
A Data Mining Framework for Valuing Large Portfolios of
Variable Annuities
Guojun Gan
Department of Mathematics
University of Connecticut
341 Manseld Road
Storrs, CT 06269-1009, USA
guojun.gan@uconn.edu
Jimmy Xiangji Huang
School of Information Technology
York University
4700 Keele Street
Toronto, Ontario M3J 1P3, Canada
jhuang@yorku.ca
ABSTRACT
A variable annuity is a tax-deferred retirement vehicle created to
address concerns that many people have about outliving their assets.
In the past decade, the rapid growth of variable annuities has posed
great challenges to insurance companies espe cially when it comes
to valuing the complex guarantees embedded in these products.
In this paper, we propose a novel data mining framework to
address the computational issue associated with the valuation of
large portfolios of variable annuity contracts. The data mining
framework consists of two major components: a data clustering
algorithm which is used to select representative variable annuity
contracts, and a regression model which is used to predict quanti-
ties of interest for the whole portfolio based on the representative
contracts. A series of numerical experiments are conducted on a
portfolio of synthetic variable annuity contracts to demonstrate the
performance of our proposed data mining framework in terms of
accuracy and speed. The experimental results show that our pro-
posed framework is able to produce accurate estimates of various
quantities of interest and can reduce the runtime signicantly.
CCS CONCEPTS
• Mathematics of computing → Nonparametric statistics
;
•
Information systems → Data mining;
KEYWORDS
data mining; data clustering; kriging; variable annuity; portfolio
valuation
1 INTRODUCTION AND MOTIVATION
A variable annuity is a life insurance product that is created by
insurance companies as a tax-deferred retirement vehicle to address
concerns many people have about outliving their assets [
26
,
31
].
Under a variable annuity contract, the policyholder (i.e., the in-
dividual who purchases the variable annuity product) agrees to
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make one lump-sum or a series of purchase payments to the in-
surance company and in turn, the insurance company agrees to
make benet payments to the policyholder beginning immediately
or at some future date. A variable annuity has two phases: the ac-
cumulation phase and the payout phase. During the accumulation
phase, the policyholder builds assets for retirement by investing
the money (i.e., the purchase payments) in several mutual funds
provided by the insurance companies. During the payout phase,
the policyholder receives payments in either a lump-sum, periodic
withdrawals or an ongoing income stream.
A main feature of variable annuities is that they contain guar-
antees, which can be divided into two main classes: guarantee d
minimum death benet (GMDB) and guaranteed minimum living
benet (GMLB). A GMDB guarantees that the beneciaries receive
a guaranteed minimum amount upon the death of the policyholder.
There are three types of GMLB: guaranteed minimum accumulation
benet (GMAB), guaranteed minimum income benet (GMIB), and
guaranteed minimum withdrawal benet (GMWB). A GMAB is
similar to a GMDB except that a GMAB is not triggered by the
death of the policyholder. A GMAB is typically triggered on policy
anniversaries. A GMIB guarantees that the policyholder receives a
minimum income stream from a specied future point in time. A
GMWB guarantees that a policyholder can withdraw a specied
amount for a specied period of time.
The guarantees embedded in variable annuities are nancial
guarantees that cannot be adequately addressed by traditional p ool-
ing methods [
4
]. If the stock market goes down, for example, the
insurance companies lose money on all the variable annuity con-
tracts. Figure 1 shows the stock prices of ve top issuers of variable
annuities during the period from 2005 to 2016. From the gure we
see that the stock prices of all these insurance companies dove dur-
ing the 2008 nancial crisis. Dynamic hedging is adopted by many
insurance companies now to mitigate the nancial risks associated
with the guarantees.
One major challenge of dynamic hedging is that it requires calcu-
lating the fair market values of the guarante es for a large portfolio
of variable annuity contracts in a timely manner [
8
]. Since the
guarantees are relatively complex, their fair market values cannot
be calculated in closed form except for special cases [
13
,
21
]. In
practice, insurance companies rely on Monte Carlo simulation to
calculate the fair market values of the guarantees. However, using
Monte Carlo simulation to value a large portfolio of variable annu-
ity contracts is extremely time-consuming because every contract
needs to be projected over many scenarios for a long time horizon.
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