U.S. patent application number 13/762914 was filed with the patent office on 2014-02-20 for system and method for managing hedging of longevity risk.
This patent application is currently assigned to JPMorgan Chase Bank, N.A. The applicant listed for this patent is Guy D Coughlan, Maximo X. Silberberg, Amit Sinha, Christopher S. Watts. Invention is credited to Guy D Coughlan, Maximo X. Silberberg, Amit Sinha, Christopher S. Watts.
Application Number | 20140052665 13/762914 |
Document ID | / |
Family ID | 47632030 |
Filed Date | 2014-02-20 |
United States Patent
Application |
20140052665 |
Kind Code |
A1 |
Coughlan; Guy D ; et
al. |
February 20, 2014 |
SYSTEM AND METHOD FOR MANAGING HEDGING OF LONGEVITY RISK
Abstract
A computer implemented method and system are provided for
implementing a longevity bond management system for managing
hedging of longevity of beneficiaries. The method may include
issuing, through a special purpose vehicle, using computer
processing components, a longevity bond having returns following a
longevity index defined for a reference population of a
pre-selected cohort of beneficiaries. The method may additionally
include receiving from investors a payment amount for investment in
the longevity bond, investing the payment amount in a collateral
pool held by a custodian, and receiving cash flows from the
investment in the collateral pool. The method may further include
entering into a swap to exchange the cash flows from the investment
for an amount equal to the difference between an actual and
best-estimate longevity index amount and calculating, using
computer processing components, based on the longevity index, a
periodic payment to the investors based on the longevity
performance of the pre-selected cohort of beneficiaries, such that
the periodic payment increases when longevity exceeds expectations
and decreases when longevity falls short of expectations.
Inventors: |
Coughlan; Guy D; (Kingsto
Upon-Thames, GB) ; Watts; Christopher S.; (London,
GB) ; Sinha; Amit; (New York, NY) ;
Silberberg; Maximo X.; (Jersey City, NJ) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Coughlan; Guy D
Watts; Christopher S.
Sinha; Amit
Silberberg; Maximo X. |
Kingsto Upon-Thames
London
New York
Jersey City |
NY
NJ |
GB
GB
US
US |
|
|
Assignee: |
JPMorgan Chase Bank, N.A
New York
NY
|
Family ID: |
47632030 |
Appl. No.: |
13/762914 |
Filed: |
February 8, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12732241 |
Mar 26, 2010 |
8374938 |
|
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13762914 |
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61163530 |
Mar 26, 2009 |
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Current U.S.
Class: |
705/36R |
Current CPC
Class: |
G06Q 40/06 20130101;
G06Q 40/08 20130101 |
Class at
Publication: |
705/36.R |
International
Class: |
G06Q 40/06 20060101
G06Q040/06 |
Claims
1-10. (canceled)
11. A computer-implemented longevity bond management system for
managing hedging of longevity of beneficiaries, the longevity bond
management system comprising: index calculation components for
calculating a longevity index defined for a reference population of
a pre-selected cohort of beneficiaries; issuance components for
issuing through a special purpose vehicle, using computer
processing components, a longevity bond having returns following
the calculated longevity index defined for a reference population
including a pre-selected cohort of beneficiaries; investor
interfacing components for receiving from investors a payment
amount for investment in the bond and forwarding a calculated
periodic payment to the investors; custodian interfacing components
for investing the payment amount in a collateral pool held by a
custodian and receiving cash flows from the investment in the
collateral pool; a swap execution engine for entering into a swap
to exchange the cash flows from the investment for an amount equal
to the difference between an actual and best-estimate longevity
index amount; and a payment calculation engine calculating, using
computer processing components, based on the longevity index, a
periodic payment to the investors based on the longevity
performance of the pre-selected cohort of beneficiaries, such that
the periodic payment increases when longevity exceeds expectations
and decreases when longevity falls short of expectations.
12. The system of claim 11, wherein the pre-selected cohort
implemented by the index calculation components comprises female
beneficiaries of male annuitants, wherein the female beneficiaries
are within a twenty to thirty year age span at inception of the
index and further defining the cohort as restricted to
beneficiaries under a maximum age.
13. The system of claim 12, wherein the cohort includes female
beneficiaries between ages sixty and eighty five at inception of
the index.
14. The system of claim 13, wherein female beneficiaries drop out
of the cohort upon reaching an age of ninety.
15. The system of claim 11, wherein the index calculation
components define the longevity index for the cohort for time t
years after inception as follows: S t observed = y = 60 91 - max (
t , 6 ) b y I t , y observed ##EQU00003## where
I.sub.t,y.sup.observed is the cohort specific survivorship index,
given by
I.sub.t,y.sup.observed=.sub.tp.sub.y.sup.f,observed[1-(1-w.sub.y.sup.-
initial).sub.tp.sub.y+k(y).sup.m,observed] where y labels the
cohort and represents age at the start of the index, b.sub.y is an
initial weight of all female beneficiaries in the cohort as a
proportion of all female beneficiaries aged sixty to eighty five,
calculated by annual annuity amount; .sub.tp.sub.y.sup.f,observed
is an observed survival rate from time 0 until time t for the age y
cohort of female beneficiaries; w.sub.y.sup.initial is an initial
weight of widows among all female beneficiaries in cohort y
calculated by annual annuity amount, k(y) is the average age
difference in years between male annuitants and female
beneficiaries in cohort y, weighted by income amount;
.sub.tp.sub.y+k(y).sup.m,observed is the observed survival rate
from time 0 to time t for the y+k(y) cohort of male annuitants.
16. The system of claim 11, wherein the investor interfacing
components invest in a low risk debt product.
17. The system of claim 11, wherein the investor interfacing
components invest in government issued bonds.
18. The system of claim 11, the swap execution components
facilitate exchanging cash flows between the special purpose
vehicle and a financial institution and allowing the financial
institution to transact with a super-national entity such that the
super-national entity directly transact with the special purpose
vehicle to enable the special purpose vehicle to receive a
difference between an actual and best-estimate longevity index.
19. The system of claim 18, wherein the swap execution components
enable the super-national entity to provide credit enhancement to a
re-insurer and the reinsurer to underwrite longevity risk.
20. The system of claim 11, wherein payment calculation components
calculate the periodic payment to investors for a payout date
comprises adding an initial annuity amount to a product of the
initial annuity amount and an initial longevity index forecast and
multiplying the sum by a difference between an actual value of the
longevity index on the payout date and an initial forecast of the
longevity index for the payout date.
