and facilitate further
corporate decision making.


Parallel session I
-

Panel D

-

Insura
nce
-
linked Securities/Personal I
njury


Session Chair
-

Wai
-
Sum Chan


"Heterogeneous Expectations and Speculative Behavior in Insurance
-
linked
Securities"

Min Zheng

From the heterogeneous
-
belief point of view, this paper uses the Tâtonnement
approach to consider a market with a riskless asset, a risky asset and an insurance
-
linked security in Walrasian scenario. Through studying the clearing pric
e and the
interaction of different investors, we give a condition for fair prices of different assets,
study the financial engineering of the insurance
-
linked security and try to give an
explanation about the failure of BNP/EIB and the success of Swiss Re
mortality bond
from the investors' viewpoint.


"Disaggregation of Chinese Life Tables from National to Provincial Level, with an
Application to Assessing Personal Injury Liabilities in China"

Felix W.H. Chan, Johnny S.H. Li, Wai
-
Sum Chan

Since 1987, the ag
e
-

and sex
-

specific population and death counts for the entire
Chinese population have been published every year. With these data, national life
tables can be constructed straightforwardly. In this paper, we develop a disaggregation
model that allows us t
o decompose life table data from national to provincial level. The
proposed model helps practitioners to assess the usefulness of a Chinese national
mortality index. Finally, we apply the results to calculate actuarially fair compensations
for personal inj
ury cases that occurred in different parts of China. [This research project
is supported by the HK Research Grants Council, GRF
-
HKU741512H]



Parallel Session I
-

Panel E

-

Modelling 1

Session
Chair
-

Andrew Cair
ns


"
An
Extensions of the Lee
-
Carter Model
For Mortality Projections"

Udi Makov

The literature on mortality projections has been dominated since the 1990's by the Lee
-
Carter (L
-
C) model, which assumes that the central death rate for a specific age follows
a log
-
bilinear form, allowing for variation
s in the level of mortality over time. This model,
with its inherent homoscedastic structure, has attracted numerous extensions, notably
with the introduction of a Poisson model governed by a similar log
-
bilinear force of
mortality. The paper will discuss
new extensions to the L
-
C

model along the following
lines: (i)
Bayesian Implementation of the L
-
C model with a broad fam
ily of embedded
ARIMA models. (ii)
Adaptation of the L
-
C model for simultaneous projection of several
populations.


"A Two
-
Stage Linear
Regression Approach To Modeling Mortality Rates Of
Different Forms"

Cary Chi
-
Liang Tsai

In this paper, we propose a two
-
stage linear regression approach to modeling mortality
rates of different forms. In stage I, we fit a mortality sequence for year y+k wi
th another
mortality sequence of equal length for year y using a simple linear regression and get
the estimated slope and intercept
parameters {a
k
} and {b
k
} for k=1,...,n. Then in stage II,
we fit {a
k
} and {b
k
} with {k}, respectively. The fitted

lines for {ak} and {bk} can be used for
forecasting mortality rates det
erministically and stochastically. Comparisons of the
forecasted error and confident intervals of mortality rates between the Lee
-
Carter and
the 2
-
stage models are given for illustrati
on.


"Mortality Modelling: Living With Unreliable Data"

Andrew Cairns, David Blake, Kevin Dowd, Amy Kessler

Typically, mortality models are fitted to historical data on the assumption that both
deaths and exposures are reasonably accurate. For some countri
es or subpopulations
with a history of good record keeping this might be true. For others, it is not.

Late in
2012 the UK Office for National Statistics (ONS) revised its population estimates for the
years 2002 to 2010 following the 2011 population census.

At some ages the difference
between the original and revised estimates was as high as 10% with consequent
changes in crude death rates.

In this presentation we will discuss the consequences for
mortality forecasts and financial calculations of such a revi
sion.

Additionally, we will
discuss how to model uncertainty in exposures data and how to fit mortality models in
the presence of such uncertainty.



