Pricing Surface
Pricing Surface
DEVELOPMENT
SECTION
Product
ISSUE 108 • NOVEMBER 2017
3 Chairperson’s Corner
By Kelly Rabin
Matters!
Abrokwah
12 Impact of VM-20 on
Life Insurance Product
Development—Phase 2
By Paul Fedchak, Jackie
Keating, Karen Rudolph, Uri
Sobel, and Andrew Steenman
Matters!
Officers
Kelly Rabin, FSA, CFA, MAAA, Chairperson
Brock Robbins, FSA, FCIA, MAAA, Vice Chairperson
Nancy Brophy, FSA, FCIA, Secretary/Treasurer
Council Members
Paul Fedchak, FSA, MAAA
Issue Number 108 • November 2017 Blake Hill, FSA, FCIA
Trevor Huseman, FSA, MAAA
Published three times a year by the Dwayne McGraw, FSA, MAAA
Product Development Section of the Lindsay Meisinger, FSA, MAAA
Society of Actuaries. Elena Tonkovski, FSA
A
s a new FSA, I remember sitting in the audience at 2. You are first to hear breaking news in the SOA product space.
SOA meetings, watching speakers present. Who were Whether that is new research, upcoming meetings to plan for, or
they? Why were they taking the time to present? How new SOA initiatives, you hear about it before the general mem‑
did they know all this stuff? I then noticed that most of the bership. This just might make you more successful at your job!
presenters were reinsurers and consultants and it was often
the same people speaking about the same topics. While their 3. You have the chance to give back. The SOA is an organization
perspectives were extremely valuable, I was working at an run mostly by a lot of volunteers and some amazing staff. If you
insurance company at the time and craved insight from those don’t lend a hand, who will? We want your fresh perspective!
who worked in the same environment. But company product
actuaries often either didn’t want to give away their secrets or The last three years on the PD Section Council have been very
weren’t encouraged by their companies to volunteer. rewarding. I have learned a lot about how the SOA works and
how to motivate volunteer leaders, as well as met some fabu‑
As a former consultant myself, I wholly recognize that consul‑ lous people who I might not have met otherwise. Our section
tants and reinsurers have a lot more financial incentive to take is stronger than ever. We have over 2600 members. We spend
time out of their busy work schedules to volunteer. Volunteering over $100,000 on research every year that directly benefits those
is not just giving back in that case—it is also part of marketing who practice in product development. We partner with other
your brand. Don’t get me wrong—speaking at a session, plan‑ sections on topics like PBR and in‑force management. I am
ning a meeting, or writing an article each take a lot of time. I am proud to have been your chair, and excited to move into my next
very grateful to each and every one of our volunteers. The SOA volunteer role as chair of the Life & Annuity Symposium for the
is as well, and has even launched a new volunteer recognition next two years.
program in the last couple years to reward volunteers for their
efforts. That said, I would love to see new volunteers and fresh How will you step up and make a difference? I hope that I get
perspectives—no matter where you work. to sit in your session next year or read your newsletter article
so I can think, “this is a really cool perspective; I’m so glad this
So, why volunteer for the SOA—and more specifically, the person decided to volunteer!” n
Product Development Section?
End View
ining this issue from multiple viewpoints along the customer
journey. Recommendations include educating customers about
the value and affordability of life insurance, reducing the fric‑
By Nitin Nayak and Stephen Abrokwah tion and waiting times in the buying process, and improving the
quality and speed of assessing/pricing customer’s mortality risk.
As a result, existing actuarial methods are being supplemented
with several nontraditional data sources and modelling tech‑
niques, which are currently in various stages of deployment.
This article provides an overview of various innovative solu‑
A
tions supporting an end-to-end underwriting process for life
ccording to a Swiss Re study, life insurance ownership insurance products.
has declined at a dramatic rate over the past 30 years
and is currently at a 50-year low.1 This situation is most EVOLUTION OF THE TRADITIONAL LIFE
pronounced among the middle market and millennial house‑ INSURANCE BUYING PROCESS
holds. Declining sales partly explain the research estimates of Life insurance plays an important role in protecting house‑
the life insurance protection gap,2, 3 which has been estimated holds and families from the dire financial impact of uncertain
to exceed USD 86 trillion globally and USD 20 trillion within mortality. Over the years, actuaries have developed robust
the United States alone. The average household protection estimates of life expectancy by using mortality tables to predict
gap within the United States is now estimated to be just under aggregate insured population mortality as well as dependable
USD 400 thousand. underwriting techniques to assess the relative risk of an indi‑
vidual. Though these techniques have been widely accepted
Independent and captive agents constitute the majority of the
within the insurance industry for many years, the traditional
existing distribution channels for life insurance products, and
life insurance underwriting process is time-consuming, invasive
they have gradually migrated toward supporting mostly high
and costly. Typically, a life insurer spends about a month and
net-worth individuals for larger face amount policies (See Fig‑
several hundred dollars underwriting each proposed insured,
ure 1). As a result, many in the mid-market segment are left to
with underwriting costs ultimately passed on to policyholders
their own sources for both educating themselves and purchasing
through increased premium rates.3
life insurance products.