21. A computer implemented method for implementing a longevity bond
management system for managing hedging of longevity of
beneficiaries, the method comprising: defining a longevity index
for a cohort for time t years after inception as follows: S t
observed = y = 60 91 - max ( t , 6 ) b y I t , y observed
##EQU00004## where I.sub.t,y.sup.observed is the cohort specific
survivorship index, given by
I.sub.t,y.sup.observed=.sub.tp.sub.y.sup.f,observed[1-(1-w.sub.y.sup.-
initial).sub.tp.sub.y+k(y).sup.m,observed] where y labels the
cohort and represents age at the start of the index, b.sub.y is an
initial weight of all female beneficiaries in the cohort as a
proportion of all female beneficiaries aged sixty to eighty five,
calculated by annual annuity amount; .sub.tp.sub.y.sup.f,observed
is an observed survival rate from time 0 until time t for the age y
cohort of female beneficiaries; w.sub.y.sup.initial is an initial
weight of widows among all female beneficiaries in cohort y
calculated by annual annuity amount, k(y) is the average age
difference in years between male annuitants and female
beneficiaries in cohort y, weighted by income amount;
.sub.tp.sub.y+k(y).sup.m,observed is the observed survival rate
from time 0 to time t for the y+k(y) cohort of male annuitants;
issuing, through a special purpose vehicle, using computer
processing components, a longevity bond having returns following
the longevity index defined for a reference population including
the cohort; receiving from investors a payment amount for
investment in the longevity bond; investing the payment amount in a
collateral pool held by a custodian; receiving cash flows from the
investment in the collateral pool; entering into a swap to exchange
the cash flows from the investment for an amount equal to the
difference between an actual and best-estimate longevity index
amount; calculating, using computer processing components, based on
the longevity index, a periodic payment to the investors based on
the longevity performance of the pre-selected cohort of
beneficiaries, such that the periodic payment increases when
longevity exceeds expectations and decreases when longevity falls
short of expectations; and forwarding the calculated period payment
to the investors.
Description
TECHNICAL FIELD
[0001] Embodiments of the invention are related generally to
systems and methods for managing longevity risk and in particular
to systems and methods for offering an investment vehicle for
hedging longevity risk and providing economic capital relief.
BACKGROUND OF THE INVENTION
[0002] Increasing human life spans have operated to create new
challenges for the elderly and for existing infrastructures that
support the elderly population. Members of the aging population are
faced with the possibility of outliving their financial resources
and therefore seek mechanisms that will guarantee financial
independence. Accordingly, financial instruments have become
available for providing long term financial security.
[0003] Corporate pensions and insurance company annuities, which
are frequently utilized by the elderly contain significant interest
rate, inflation, and longevity risks for the providers of such
products including life insurers and pension plans. Under favorable
market conditions in which high equity returns are realized,
pension plan providers may not suffer from the impact of longevity
improvements. However, as market conditions deteriorate and poor
equity returns prevail, pension plan providers are impacted by the
longevity improvements that have occurred over time. Furthermore,
life insurers providing annuities face risks due to unanticipated
changes in mortality rates.
[0004] To combat the risks mentioned above, pension plan providers
and life insurers can attempt to transfer or hedge longevity risk.
Longevity bonds are among the financial instruments that have
developed and provide a form of insurance for betting against
outliving savings through mortality rates. Longevity bonds pay a
coupon that is proportional to the number of survivors in a
selected birth cohort. If the cohort is defined, for example, as
the number of individuals turning age sixty-five in the year that
the bond is issued, the coupon the following year would be
proportional to the number in the cohort that survive to the
current year. Since this payoff approximately matches the liability
of annuity providers, longevity bonds can theoretically be used to
create an effective hedge against longevity risk.
[0005] However, a number of issues arise with the trading of
mortality linked securities. Such issues may be related to the
liquidity, basis risk, and credit risk. In order to make the
securities attractive to hedgers, liquidity and low basis risk are
desirable. In order to enhance liquidity, the design of the
security should be transparent such that risks and potential
returns are predictable. Furthermore, the reference population
should be based on data from a reliable public source. Ultimately,
in order to create a liquid market in mortality linked securities,
the designed securities must be attractive for both buyers and
sellers.
[0006] Thus, when providing payments linked to a survivorship
index, it is important to implement an accurate predictive model.
As stated above, pension funds and annuity providers face growing
risks due to the increasing life spans as they may have guaranteed
fixed or variable payments for a life span that has become
unexpectedly lengthy. Thus, the longevity risk created by
increasing life spans in conjunction with interest rate risk has
caused problems for the annuity market. As annuity markets continue
to grow, the risks and consequences of underestimating mortality
improvements also continue to grow. Accordingly, a solution is
needed for enhancing the predictive accuracy of the longevity bond
model in order to further reduce risks.
[0007] Furthermore, in some instances, for example when a bond is
issued by a government or government sponsored entity, the yield on
the bond is too low to attract investors. Thus, investors have been
reluctant to accept currently existing structures for issuing
longevity bonds. The combination of the low yield and an imperfect
demographic structure failing to adequately define a cohort for
predictive accuracy have been deficiencies of previously attempted
longevity bond systems. Thus, a solution is needed for providing a
structure for issuing a longevity bond that will operate based on a
demographically sound index and generate a sufficiently high yield
for attracting investors.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] The present invention is described in detail below with
reference to the attached drawings figures, wherein:
[0009] FIG. 1 is a work flow diagram illustrating work flow between
system participants in accordance with a first embodiment of the
invention;
[0010] FIG. 2 is a work flow diagram illustrating work flow between
system participants in accordance with a second embodiment of the
invention;
[0011] FIG. 3 is flow diagram illustrating work flow between system
participants in accordance with a third embodiment of the
invention;
[0012] FIG. 4A is a block diagram illustrating an operating
environment for implementing the method and system of the
invention;
[0013] FIG. 4B is a block diagram illustrating a longevity bond
management system in accordance with an embodiment of the
invention;
[0014] FIG. 5 is a block diagram illustrating a computing
environment for implementing the method and system of the
invention;
[0015] FIG. 6 is a flow chart illustrating a method in accordance
with an embodiment of the invention;
[0016] FIG. 7 is a diagram illustrating subgroups of a reference
population over time in accordance with an embodiment of the
invention;
[0017] FIG. 8 is a block diagram illustrating operation of a
hedging instrument in accordance with an embodiment of the
invention;
[0018] FIG. 9 is a chart illustrating hedging of longevity in
accordance with an embodiment of the invention;
[0019] FIGS. 10A and 10B are charts illustrating survivorship of
annuitants in accordance with an embodiment of the invention;
[0020] FIG. 11 is a diagram illustrating evolution of a reference
population in accordance with an embodiment of the invention;
[0021] FIG. 12 is a chart illustrating longevity index weights in
accordance with an embodiment of the invention;
[0022] FIG. 13 is a chart illustrating economic capital relief in
accordance with an embodiment of the invention; and
[0023] FIG. 14 is a chart illustrating a cash flow profile in
accordance with an embodiment of the invention.
SUMMARY OF PREFERRED EMBODIMENTS
[0024] In one aspect of the invention, a computer implemented
method for is provided implementing a longevity bond management
system for managing hedging of longevity of beneficiaries. The
method includes issuing, through a special purpose vehicle, using
computer processing components, a longevity bond having returns
following a longevity index defined for a reference population of a
pre-selected cohort of beneficiaries. The method additionally
includes receiving from investors a payment amount for investment
in the longevity bond, investing the payment amount in a collateral
pool held by a custodian, and receiving cash flows from the
investment in the collateral pool. The method further includes
entering into a swap to exchange the cash flows from the investment
for an amount equal to the difference between an actual and
best-estimate longevity index amount and calculating, using
computer processing components, based on the longevity index, a
periodic payment to the investors based on the longevity
performance of the pre-selected cohort of beneficiaries, such that
the periodic payment increases when longevity exceeds expectations
and decreases when longevity falls short of expectations. The
method further includes forwarding the calculated period payment to
the investors.