Parallel session II
-

Panel A

-

Mortality
-
linked securities 2

Session Chair


Hong
-
Chih Huang


"A Bayesian Pricing
of Longevity Derivatives under Stochastic Interest Rates
"

Takahiro Fushimi,

Atsuyuki Kogure, Yoshimitsu Takamatsu

In the existing methodologies of pricing mortality
-
linked securities it is usually the case
that only the mortality risk i
s modeled to change in a stochastic manner and the interest
rate is kept fixed at a pre
-
specified level. In this paper we tackle the problem of how to
incorporate interest rate risk into pricing mortality
-
linked securities. In particular, we
consider the p
ricing of an EIB/BNP type longevity bond. With the issue of parameter
uncertainty in mind, we propose to use a Bayesian methodology in line with Kogure, Li
and Kamiya (2013).


"Modeling
Multi
-
Country
Mortality Dependence and
its Application in
Pricing
Survivor Swap
s: a Dynamic Copula

Approach”

Sharon S. Yang,
Hong
-
Chih Huang, Chou
-
Wen Wang

This paper introduces mortality dependence in mortality modeling using a dynamic
copula approach. Specifically, we use the time
-
varying copula models to capture the
m
ortality dependence across countries. The goodness of fits of different dynamic
copula models and the pattern of mortality dependence are assessed using empirical
mortality data. In addition, we deal with basis risk in pricing survivor securities. To
under
stand the effect of mortality dependence and basis risk, we build a valuation
framework for pricing a survivor swap. The fair swap rates of a survivor swap are
investigated numerically.


Parallel Session II
-

Panel B

-

Pension S
ystems


Session Chair
-

Zaigui Yang


"Public Pension with

Longevity and Population Growth Rate in China"

Qiang Cui

T
his paper
investigates

China

s urban public pension system by employing an
exogenous growth
OLG model (Overlapping generations model) with lifetime
uncertainty
fact
or
.
W
e examine the effects of the life expectancy, population growth rate,
firm contribution rate and individual contribution rate on the physical capital
-
labor ratio,
saving rate, individual account, social pool fund and individual utility
level
.

Through
these analyses
, we can get the direction of exogenous variables influence the
endogenous
variables
.

T
hen, according to the situation of China, we estimate the
parameter values and simulate to
obtain

the effects and their intensities.
Based on the
above work
s
, we

can make suggestions to the government.
For

different policy
objectives
,
the government can formulate policies to adjust

relevant
e
conomic variables
to the appropriate level.


"Rural Public Pension, Uncertain Lifetime, Family Transfers And
Endogenous
Growth"

Zaigui Yang

W
e
investigate
the
new

type

rural public pension
in

China

with

an endogenous growth

model. We examine the effects of
life expectancy,
individual contribution rate, village
subsidy rate, local government allowance rate and bas
ic benefit rate on
peasant

s

labor
income growth rate, population growth rate, saving rate, consumption ratio, education
expense ratio
,

gift ratio and

bequest ratio
. I
ntegrating the effects and their intensities
and the rural economic goals,

i
t
ha
s
more
advantages than disadvantages

to

raise the

basic benefit rate, local government allowance rate and village subsidy

rate
, reduce the
individual

contribution

rate, and improve the living and medical conditions
.



Parallel Session II
-

Panel C

-

Mortality F
or
ecasting 1

Session Chair
-

Andrew Hunt


"The Choice of Sample Size for Mortality Forecasting: A Bayesian
Learning
Approach"

Anja De Waegenaere, Hong Li, Bertrand Melenberg

In this paper we focus on the choice of sample size for some widely used extrapolati
on
mortality models by using a Bayesian Learning approach. We reformulate several
popular stochastic mortality models into Bayesian models by including the sample size
as an extra parameter. In particular, we estimate the (conditional) posterior distributi
on
of the sample size, and update the posterior distributions as new data arrives. We find
that the posterior distributions of the sample size are significantly different for each
combination of age, gender, and forecasting horizon, suggesting that it is n
ot optimal to
choose a universal sample size regardless of age and gender. Furthermore, the
Bayesian models perform better than the original models in more cases in the out
-
of
-
sample forecast.


"
Forecasting ESRD Incidence and Mortality Based on

Taiwan's Po
pulation Data"

Shing
-
Her Juang, Chih
-
Hua Chiao, Yin
-
Ju Lin, Hsin
-
Yi Li

The
purpose
s

of this paper are to
(1)
m
odel the incidence data
through
an age
-
and
-
period model and (2)
discuss
the relationship between ES
R
D (e
nd
s
tage
r
enal
d
isease
)
mortality and
Taiwan

s national life table.