Over the years, the life insurance industry has been gradually
With a greater availability of both internal and external data,
streamlining the underwriting and customer sales processes to
along with advances in predictive models, an increase in
make them less invasive and to provide a more timely response.
Figure 1 Some early enhancements included simplified issue products
with easier application requirements and nonmedical underwrit‑
Individual Life Insurance Sales4
Individual life insurance sales ing for smaller face amounts, and refinements of underwriting
guidelines based on protective value studies.
USD Million
200,000 20 The increased availability of individual-level data, new sources
180,000 18
160,000 16
of nontraditional information, and advances in machine learn‑
140,000 14 ing techniques have created an opportunity for life insurers to
120,000 12 embrace innovations in various areas along the insurance value
100,000 10 chain. In the context of underwriting, this innovative revolution
80,000 8
60,000 6
utilizes predictive analytics, underwriting automation and busi‑
40,000 4 ness intelligence to underwrite with faster turnaround times,
20,000 2 reduced costs and fewer invasive medical requirements. This
0 0 win-win situation for insurers and prospective policyholders
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New accelerated approaches bring mortality cost much closer to fully underwritten levels
Nonmed UW
Nonmedical Underwriting ($$$) Full Underwriting
• No blood/urine • MD/Paramed with blood/urine
• Rx, MVR, MIB • Rx, MVR, MIB
Accelerated UW
• Higher price to account for no fluids • Lowest price
($$)
Accelerated Underwriting
• No blood/urine
Fully Pricing differential depends on the choices
• Rx, MVR, MIB
underwritten insurers make in the design of their program
• Predictive model triage approach
• Prices closer to fully UW due to P.M. ($) • Percent qualifying for AU
• Model type & thresholds of predictive risk scores
• Monitoring safeguards pre/post issue
implications. Figure 2 shows the relative increase/decrease of • A simple application process requiring fewer questions, with
mortality costs for various approaches being explored within the as many fields in the application prefilled with user-specific
industry. In comparison to a full underwriting process with its information as appropriate
detailed and time-intensive procedures, the faster nonmedical
(no paramedical exam, blood or urine test, or attending phy‑ • A quote delivered in real time describing the policy coverage
sician statement) underwriting process increases the expected and associated premium and payment options, similar to the
mortality cost. Alternatively, transitioning from nonmedical experience of purchasing automobile insurance online
underwriting to fluid-less underwriting, supplemented with
• A set of relevant quote alternatives, each outlining policy
predictive analytics, can bring expected mortality to levels closer
coverages and associated premiums for the user to compare
to that of a fully underwritten process.5
to the face amount originally requested by user
LIFE INSURANCE FOR THE MIDDLE MARKET
• A view of life insurance and related products (e.g., riders and
AND MILLENNIAL GENERATION CONSUMERS
term periods purchased by the consumer’s peers in order to
Life insurers can learn much from other industries, including
assist with decision making)
online retail and personal banking, to improve the customer
satisfaction of their consumers. This is especially true for the Figure 3
millennial generation who would likely prefer to purchase Consumer Satisfaction with Online Experience by Industry 6
life insurance products online. Figure 3 shows the results of a
consumer survey regarding satisfaction with online experiences
across various industries. Clearly, the insurance industry lags Telco & Cable 3.5
Real estate 3.8
behind when it comes to delivering a satisfactory online con‑
Insurance 4.0
sumer experience. Health care providers 4.1
Government services 4.2
To increase customer satisfaction, especially for the millennial Automobiles 4.3
Industry
generation, we suggest primary insurers offering life insurance Electricity, gas, water 5.0
products consider the following consumer expectations: Supermarkets 5.8
Hotels 8.5
Airlines 8.9
• The ability for the consumer to get a quick tutorial on life
Electronics retail 10.0
insurance products, with a concise explanation of their benefits Media retail 11.1
Online merchants 11.8
• An individualized needs analysis for each consumer, along Personal banking 15.2
with a recommendation for various life insurance products 0 2 4 6 8 10 12 14 16
(term versus permanent), and face amounts based on their Relative utility score
individual life situation.
The next section presents a view of the end-to-end process for life insurers will leverage these platforms as key distribution
purchasing life insurance products from the perspective of a life channels. For example, many life insurance carriers like Mas‑
insurer. sachusetts Mutual Life Insurance Company (Haven Life) and
AAA Life Insurance Company have begun offering sales via
OVERVIEW OF INNOVATIONS FOR ACCELERATED online and other digital platforms.