[0025] In a further aspect of the invention, a computer-implemented
longevity bond management system is provided for managing hedging
of longevity of beneficiaries. The longevity bond management system
comprises index calculation components for calculating a longevity
index defined for a reference population of a pre-selected cohort
of beneficiaries and issuance components for issuing through a
special purpose vehicle, using computer processing components, a
longevity bond having returns following the calculated longevity
index defined for a reference population including a pre-selected
cohort of beneficiaries. The system additionally includes investor
interfacing components for receiving from investors a payment
amount for investment in the bond and forwarding a calculated
periodic payment to the investors and custodian interfacing
components for investing the payment amount in a collateral pool
held by a custodian and receiving cash flows from the investment in
the collateral pool. A swap execution engine may be provided for
entering into a swap to exchange the cash flows from the investment
for an amount equal to the difference between an actual and
best-estimate longevity index amount. Additionally, a payment
calculation engine may be provided to calculate, using computer
processing components, based on the longevity index, a periodic
payment to the investors based on the longevity performance of the
pre-selected cohort of beneficiaries, such that the periodic
payment increases when longevity exceeds expectations and decreases
when longevity falls short of expectations.
[0026] In yet a further aspect of the invention, a computer
implemented method is provided for implementing a longevity bond
management system for managing hedging of longevity of
beneficiaries. The method comprises defining a longevity index for
a cohort for time t years after inception as follows:
S t observed = y = 60 91 - max ( t , 6 ) b y I t , y observed
##EQU00001##
where I.sub.t,y.sup.observed is the cohort specific survivorship
index, given by
I.sub.t,y.sup.observed=.sub.tp.sub.y.sup.f,observed[1-(1-w.sub.y-
.sup.initial).sub.tp.sub.y+k(y).sup.m,observed] where y labels the
cohort and represents age at the start of the index, b.sub.y is an
initial weight of all female beneficiaries in the cohort as a
proportion of all female beneficiaries aged sixty to eighty five,
calculated by annual annuity amount; .sub.tp.sub.y.sup.f,observed
is an observed survival rate from time 0 until time t for the age y
cohort of female beneficiaries; w.sub.y.sup.initial is an initial
weight of widows among all female beneficiaries in cohort y
calculated by annual annuity amount, k(y) is the average age
difference in years between male annuitants and female
beneficiaries in cohort y, weighted by income amount, and
.sub.tp.sub.y+k(y).sup.m,observed is the observed survival rate
from time 0 to time t for the y+k(y) cohort of male annuitants. The
method additionally includes issuing, through a special purpose
vehicle, using computer processing components, a longevity bond
having returns following the longevity index defined for a
reference population including the cohort. The method further
includes receiving from investors a payment amount for investment
in the longevity bond, investing the payment amount in a collateral
pool held by a custodian, and receiving cash flows from the
investment in the collateral pool. Additionally, the method
includes entering into a swap to exchange the cash flows from the
investment for an amount equal to the difference between an actual
and best-estimate longevity index amount. The method also includes
calculating, using computer processing components, based on the
longevity index, a periodic payment to the investors based on the
longevity performance of the pre-selected cohort of beneficiaries,
such that the periodic payment increases when longevity exceeds
expectations and decreases when longevity falls short of
expectations and forwarding the calculated period payment to the
investors.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0027] Embodiments of the present invention are directed to a
system for issuing and managing longevity bonds and hedging
longevity risk The system and method rely on a special purpose
vehicle (SPV) for issuing the longevity bonds. The SPV may be a
limited company or partnership created to fulfill the objectives of
the longevity bond management system and is preferably an offshore
bankruptcy-remote company. The SPV issues the longevity bonds with
the full support of a national insurance rate in order to provide
an attractive investment for insurance companies. The SPV provides
a vehicle for blending in credit risk in a customized way. Without
an SPV, the system is linked to the credit quality of an existing
issuer. Through integration of the SPV, customization of credit
exposure accompanying longevity is enabled.
[0028] Moreover, embodiments of the invention define a target
population whose longevity risk is being hedged and a corresponding
longevity index. The target population is defined broadly enough so
that sufficient data can be collected, but specifically enough in
order to enhance predictability and reduce risk.
[0029] As will be further described herein, an annuity is a policy
that pays a fixed amount periodically for life in return for an
initial premium. An annuitant refers to a person receiving an
annuity or pension payment. With particular reference to the
embodiments described herein, a male annuitant or affiliado may be
the policy holder whose spouse will receive a pension payment
(annuity) after he dies. The female spouse, also referenced as a
female beneficiary, or beneficiaria will start receiving a pension
payment when her husband has died as long as she is still
alive.
[0030] FIG. 1 is a block diagram illustrating work flow diagram
providing an operating structure for a system in accordance with a
first embodiment of the invention. As illustrated, participants may
include a re-insurer 10, a financial institution 20, a
super-national entity 30, an insurance company 40, a custodian 50,
policy holders 60, and an SPV 70.
[0031] As provided by reference numeral 1, the insurance company 40
purchases a longevity bond from the SPV 70. In embodiments of the
invention, the insurer 40 is a Chilean life insurance company that
purchases a twenty five year Unidad de Fomento (UF) denominated
longevity Bond issued by the SPV 70. The UF is the consumer price
index (CPI) published daily by the national statistics institute of
Chile. Each year, the insurer 40 receives an initial annuity amount
multiplied by an initial forecast of the longevity index (i.e. the
expected or best estimate), added to the initial annuity amount and
multiplied by the difference between actual value of the longevity
index at the date of the payout minus initial forecast of the
longevity index for that date. In embodiments of the invention, a
longevity bond management system operated by, integral with, or
accessed by the SPV 70 or financial institution 20 is provided in
order to determine the amount of the aforementioned payments.
[0032] In step 2 of FIG. 1, the SPV 70 invests in a portfolio of
products from the custodian 50 holding the products in a collateral
account. The SPV 70 receives coupon and principal from the
investment. The nature of the portfolio of products may for example
be a low risk debt type product, or alternatively may be bonds of a
higher strength with some element of credit risk to help reduce
cost of the longevity hedge. In embodiments of the invention, the
collateral is invested in BTUs/BCUs, which are bonds in UF issued
by the Chilean government, and therefore subject to credit risk of
the Chilean government.
[0033] In step 3, the SPV 70 enters into a swap with the financial
institution 20 to exchange the cash flows from the investment in
Step 2 and receive a "best estimate" annuity cash flow. The annual
payments correspond to the "best estimate" expectation of the
longevity index in each year at inception. The financial
institution 20 may reconstitute the actual bond cash flows into the
survivorship profile of cash flows.
[0034] In step 4 of FIG. 1, the financial institution 20 fronts the
SPV 70 for entering into a longevity swap with the super-national
entity 30/re-insurer 10 to receive the difference between the
actual and best-estimate longevity index level in each year. The
super-national entity 30 provides credit enhancement to the
re-insurer 10 and the re-insurer 10 is provided to underwrite
longevity risk. In embodiments of the invention, the super-national
entity may, for example, include the world bank.