The data
analyzed

for this study is
from
Taiwan

s NHIRD (National Health Insurance Research Database), nearly

fourteen

year
s
of

longitudinal data.

The typical age of onset for
ESRD
is 40 to 74 and the population
observed inclu
des
32,943 female and 31,851 male patients.
Results indicate that older
females are at a higher risk for developing ESRD than others.
Our analysis

also

indicates that

there is a

period effect
for
ESRD incidence and ESRD
mortality
are highly
correlated with

the national mortality.


"Projecting Mortality: Coherence and Co
-
integration in Multi
-
Population
Projections"

Andrew Hunt, David Blake

It is widely believed that the evolution of mortality rates in related populations should
show similar trends, caused b
y the same underlying developments in health and
medicine. In many practical applications for mortality models we need to allow for this,
for instance to capture the interdependence between mortality rates for men and
women in the same country. We investig
ate one method of achieving this by using co
-
integration to model the relationship between comparable demographic trends in
multiple countries and project them coherently into the future. We then give an
application of this to the modelling of the Swiss Re

Kortis bond.


Parallel Session II
-

Panel D

-

Longevity R
isk

Session Chair
-

Tom Terry


"Longevity Risk Existence Analysis: Case in Beijing"

Xiaoting G
ao
, Zan Zhao

The main objective of this paper is to offer a detailed analysis
of the existence of
longevity

in Beijing
. Starting from the construction of life table of the old (60 years and
older)
,

we used various models, like Logistic, Gompertz and Heligman & Pollard to
estimate
the

mortality rate in two age group : 60 to 85 and 85 to 99. The best mod
el is
used to smooth the life table, and make the comparison on life expectancy and mortality
rate from 2000 to 2010. Considering the data on disease and pollution, we give final
conclusion and projection.


“Longevity Risk in China and its Financial Impact
: Evidence from Model Test”

Wei Xiao, Chenzhe Liu

Longevity risk of China was proved by Li and Liu (2010) using

data from 1993 to 2008
to fit the Lee
-
Carter mortality model. But as the mortality

data of China is only available
since 1980s, the data might
be not enough

to provide satisfactory forecast result, we
propose to enhance the Chinese data

by generating data from a correlation model
between the available Chinese data

and those of other country which has sufficient
data. The forecast ability and

the
goodness of fitted of the model with the generated
data will be shown by

comparing with that of the origin Lee
-
Carter model. Then the
financial impact

of longevity risk will be revealed by estimation of deficit of the public
pension

and social security sys
tem due to the forecast error.


"Communicating Longevity Risk:
Beyond the Definitions

"

Liaw Huang, Tom Terry

Despite persistent efforts to educate and communicate about longevity risk and its
potentially harmful effects, the marketplace for longevity risk

mitigation solutions has
been slow to develop. We propose that, in part, the problem stems from the lack of a
common definition and the resulting lack of a consistent understanding of longevity risk.
We examine and critique various definitions used by f
inancial and policy communities,
as well as the public at large. Finally, we suggest that a concerted effort to address this
semantic murkiness is an essential ingredient for the success of marketplace solutions
and broader public policy initiatives.


Parallel Session II
-

Panel E

-

Modelling 2

Session Chair


Johnny Li


"Comparison and Evaluation of
Fuzzy Regression Methods in Lee
-
Carter Model"

Diheng Huang

Lee
-
Carter model has been highly accepted in mortality formulation and forecasting,
however, hom
oscedasticity assumptio
n is often violated in practice,
and one solution is
to combine

fuzzy regression with Lee
-
Carter model to estimate parameters and project
life expectancy. In this paper, three f
uzzy regression methods are considered

(i)
uses

minimum
fuzziness criter
ion

(ii)

combines

least
-
squares regression
and minimum
fuzziness criterion

(iii) also
a least squares fuzzy regression but using maximum
compatibility criterion. All these methods are utilized to both long
-
period

death rates
(
Canadian data)

and sho
rt
-
period death rates (
Chinese data) to analyze the
comparative advantages and disadvantages of each method, and how the quality of
data set might influence the results of the fuzzy regression.


"Methods of Improving Lee
-
Carter Model
-

Based on Chi
na's Mortality Data"

Lifeng Yang, Xiuye Meng


Longevity is being more and more notable in China. As a classical model of quantifying
longevity risk and predicting mortality, Lee
-
Carter model draw attention of Chinese
scholars. The paper counters the
vulnerability that an ordinary Lee
-
Carter model cannot
figure out a global optimal estimation of the arguments, and proposes three improving
means of Random Adjustment

(RA), Simulating Annealing

(SA) and Multi
-
LC model.
We prove the availability and the ef
ficiency of the three means, and analyze the
applying environment of the model, by fitting the China gross mortality data. We then
work out the unavailability of Lee
-
Carter model where the mortality is extremely high.


"A Step
-
by
-
Step Guide to Building Two
-
Population Stochastic Mortality Models"

Johnny Li, Rui

Zhou, Mary R. Hardy

Two
-
population mortality models play a crucial role in the securitization of longevity risk.
In this paper, we discuss a systematic process for constructing a two
-
population
mortal
ity model for a pair of populations. The process encompasses three steps,
namely (1) determining the necessary conditions for biological reasonableness, (2)
identifying an appropriate base model specification, and (3) choosing a suitable time
-
series proces
s and correlation structure for projecting the period and cohort effects into
the future. In our discussion, we not only consider existing models, but also introduce
several significant new models, including a two
-
population version of the celebrated
Cairn
s
-
Blake
-
Dowd model.



Parallel Session III
-

Panel A

-

Annuities

Session C
hair
-

Ralph Rogalla


"A Regime
-
Switching
Framework for the Valuation of a

Guaranteed Annuity
Option"

Huan Gao, Rogemar Mamon, Anton Tenyakov
,
Xiaoming Liu

We introduce three Markov
-
modulated models for the evolution of mortality rates and
construct a valuation setting for guaranteed annuity option, where the interest and
mortality risk factors are driven by two independent Markov chains. Thus, both factors
for pricing are regime
-
swi
tching. To get closed
-
form valuation formulae, the change of
reference probability measure technique is employed. Numerical results under various
different regime pair conditions are provided and they are compared with those
obtained from Monte Carlo simul
ation to evaluate efficiency of the proposed approach.


"Efficient Valuation of GMWB Annuities: A Variance Reduction Approach"

Jennifer L. Wang
, Ming
-
hua Hsieh, Yu
-
Fen Chiu

Variable annuities (VAs) with guarantees are popular insurance contracts for retirement
saving. However, after recent financial crisis, most insurers are not willing to provide
guarantee products such as GMWB or GMMB because these types of guarantees are
too costly. Fair valuation and hedging strategies are crucial for the risk management of
GMWB. Previous research use Monte Carlo method to value GMWB. But most
scenarios turn out to be out
-
of
-
money. This implies crude Monte Carlo method is very
ineffic
ient. This paper proposes an efficient Monte Carlo valuation method by using the
techniques of control variates. We further compare the efficiency of the proposed
approach with traditional methods numerically. We demonstrate that our proposed
efficient
valuation method is indispensable for designing hedging strategies of GMWB
annuity contracts.


"Research on Annuity Puzzle in China from Institutional Perspective"

Wei Wang, Ning Zhang

About the limited size of annuity market in China is another story whi
ch different from
other advanced market economies. I
t is unable to understand the a
nnuity

p
uzzle
of
Chinese
society with
out studying
the pension
system r
eform
, since

pension systems
provide
s

insurance in the form of annuities, which can be effective tools
in covering
longevity risk. Viewed from an institutional perspective, the pursuit of this objective
faces a series of constraints such as imperfect information, path dependency,
transaction cost, governance structure, etc. It is
supposed
that the nature of

reform

is
b
enefits

of

p
ublic
-
p
rivate
m
ix, so the analysis model is constructed and econometric
tools is employed to find the key variables in affecting the sustainability and efficiency of
annuity market
in China
.


"Optimal Life Cycle Portfolio Choice
with Variable Annuities Offering Liquidity
and

Investment Downside Protection"
,

Vanya Horneff, Raimond Maurer, Olivia S. Mitchell
,
Ralph Rogalla

We evaluate the lifecycle consumption and portfolio allocation patterns resulting from
access to Guaranteed Mi
nimum Withdrawal Benefit (GMWB) variable annuities, one of
the most rapidly growing financial products. The particular attraction of these products is
that they offer access to equity investments with downside protection, hedging of
longevity risk, and par
tially refundable premiums. Welfare rises since policyholders
exercise the product flexibility by taking withdrawals, and dynamically adjusting their
portfolios and consumption streams. At retirement, they annuitize substantial sums.
Differences across ind
ividuals’ cash out and annuitization patterns result from variations
in realized equity market returns and labor income trajectories.