[0035] The financial institution 20 provides a transformation that
enables the super-national entity 30 to directly transact with the
SPV 70, as typically super-national entities would encounter
difficulties attempting to directly interface with the SPV 70.
[0036] Thus, in Step 5, the swap is completed after the financial
institution 20 has acted as an intermediary between the
super-national entity 30 and the SPV 70. Thus the SPV 70 receives
the difference between the actual and best-estimate longevity
index. Credit risk to swap counterparties may be mitigated via
collateral agreements.
[0037] Finally, in step 6, the insurance company 40 receives the
annual payments linked to the actual longevity index and is able to
make payments to policy holders 60.
[0038] In summary, the use of the SPV 70 for issuance of longevity
bonds enables a blending of credit risk with the longevity. Thus,
the result is somewhat analogous to the behavior an insurer taking
on an annuity portfolio, such that it takes on longevity risk of
annuity and invests in corporate bonds with credit risk. In the
present system, these risks are blended into the issuance of the
longevity bond product.
[0039] In an embodiment of the invention, the longevity bond
created is a longevity bond for Chilean Insurers. In the displayed
embodiment, the longevity bond is a UF-denominated amortizing bond
with a maturity of twenty five years. The bond is sponsored by the
super-national entity and structured by the financial institution.
The reinsurer performs longevity risk underwriting. Bond proceeds
are invested in a portfolio of government BTUs. This investment
provides cash flows that match longevity risk of the liability,
with the security of Chilean government risk. The structure
described above provides a higher yield than BTUs, thus offsetting
the cost of longevity hedge.
[0040] FIG. 2 illustrates a work flow diagram in accordance with an
alternative embodiment of the invention. In FIG. 2, a reinsurer
210, a financial institution 220, a super-national entity 230, an
insurer 240, a custodian 250, policy holders 260, and SPV 270
participate in the process.
[0041] As provided by reference numeral 1, the insurance company
240 purchases a longevity bond from the SPV 270. As set forth
above, periodically the insurer 240 receives an initial annuity
amount multiplied by an initial forecast of the longevity index
(i.e. the expected or best estimate), added to the initial annuity
amount and multiplied by the difference between actual value of the
longevity index at the date of the payout minus initial forecast of
the longevity index for that date. In embodiments of the invention,
a longevity bond management system operated by, integral with, or
accessed by the SPV 270 or financial institution 220 is provided in
order to determine the amount of the aforementioned payments.
[0042] In step 2 of FIG. 2, the SPV 270 invests in a portfolio of
products from the custodian 250 holding the products in a
collateral account. The SPV 270 receives coupon and principal from
the investment. In step 3, the SPV 270 enters into a swap with the
financial institution 220 to exchange the cash flows from the
investment in Step 2 and receive a "best estimate" annuity cash
flow. The annual payments correspond to the "best estimate"
expectation of the longevity index in each year at inception. The
financial institution 220 may reconstitute the actual bond cash
flows into the survivorship profile of cash flows.
[0043] In step 4 of FIG. 2, the SPV 270 enters into a longevity
swap with the super-national entity 230 to receive the difference
between the actual and best best-estimate longevity index level in
each year. The super-national entity 230 provides credit
enhancement to the re-insurer 210 and the re-insurer 210 is
provided to underwrite longevity risk. Thus, in Step 5, the
insurance company 240 receives the annual payments linked to the
actual longevity index and is able to make payments to policy
holders 260.
[0044] FIG. 3 illustrates a work flow diagram in accordance with an
alternative generalized embodiment of the invention. In FIG. 3, a
reinsurer 310, an insurer 340, a custodian 350, annuitants or
policy holders 360, and an SPV 370 participate in the process.
[0045] As provided by reference numeral 1, the insurance company
340 purchases a longevity bond from the SPV 370. Periodically, for
example, each year, the insurer 340 receives an initial annuity
amount multiplied by an initial forecast of the longevity Index,
added to the initial annuity amount and multiplied by the
difference between actual value of the longevity index at the date
of the payout minus initial forecast of the longevity index for
that date. In embodiments of the invention, a longevity bond
management system operated by, integral with, or accessed by the
SPV 370 is provided in order to determine the amount of the
aforementioned payments.
[0046] In step 2 of FIG. 3, the SPV 370 invests in a portfolio of
products from the custodian 350 holding the products in a
collateral account. The SPV 370 receives coupon and principal from
the investment. In step 3, the SPV 370 enters into a swap with the
reinsurer 310 to exchange the cash flows from the investment in
Step 2 and receive a "best estimate" annuity cash flow. The annual
payments correspond to the "best estimate" expectation of the
longevity index in each year at inception. In step 4 of FIG. 3, the
insurance company 340 receives the annual payments linked to the
actual longevity index and is able to make payments to policy
holders 360.
[0047] While FIGS. 1-3 show the work flow between participating
parties, FIG. 4A is provided to illustrate an operating environment
for execution of the work flow illustrated in FIG. 1. In FIG. 4,
the parties that may be involved in the process, including a
reinsurer 410, financial institution 420, a super-national entity
430, a life insurer 440, a custodian 450, policy holders 460a, 460b
. . . 460n, an SPV 470, and a longevity bond management system 480
may be connected over a network 490. The network 490 may be, for
example the Internet, and all of the aforementioned participants
are embodied by computing systems capable of connecting over the
network 490.
[0048] Various networks 490 may be implemented in accordance with
embodiments of the invention, including a wired or wireless local
area network (LAN) and a wide area network (WAN), wireless personal
area network (PAN) and other types of networks. When used in a LAN
networking environment, computers may be connected to the LAN
through a network interface or adapter. When used in a WAN
networking environment, computers typically include a modem or
other communication mechanism. Modems may be internal or external,
and may be connected to the system bus via the user-input
interface, or other appropriate mechanism. Computers may be
connected over the Internet, an Intranet, Extranet, Ethernet, or
any other system that provides communications. Some suitable
communications protocols may include TCP/IP, UDP, or OSI for
example. For wireless communications, communications protocols may
include Bluetooth, Zigbee, IrDa or other suitable protocol.
Furthermore, components of the system may communicate through a
combination of wired or wireless paths.
[0049] Furthermore, as illustrated in FIG. 4A, the longevity bond
management system 480 is connected to the parties over the network.
The longevity bond management system 480 includes a computing
system having a processor executing software modules for managing
the work flow illustrated in FIGS. 1-3. The longevity bond
management system 480 is responsible for determination of payment
amounts, indices, and other factors required to implement the work
flow as will be described herein The longevity bond management
system 480 may be a discrete system as shown in FIG. 4. In
alternative embodiments, the longevity bond management system 480
may be distributed so as to be located components in the systems of
participants, for example with the SPV system 470 and with the
financial institution system 420. The software modules implemented
by the processor of the longevity bond management system 480
include instructions for executing all of the functions described
herein below.
[0050] FIG. 4B is a block diagram illustrating exemplary components
of the longevity bond management system 480 in accordance with an
embodiment of the invention. The longevity bond management system
may include integral or discrete components or modules for
performing all of the functions described herein. In FIG. 4B, the
longevity bond management system 480 is illustrated as including a
data gathering engine 482, rules and definitions 484, and index
calculator 486, bond structuring/issuance components 488, periodic
payment calculator 490, investor interfacing components 492,
custodian interfacing components 494, and swap execution engine
496. All of the components may be interconnected in any chosen
configuration. Furthermore, each component may comprise a
combination of software and a distinct computing machines or
alternatively all of the components may include software components
running on a single or multiple computing machines. As
illustrating, the data gathering engine 482 may gather data from
publicly available databases and other sources 472 in order to
formulate the index and make periodic updates. Based on the data
collected as well as rules and definitions stored in the database
484, the index calculator may calculate the index at various points
in time. The bond structuring/issuance components 488 may structure
and issue the bond relative to the calculated index. The periodic
payment calculator 490 may calculate payments to the investors as
further explained herein based on both the initially calculated
index and the index calculated as of a particular payout date.
Investor interfacing components 492 and custodian interfacing
components 494 serve to facilitate the functions described herein
with respect to the investors and custodian. Additional interfaces
may be provided for communication with other entities such as the
super-national entity, the re-insurer, the financial institution,
and the SPV. The swap execution engine 496 facilitates the swap
involving the SPV and other parties such as the financial
institution, super-national entity, and re-insurer.
[0051] All of the components shown in FIGS. 1-4 above may be,
include, or be implemented by a computer or multiple computers.
FIG. 5 illustrates a possible computing environment for
implementing the longevity bond management system 480. The
components may be described in the general context of
computer-executable instructions, such as program modules, being
executed by a computer. Generally, program modules include
routines, programs, objects, components, data structures, etc. that
perform particular tasks or implement particular abstract data
types.
[0052] FIG. 5 is a block diagram illustrating a computing system
500 implementing a longevity bond management system components 580
in accordance with an embodiment of the invention. This
configuration is merely exemplary and should not be construed as
limiting. It is likely that multiple computing systems or devices
will be utilized to implement the method and system in accordance
with embodiments of the invention. The computing system 500 may
include a processing unit 510, a peripheral interface 520, a user
input interface 530, a system bus 540, a system memory 550, a
network interface 5900, a connected modem 592, and a memory
interface 594. The system bus 540 may be provided for coupling the
various system components. In embodiments of the invention, certain
components, such as modem 592, need not be included.
[0053] Computers typically include a variety of computer readable
media that can form part of the system memory and be read by the
processing unit. By way of example, and not limitation, computer
readable media may comprise computer storage media and
communication media. The system memory 550 may include computer
storage media in the form of volatile and/or nonvolatile memory
such as read only memory (ROM) 560 and random access memory (RAM)
570.
[0054] A basic input/output system (BIOS) 562, containing the basic
routines that help to transfer information between elements, such
as during start-up, is typically stored in ROM 560. RAM 570
typically contains data and/or program modules that are immediately
accessible to and/or presently being operated on by processing
unit. The data or program modules may include an operating system
574, country identification system 200, other program modules 576,
and program data 582. The operating system may be or include a
variety of operating systems such as Microsoft Windows.RTM.
operating system, the Unix operating system, the Linux operating
system, the Xenix operating system, the IBM AIX.TM. operating
system, the Hewlett Packard UX.TM. operating system, the Novell
Netware.TM. operating system, the Sun Microsystems Solaris.TM.
operating system, the OS/2.TM. operating system, the BeOS.TM.
operating system, the Macintosh.TM..RTM. operating system, the
Apache.TM. operating system, an OpenStep.TM. operating system or
another operating system of platform.
[0055] At a minimum, the memory 550 includes at least one set of
instructions that is either permanently or temporarily stored. The
processor 510 executes the instructions that are stored in order to
process data. The set of instructions may include various
instructions that perform a particular task or tasks, such as those
shown in the appended flowcharts. Such a set of instructions for
performing a particular task may be characterized as a program,
software program, software, engine, module, component, mechanism,
or tool. The longevity bond management system 580 may include a
plurality of software processing modules stored in a memory as
described above and executed on a processor in the manner described
herein. The program modules may be in the form of any suitable
programming language, which is converted to machine language or
object code to allow the processor or processors to read the
instructions. That is, written lines of programming code or source
code, in a particular programming language, may be converted to
machine language using a compiler, assembler, or interpreter. The
machine language may be binary coded machine instructions specific
to a particular computer. Any suitable programming language may be
used in accordance with the various embodiments of the invention.
Illustratively, the programming language used may include assembly
language, Ada, APL, Basic, C, C++, COBOL, dBase, Forth, FORTRAN,
Java, Modula-2, Pascal, Prolog, REXX, and/or JavaScript for
example. In embodiments of the invention, Ab Initio.TM. software is
implemented and structured query language (SQL) is implemented for
coding.
[0056] Further, it is not necessary that a single type of
instruction or programming language be utilized in conjunction with
the operation of the system and method of the invention. Rather,
any number of different programming languages may be utilized as is
necessary or desirable.
[0057] Also, the instructions and/or data used in the practice of
the invention may utilize any compression or encryption technique
or algorithm, as may be desired. An encryption module might be used
to encrypt data. Further, files or other data may be decrypted
using a suitable decryption module.
[0058] The computing environment may also include other
removable/nonremovable, volatile/nonvolatile computer storage
media. For example, a hard disk drive may read or write to
nonremovable, nonvolatile magnetic media. A magnetic disk drive may
read from or writes to a removable, nonvolatile magnetic disk, and
an optical disk drive may read from or write to a removable,
nonvolatile optical disk such as a CD ROM or other optical media.
Other removable/nonremovable, volatile/nonvolatile computer storage
media that can be used in the exemplary operating environment
include, but are not limited to, magnetic tape cassettes, flash
memory cards, digital versatile disks, digital video tape, solid
state RAM, solid state ROM, and the like. The storage media are
typically connected to the system bus through a removable or
non-removable memory interface.
[0059] The processing unit 510 that executes commands and
instructions may be a general purpose computer, but may utilize any
of a wide variety of other technologies including a special purpose
computer, a microcomputer, mini-computer, mainframe computer,
programmed micro-processor, micro-controller, peripheral integrated
circuit element, a CSIC (Customer Specific Integrated Circuit),
ASIC (Application Specific Integrated Circuit), a logic circuit, a
digital signal processor, a programmable logic device such as an
FPGA (Field Programmable Gate Array), PLD (Programmable Logic
Device), PLA (Programmable Logic Array), RFID processor, smart
chip, or any other device or arrangement of devices that is capable
of implementing the steps of the processes of the invention.
[0060] It should be appreciated that the processors and/or memories
of the computer system need not be physically in the same location.
Each of the processors and each of the memories used by the
computer system may be in geographically distinct locations and be
connected so as to communicate with each other in any suitable
manner. Additionally, it is appreciated that each of the processor
and/or memory may be composed of different physical pieces of
equipment.