P
a
rallel Session III
-

Panel B

-

Mortality F
orecasting

Session Chair
-

Julien Tomas


"Prediction Intervals for Future
Mortality Rates"

Ah Pooi, W.Y. Pan and Y.C. Wong

The vector
of
N

age
-
specific mortality rates in year
t+1

is modelled to be dependent on
the vector in the present year t and
l

1

other vectors before year t via a conditional
distribution which is derived
from an
N(l+1)
-
dimensional power
-
normal distribution. The
prediction intervals based on the cond
itional distributions when
l=1
and

2

are found to
have good ability of covering the observed United States age
-
specific mortality rates in
the years from 2005
to 2009 when the
N(l+1)
-
dimensional power
-
normal distributions
are estimated using the US mortality data from 1933 to 2004 .


"
Swiss coherent mortality model as a basis for developing longevity de
-
risking
solutions for Swiss pension funds: a practical appr
oach
"

Ljudmila Bertschi,
Cheng Wan

We illustrate the application of our stochastic coherent mortality model developed for
Swiss pension funds based on the reference population of thirteen countries for a
pensioner portfolio of a real pension fund. The last

research study carried out by the
Swiss Federal Office for Social Security on dependency of mortality rates from the
socio
-
economic status is considered. We compare the impact of longevity risk with
other (investment) risks faced by Swiss pension funds on

their funding strategies. In the
end the sensitivity of reference population, other modelling parameters and possible
impact on results are discussed.


"
Forecasting Mortality

in the Presence of Missing Data: An Application to
Chinese Population"

Ping An,
Ken Seng Tan, Johnny Li

When one attempts to calibrate a stochastic mortality table to Chinese population, one
complication is the missing data as for some years the death rates are not available.
T
he primary objective of this paper is to investi
gate how
we can apply a stochastic
mortality model in the presence of missing da
ta. A
st
atistical tool called “multiple
imputation”

is used

to address this issue
. To validate the proposed method, we use
data from populations for which complete mortality data are av
ailable. Furthermore, in
order to reflect the coherent mortality for rural and urban people, we use Augmented
Common Factor model
-
an extension of the Lee
-
Carter method to project Chinese
mortality.


"A New Non
-
Parametric Approach to Smoothing and Forecasti
ng of Mortality"

Julien Tomas, Frederic Planchet

We illustrate the smoothing and forecasting of mortality through a new strictly non
-
parametric framework. We use local kernel
-
weighted log
-
likelihood techniques to
graduate the observed mortality. The
extrapolation of the smoothed surface is
performed by identifying the mortality components and their importance over time using
functional principal components analysis. Then time series methods are used to
extrapolate the time
-
varying coefficients. We inv
estigate the divergences in the mortality
surfaces generated by a number of previously proposed models.


Parallel Session III
-

Panel C

-

Modelling 3

(Session Chair
-

Jack C Yue)


"A Study of Mortality Compression and Longevity Risk


Jack C Yue

In this stu
dy, we use statistical methods to evaluate the mortality compression, in order
to reduce the influence of data quality. In addition to the nonparametric methods used in
the previous studies, such as shortest confidence interval on the distribution of age
-
a
t
-
death and the modal age, we consider optimization methods for estimating the standard
deviation of age
-
at
-
death distribution. In specific, we compare the SD(M+) proposed by
Kannisto (2000) to the proposed method, and check which method has a smaller MSE
(Mean Squared Error).


"Bayesian

Mode
lling of Longevity a
nd Lifespan Extension"

Ramona Meyricke, Michael Garratt

Agreement on models to quantify and forecast longevity risk is a precondition for a
liquid longevity market but has not yet been reached. While

a range of mortality
modelling issues have been directly addressed in order to price longevity
-
linked
securities, the potential impact of drugs that extend lifespan has received almost no
attention. Human clinical trials for lifespan extension drugs are u
nderway, however, and
effective drugs could be on the market within five to ten years. As many longevity
-
linked
securities are issued with long maturities, it is important to quantify the potential impact
of this development on longevity risk and on longev
ity
-
linked securities. We develop a
framework for quantifying the impact of lifespan extension drugs on mortality rates,
allowing for uncertainty in the potential impact of such drugs.