[0061] A user may enter commands and information into the computer
through a user interface 530 that includes input devices such as a
keyboard and pointing device, commonly referred to as a mouse,
trackball or touch pad. Other input devices may include a
microphone, joystick, game pad, satellite dish, scanner, voice
recognition device, keyboard, touch screen, toggle switch,
pushbutton, or the like. These and other input devices are often
connected to the processing unit through a user input interface
that is coupled to the system bus, but may be connected by other
interface and bus structures, such as a parallel port, game port or
a universal serial bus (USB).
[0062] One or more monitors or display devices may also be
connected to the system bus via an interface 520. In addition to
display devices, computers may also include other peripheral output
devices, which may be connected through an output peripheral
interface. The computers implementing the invention may operate in
a networked environment using logical connections to one or more
remote computers, the remote computers typically including many or
all of the elements described above.
[0063] Various networks may be implemented in accordance with
embodiments of the invention. These networks may include any of
those described above with reference to FIG. 4. Although many other
internal components of the computer are not shown, those of
ordinary skill in the art will appreciate that such components and
the interconnections are well known. Accordingly, additional
details concerning the internal construction of the computer need
not be disclosed in connection with the present invention.
[0064] Those skilled in the art will appreciate that the invention
may be practiced with various computer system configurations,
including hand-held wireless devices such as mobile phones or PDAs,
multiprocessor systems, microprocessor-based or programmable
consumer electronics, minicomputers, mainframe computers, and the
like. The invention may also be practiced in distributed computing
environments where tasks are performed by remote processing devices
that are linked through a communications network. In a distributed
computing environment, program modules may be located in both local
and remote computer storage media including memory storage
devices.
[0065] Although the aforementioned components are shown as discrete
modules, each of the modules may alternatively be integrated with
one another. If the modules are discrete, multiple modules may
operate cooperatively as will be further explained below.
[0066] Although many other internal components of the computer are
not shown, those of ordinary skill in the art will appreciate that
such components and the interconnections are well known.
Accordingly, additional details concerning the internal
construction of the computer need not be disclosed in connection
with the present invention.
[0067] FIG. 6 is a flow chart illustrating a method in accordance
with an embodiment of the invention. The method begins in S600 and
the system defines an index to provide a longevity hedge in S610.
In S620, the system issues a bond linked to the defined index. In
S630, the system sells the bond to investors and in S640 the system
purchases fixed rate instruments. In S650, the system conducts a
mortality swap and in S660, the system passes flow based on the
longevity index back to the investors. The method ends in S670.
Although shown in a specific order, the order of these method steps
may be altered without departing from the scope and spirit of the
invention. In embodiments of the method, these steps are performed
by or with the assistance of one or more processors executing
software modules as described above. Furthermore, each of the steps
described above may include additional sub-steps, which will be
described in greater detail below.
[0068] In S610, the bond is structured by defining an index. In
embodiments of the invention, the index is related to a sub-group
of an annuitant population. The sub-group may include surviving
female spouses who become annuitants upon the death of their
husbands. Thus, the longevity index is an index of surviving female
spouses that determines bond cash flows. Cash flows increase if the
female spouses live longer than expected and decrease if they die
earlier than expected. The longevity index is an index of those
surviving female spouses in a particular cohort who are alive and
receiving an annuity (pension) at any time over the life of the
bond
[0069] Thus, at any given time during the life of the bond, the
annuitants may include: (1) initial annuitants or surviving spouses
who are widows and receiving an annuity at start of the index; and
(2) later annuitants, which includes surviving spouses who were not
initial annuitants, but whose husband has subsequently died and are
now annuitants In embodiments of the invention, the cohort refers
to the closed group of female spouses who are initially aged sixty
to eighty five years old at the inception date of the longevity
bond. A lifetime of the hedge, such as twenty five years, may also
be defined. Although these figures relate to an embodiment of the
invention, the selection of a cohort may include various age spans,
such as, for example, five years to forty years.
[0070] Furthermore a maximum age, such as ninety years, may be
established for members of the cohort. Exposure to those over a
given age cannot be reliably priced due to the limited amount of
mortality information currently available for those ages. Hence the
system may stop hedging payments to surviving female spouses should
they live beyond a pre-defined age, because the cohort should be
selected so that ample data is available. A maximum age for the
cohort may be raised for future embodiments if more data becomes
publicly available. Additionally, the index is weighted by the
amount of each surviving spouse's annuity payment.
[0071] Thus, the underlying exposure is the stream of annuity cash
flows (pension payments) paid to widows periodically, for example
yearly. The longevity risk that is hedged is the risk associated
with the length of time over which pension payments are made to the
surviving female spouses. This longevity risk is thus contingent on
two mortality rates including the male mortality rate of the male
annuitant and the female mortality rate of the female beneficiary.
The annuity payments to the female beneficiary begin upon the death
of the associated male annuitant and the annuity payments to the
female beneficiary stop upon the female beneficiary's death.
[0072] An objective is to provide regulatory capital relief and
economic capital relief as a benefit for longevity risk management.
In the embodiment described above, the bond hedges the cash flow
risk related to female spouses. The insurer receives payments each
year related to the level of the longevity index of surviving
female spouses.
[0073] The longevity hedge removes the uncertainty in the time over
which pension payments are made to the female beneficiary, by
exchanging the uncertain set of payments for a certain fixed set of
payments. The hedge is based on the longevity index, which reflects
the longevity of the total reported population of female
beneficiaries or the reference population. The bond cash flows
include payments to the insurer linked to the longevity index
described above. The longevity component of bond cash flow can be
characterized as
Longevity component in year t=Notional.times.S.sub.t+Time
Adjustment (1)
[0074] Where t=0 corresponds to the start of the hedge and the
inception of the longevity index. S, the longevity index,
corresponds to the pensions paid to the reference population of
female beneficiaries, which closely tracks the actual payments of
an insurer to its own target population of female beneficiaries,
which is a subset of the reference population. As a result the
longevity hedge provides effective reduction in the longevity risk
associated with the target population of female beneficiaries.
[0075] Thus, in summary, the longevity index S.sub.t is a
survivorship index related to a reference population of female
beneficiaries for which data has been collected. The index cohort
may be further defined at the inception of the index to be within a
specific age range, such as for example, sixty to eighty five
years, at the inception of the hedge. Furthermore, the cohort may
be further limited to have a maximum age, such as for example,
ninety years. A purpose of the index is to track the pension
payments made by live insurers to female spouses, once their
husbands have died.
[0076] Thus, based on the definition of the index, if female
beneficiary mortality rates are lower than expected, the index will
be higher than expected as more female beneficiaries will survive.
If male mortality rates are lower than expected, then the index
will be lower than expected, as there will be more husbands still
alive and therefore fewer female spouses receiving an annuity.
[0077] The longevity index reflects the full population or
reference population for which data is collected and therefore
reflects the combined population of beneficiaries of all insurers
at that time. In contrast, the target population of beneficiaries
of a single insurer will be a subset of the reference population of
beneficiaries in the index. While both populations should track
each other closely, there will be small differences in the
mortality experience of each. Residual basis risk will exist due to
the differing identities of the target population and the reference
population and for portfolios with small number of lives, sampling
risk will be present and regardless of the portfolio size.
[0078] In embodiments of the invention, the longevity index
definition formula for time t years after hedge starts is as
follows:
S t observed = y = 60 91 - max ( t , 6 ) b y I t , y observed ( 2 )
##EQU00002##
[0079] Where I.sub.t,y.sup.observed is the cohort specific
survivorship index, given by
I.sub.t,y.sup.observed=.sub.tp.sub.y.sup.f,observed[1-(1-w.sub.y.sup.ini-
tial).sub.tp.sub.y+k(y).sup.m,observed] (3)
[0080] and the symbols in the equations are defined as follows:
[0081] (a) y labels the cohort and can be thought of as the age at
the start of the index, i.e. at time 0, 1 Jan. 2009; (b) b.sub.y is
the initial (i.e., time zero) weight of all female beneficiaries in
cohort y as a proportion of all female beneficiaries aged sixty to
eighty five, calculated by annual annuity amount;
(c).sub.tp.sub.y.sup.f,observed is the observed survival rate from
time 0 until time t for the age y cohort of female beneficiaries;
(d) w.sub.y.sup.initial is the initial (i.e., time zero) weight of
widows among all female beneficiaries in cohort y calculated by
annual annuity amount; (e) k(y) is the average age difference in
years between husbands and female beneficiaries in cohort y,
weighted by income amount; (f) .sub.tp.sub.y+k(y).sup.m,observed is
the observed survival rate from time 0 to time t for the y+k(y)
cohort of males.
[0082] In order to calculate mortality rates, "Insurance Age" (IA)
needs to first be calculated:
IA=exact date of opening of the policy-exact date of birth (4)
[0083] Using this precise (i.e. non-rounded) figure, the date of
birth is recalculated (and called "VYB") as follows:
VYB=year in which policy was opened-IA (5)
[0084] The following ages may then be calculated, given a specific
"observation period" for calculation of exposures as illustrated in
Table 1 below.
TABLE-US-00001 TABLE 1 yi age at year at which the observation
which starts - VYB the observation starts zi age at year at which
the observation which ends - VYB the observation period ends
.theta.i exact IA + exact death - exact age of opening of the
policy death .phi.i renunciation renunciation year - VYB age
[0085] Based on this information, the exposure at age x, Ex, can be
calculated.
Ex=sum of all the individuals satisfying: (5)
yi<x+1 (i)
zi.gtoreq.x+1 (ii)
.theta.i=0 or x.ltoreq..theta.i (iii)
.phi.i=0 or x.ltoreq..phi.i (iv)
[0086] Additionally, the deaths at age x, .THETA.x, can be
calculated.
.THETA.x=sum of exposed individuals at age x
satisfying:x<.theta.i.ltoreq.x+1 (6)
[0087] Furthermore, the mortality rate q.sub.x can be defined
as
q.sub.x=E.sub.x/.THETA..sub.x (7)
[0088] The following Table 2 shows an example of how pension
payments for a single age sample population of female beneficiaries
might develop over time: For the cohort of female beneficiaries
aged 60 on 1 Jan. 2009, at start date (time 0) for the index of 1
Jan. 2009 (t=0 is 1 Jan. 2009, t=1 is 1 Jan. 2010, t=2 is 1 Jan.
2011, etc. . . . ), with the following weights and mortality
rates.
TABLE-US-00002 TABLE 2 Mortality Rates Survival Rates Weights
female male female male q.sub.60,2009.sup.f = 2%
q.sub.65,2009.sup.m = 5% .sub.0p.sub.60.sup.f = 100%
.sub.0p.sub.65.sup.m = 100% k(60) = 5 q.sub.61,2010.sup.f = 3%
q.sub.66,2010.sup.m = 6% .sub.1p.sub.60.sup.f = 100% .times. 98% =
.sub.1p.sub.65.sup.m = 100% .times. 95% = w.sub.60.sup.initial =
50% q.sub.62,2011.sup.f = 4% q.sub.67,2011.sup.m = 7%
.sub.2p.sub.60.sup.f = 98% .times. 97% = 95% .sub.2p.sub.65.sup.m =
95% .times. 94% = 89% .sub.3p.sub.60.sup.f = 95% .times. 96% = 91%
.sub.3p.sub.65.sup.m = 89% .times. 93% = 83%
TABLE-US-00003 TABLE 3 Date Payment 2000 .times.
I.sub.t,y.sup.observed = 2000 .sub.tp.sub.y.sup.f,observed [1 - (1
- w.sub.y.sup.initial) .sub.tp.sub.y+k(y).sup.m,observed] 1 Jan
2009 2000 .times. I.sub.0,60.sup.observed = 2000 100% [1 - (1 -
50%) 100%] = 1000 1 Jan 2010 2000 .times. I.sub.1,60.sup.observed =
2000 98% [1 - (1 - 50%) 95%] = 1029 1 Jan 2011 2000 .times.
I.sub.2,60.sup.observed = 2000 95% [1 - (1 - 50%) 89%] = 1052.31 1
Jan 2012 2000 .times. I.sub.3,60.sup.observed = 2000 91% [1 - (1 -
50%) 83%] = 1067.27
[0089] If the yearly annuity corresponding to all female
beneficiaries is 2000, the index payments corresponding to the
cohort are as illustrated in TABLE 3.
[0090] FIG. 7 is provided to further illustrate subgroups of a
selected reference population at two separate points in time 710
and 720. At t=0 or 710, the reference population is divided into an
A group of initial annuitants and B group of initial
non-annuitants. Over time some number of initial annuitants in the
A group and initial non-annuitants in the B group will die.
Furthermore, some of the initial non-annuitants in the B group will
become annuitants B(2). These divisions within the A group and the
B group are illustrated at 720 at later time t>0.
[0091] FIG. 8 broadly illustrates the process of longevity hedging.
A longevity bond 810 is issued. An investor, shown as life insurer
830 receives floating payments 820 linked to the longevity index
that reflect the realized mortality experience of the total target
population. Ultimately, members of the target population 850, who
are female beneficiaries in accordance with an embodiment of the
invention, receive pension payments determined by the realized
mortality experience of the insurer's population.
[0092] FIG. 9 is a chart illustrating the evolution of annuity
payments for participants in a policy over time. An x-axis 902
represents time and y-axis 904 represents payments. Shaded bars 910
represent a male annuity and white bars 910 represent a female
beneficiary annuity 912. As illustrated, at a first point in time,
the male annuitant retires and he begins receiving annuity
payments. At a second point in time, the male annuitant dies and
annuities to his female beneficiary begin. Finally, at a third
point in time, the female beneficiary dies and the annuity
terminates.
[0093] FIG. 10A is a graph illustrating survivorship of initial
annuitants and graph 10B illustrates survivorship of later
annuitants. Time is shown on x-axes 1002 and 1022 and survivorship
is shown on y-axes 1004, 1024. As illustrated, survivorship of
initial annuitants decreases over time. Survivorship of later
annuitants increases to a peak and subsequently decreases over
time.
[0094] FIG. 11 further illustrates the reference population.