“Longevity Bonds Pricing Model Driven by OU Jump Process of Mortality

Index
and Affine Stochastic Interest Rate Model”

Jianwei Gao, Le Yang, Lizhi Wang

This paper studies the longevity bond pricing problem where the mortality rate index
follows an Ornstein
-
Uhlenbeck

(OU) Process with jumps and the stochastic interest rate
model is described by an affine dynamics. We use hierarchical techniques to price the
longevity bond so as to meet the demand of investors with different risk preferences.
Furthermore, the explicit
formula for the longevity bond pricing is derived by applying
Wang transform. Finally, an example is provided to examine our model. The results
show that the expression of the Price model has a good operational feature.


"A Relational Model Approach to Dea
l with the Longevity Risk"

Hsin Chung Wang, Jack C Yue

In this study, we a
pply

the idea of
Wang and Yue (2011), i.e., a

r
elational
m
odel
a
pproach
, to deal with the longevity risk. The proposed relational model emphasizes the
relationship

of mortality rates

between consecutive ages, and it is shown to be more
accurate than the Lee
-
Carter model in mortality prediction. We also compare the
proposed method, such as the model by Renshaw and Haberman (2006), and the CBD
model (Cairns et al., 2006). We modify this

relational model
to
price annuity products
and found that the proposed model has better performance with respect to prediction
errors.


Parallel Session III

-

Panel D

-

Modelling
4

Session Chair
-

Hua Chen


"A Common Age Effect Model for the Mortality of
Multiple Populations"

Torsten Kleinow

We introduce a stochastic mortality model allowing us to simultaneously generate
scenarios for mortality improvements in a number of populations in a consistent way. To
build the proposed model we investigate to what extent a common age effect can be
found

among the mortality experiences of several countries and use an extension of the
principal component analysis to estimate a common age effect in an age
-
period model
for multiple populations. In a second step we then analyse the resulting period effects.
T
he fit of the proposed multiple population model is compared to age
-
period models
fitted to each country individually.


"Love and Death
: A Freund Model with Frailty"

C Gourieroux , Yang Lu

We introduce new models for analyzing the mortality dependence betw
een individuals
in a couple. The mortality risk dependence is usually taken into account in the actuarial
literature by introducing an Archimedean copula. This practice implies symmetric effects
on the remaining lifetime of the surviving spouse. The new mo
del allows for both
asymmetric reactions by means of a Freund model, and risk dependence by means of
an unobservable common risk factor (or frailty). The model is applied to insurance
products such as joint life policy, last survivor insurance, or contract
s with reversionary
annuities.


"Longevity Hedges across Populations: A Two
-
Factor Model Approach"

Linus Fang
-
Shu Chan, Cary Chi
-
Liang Tsai,

Chenghsien Tsai

Managing mortality risk is difficult, and employing the assets linked to mortality rates
looks prom
ising. We advocate of enlarging the scope of the reference mortality rates to
a region to attract more participants and enhance diversification benefits.

We propose to tackle the resulted basis risk by establishing functional relations among
the mortali
ty rate curves between countries/regions. The preliminar results show that
the model works quite well in terms of fitting errors on three country
-
region pairs. We
further derive closed
-
form solutions for the dollar durations of the longevity bond linked
to regional mortality rates with respect to individual countries’ mortality shocks.


"
A
Mul
ti
-
Population Mortality Model via the

Factor Copula Approach"

Hua Chen, Richard MacMinn, Tao Sun

Modeling mortality co
-
movements for different populations have significant implications
for mortality/longevity risk management. In this paper, we apply a two
-
stage procedure
commonly used for credit risk modeling to capture mortality dependence for multip
le
populations. In the first stage, we filter the mortality dynamics of each population using
the ARMA
-
GARCH process, removing abnormalities from the mortality data. In the
second stage, we model the residual risk using a factor copula model that is widely

applicable to high dimension data. We then use this model to price a bond similar to the
Swiss Re Kortis bond and analyze the hedging effectiveness.