Columns of FIG. 11 are divided to show an initial time 1102,
scenario 1140, and a later time 1152. At 1102 (t=0), all female
beneficiaries 1112 are divided into groups of initial annuitants
1120 who are already receiving a pension and initial non-annuitants
1130 whose husbands are still alive and who are not receiving a
pension.
[0095] Initial annuitants 1120 who survive over time 1141 will
continue receiving a pension and will be grouped as initial
annuitants receiving a pension at 1160. If an initial annuitant
receiving a pension dies 1142, this initial annuitant will be
classified as dead and not receiving a pension at 1162.
[0096] From the pool of initial non-annuitants 1130, a number of
scenarios are feasible. First, the female beneficiaries may survive
and the male annuitant may die at 1143, making the female
beneficiary a later annuitant receiving a pension at 1170.
Alternatively, the female beneficiary and male annuitant may both
survive at 1144, such that the female beneficiaries remain
non-annuitants at 1172. As a further alternative, the female
beneficiary may die and the male annuitants may survive at 1145,
making the female beneficiary dead and not receiving a pension at
1174. As a final alternative, both the female beneficiary and male
annuitant may die at 1146, making the female beneficiary dead and
not receiving a pension at 1176.
[0097] FIG. 12 is a table 1200 illustrating weights for the
longevity index. The longevity index requires weights to determine
the proportion of different groups in the index. The longevity
index reflects the total pension amount being paid to beneficiaries
at any point in time. The index depends on observed mortality rates
for both males and females over time and observed initial weights
of (i) different age cohorts and (ii) widowed beneficiaries versus
non-widowed beneficiaries. The index is weighted by the amount of
each beneficiary's annuity payment. The relative weightings between
different age groups and between annuitants and non-annuitants in
the index are determined by the data set at inception.
[0098] In particular, weights are provided for different ages,
initial annuitant vs. initial non-annuitant beneficiaries, and
average age difference between male annuitants and female
beneficiaries. As shown in FIG. 12, the initial values of these
weights at inception of the index are set to be identical to those
for the entire available data set. The target population being
hedged needs to be designated carefully to reflect that portion of
the total insurer population that has the same weights as the index
weights.
[0099] The table 1200 includes columns showing age 1210, cohort
weights by age 1220, initial annuitants % 1230, and age difference
in years between male annuitant and female beneficiaries 1240.
[0100] FIG. 13 is a table 1300 illustrating risk reduction 1320 and
economic capital relief 1310 in connection with the specific
reference population described above. Any reduction in risk leads
to a reduction in the amount of economic capital required to
support the business. By reducing the amount of capital supporting
the business, there is an immediate benefit in terms of saving the
cost of providing that capital. As illustrated in FIG. 13, the
economic risk within a typical portfolio of annuities is calculated
to be 6.3% of the current value of the liabilities. the economic
risk capital with both a portfolio of male annuitants and female
beneficiaries are calculated to be 3.9% and 10.5% respectively of
the value of their respective liabilities. The higher number for
female beneficiaries reflects the fact that the duration of their
annuity payments is much greater.
[0101] The model suggests that: about 72% of the longevity risk is
contained in the first twenty five years cash flows, which are the
years being hedged by the bond. The model further suggests that
about 95% of the longevity risk in the first twenty five years cash
flows are being hedged by the bond. This suggests that the
reduction in economic risk capital is about
10.5%.times.72%.times.95%=7.2%. Overall, this suggests that the
reduction in economic risk capital is about
10.5%.times.72%.times.95%=7.2% as a result of the proposed
longevity hedge. Longevity risk within a portfolio of annuities is
concentrated within the contingent pensions such as those to the
female beneficiaries as payments to those policyholders have a
significantly longer duration than the portfolio as a whole.
Consequently, the economic risk capital for a portfolio of
contingent beneficiaries pensions, as a percentage of the value
their liabilities, is much higher than for a portfolio of male
annuitant pensions.
[0102] FIG. 14 is a chart 1400 illustrating management of a cash
flow mismatch 1414 between collateral flows 1412 received by the
financial institution and annuities 1410 paid by the financial
institution. An x-axis 1402 represents time and a y-axis 1404
represents cash flow.
[0103] Overall, the use of a longevity bond for hedging provides a
benefit to insurers in the form of reduction in regulatory capital,
economic capital, and increased certainty of future cash flow. The
cost of the hedge should be formulated at a price at which a third
party will take longevity risk. In embodiments of the invention,
reduced costs of the hedge may be created through increased size of
bond issuance through reduction in fixed costs.
[0104] Thus, the longevity bond is structured by the longevity bond
management system as a bond with an amortizing profile, such that
the insurer, as the hedging party, makes an up-front payment and
receives a series of annual payments over the course of the hedge
duration. The payments are adjusted by the actual longevity
performance of the beneficiary population relative to a projected
longevity performance based on a longevity index. Thus, if the
beneficiaries tend to live longer than anticipated, the cash flows
to the hedging party increase. If the beneficiaries have a shorter
life span than expected, cash flows are downwardly adjusted. Thus,
the hedging party benefits from a substantial removal of longevity
risk at a modest cost. Furthermore, the removal of the risk may
reduce capital reserve requirements imposed by regulatory
authorities so that capital is freed for other uses.
[0105] The longevity bond and management system provide at least
three features to address insurers' requirements. First, the
longevity bonds provide a longevity hedge in order to offset
exposure to risk. In this instance, the longevity bond provides a
hedge of longevity risk associated with the insurer's annuity
portfolio. In specific embodiments of the invention, the longevity
bond specifically hedges the longevity risk associated with the
sub-group of the annuitant population corresponding to specific
beneficiaries. The longevity bond is tied to a longevity index of
these beneficiaries that determines bond cash flows. Cash flows
increase if the beneficiaries have a longer life span than expected
and decrease if the beneficiaries lives span a shorter duration
than expected.
[0106] Secondly, the longevity bonds provide an attractive
investment to insurers. The bond proceeds may be invested in a
portfolio of low risk debt type products. This product may be, for
example, a government bond or a high-grade corporate bond. In
embodiments of the invention, the bond proceeds are invested in a
portfolio of government BTUs (Chilean government bonds). This
allows for cash flows that match longevity risk of the liability,
with the security of Chilean government risk. Similar embodiments
may be implemented across varying governments and currencies. The
structure provided for implementing the longevity bonds allows for
a higher yield than BTUs and thus offsets cost of longevity hedge.
In yet additional embodiments, bond proceeds may be invested in
bonds of higher strength with some element of credit risk in order
to reduce the cost of the longevity hedge.
[0107] Finally, the proposed longevity bond management system and
method provides economic capital relief to insurers as a benefit
for longevity risk management. The longevity bond hedges the cash
flow risk related to beneficiaries. The insurer receives payments
each year equal to the level of a longevity index of the
beneficiaries.
[0108] While particular embodiments of the invention have been
illustrated and described in detail herein, it should be understood
that various changes and modifications might be made to the
invention without departing from the scope and intent of the
invention.
[0109] From the foregoing it will be seen that this invention is
one well adapted to attain all the ends and objects set forth
above, together with other advantages, which are obvious and
inherent to the system and method. It will be understood that
certain features and sub-combinations are of utility and may be
employed without reference to other features and
sub-combinations.
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