UNDERWRITING IN LIFE INSURANCE
This process starts with the customer being presented an online Another challenge faced by life insurers is the application format,
insurance application in a shorter form and with prefilled which today contains upwards of 60 questions covering a variety
responses (where possible) to make it more likely to be com‑ of individual details along with invasive medical tests and a long
pleted. At the end of the process, the customer will be offered wait time of approximately 45 to 60 days.7 For the millennial and
multiple affordable and suitable quotes within minutes based on most middle-market consumers, the large number of questions
an individualized needs analysis. Figure 4 provides descriptions and the time commitment required can be a deal-breaker. From
of these steps. an insurer’s point of view, this long-form application is necessary
to properly assess the applicant’s mortality risk and to prevent
Step 1. User Interaction anti-selection. However, not all questions in the application
Most millennials are very comfortable using mobile technology questionnaire have the same predictive power. Machine learning
for their online interactions, both in the social world of friends techniques can identify the most important features for predict‑
as well as the commercial world of transactions. Additionally, ing mortality risk so the least useful features can be removed
they expect to make their own decisions (self-service) and prefer to simplify the questionnaire. Some insurers are exploring the
only occasional hand-holding to complete any transaction. So extent to which the application can be prefilled with data from
although digital, mobile and online platforms are not currently other internal and external sources. This should make it easier
the dominant channels for most insurers to interact with poten‑ for the consumer who can now focus mostly on correcting any
tial customers, we expect that within the next few years, many incorrect prefilled information. Additionally, many insurers are
Figure 4
End-to-End View of Accelerated Underwriting Process
Data Providers
Multiple
Quote Offers
MVR Rx
... MIB ...
User Interface Public
Data
Actuarial
Databases
2 3
Option 1
2. Fluid-less Risk
Score Prediction
8. Instant Quotes
Provided to User
Risk Rating with Final
Smoking Status Risk Rating
Pass 5. Risk Score 6. External 7. Mortality-
4. Triage Rules to Risk Class Rules Engine Based
Application Conversion (Life Guide) Pricing
Predicted Fail
Smoker
1. Behavioral Status Client Risk
Economics Design Preferences
3. Smoker
Propensity
Insurance Application Prediction
Platform 9. Traditional
Underwriting Process
Table 1
Sample Data Elements for Building Mortality Risk-Related Predictive Models
Third-Party Data • MIB for medical information To validate proposed insured’s prior medical
• Rx for prescription history and insurance purchase history, prescription
• MVR for motor vehicle record profile and propensity to take risks (e.g., through
review of proposed insured’s driving record)
Public Data • Properties, professional licenses, criminal To validate applicant-provided data as well as to
history fill in missing information
Financial • Income and employment history Used as one of the predictors to predict
• Short-term and long-term debt (mortgage) mortality risk, especially for low-risk individuals
• Bankruptcies, liens
Credit History • Credit score Used as one of the predictors to predict
mortality risk, especially for low-risk individuals
Digital Imaging • Facial image analysis To assess individual’s age group, BMI, and
smoking status
Social Data • Publicly available social media such as To verify identity, hobbies, smoker status, and
Facebook, LinkedIn and Snapchat use of alcohol or drugs, although the hit-rate
may be low
Population-level • Zip code and state-level published data on Although coarse in granularity, the data can still
Open Data education levels, median income, disease, risky be useful to fill in missing data on individuals.
behavior etc., from sources such as U.S. Census, The tobacco-related data can be used for smoker
U.S. Centers for Disease Control propensity prediction
• County/state tobacco taxes and regulations
Medical • Access to electronic medical records To assess current and future risk related to
health and mortality
Health and Wellness • Vital statistics, heart rate, physical activity To assess current and future risk related to
data collected from wearables and internet- health and mortality
enabled devices
• Food preferences, psychological and emotional
health from wellness websites and programs
0.0 0.2 0.4 0.6 0.8 1.0 their risk rating and their predicted smoker/nonsmoker status.
The figure illustrates the sequence of applications and third-
False Positive Rate (Fallout)
party databases used to triage applications in preparation for
assigning them to a risk class.
Note: Steep slope of ROC curve indicates model predicts more true-positives with very few
false-positives at threshold = 0.8
Step 5. Risk Classification Using Risk Score Thresholds
There are two approaches to predicting the mortality risk of a
Step 3. Smoker Propensity Prediction
proposed insured applicant by using a risk score: either use the
After age and gender, tobacco usage is the most important score to predict the risk class that would have been assigned by
determinant of mortality risk and hence of life insurance policy an underwriter, or use the score to predict the expected mortal‑
premium. According to the Centers for Disease Control (CDC), ity, which can then be converted into an appropriate risk class.
overall mortality among both male and female smokers in the
United States is about three times higher than that among simi‑
lar people who never smoked.10
If RSM<X
Standard Risk & SM Model ≠ NS Action
Self-declared NS + NS vs SM prediction Issue at Risk
+ App & third party data Class determined
y by UW
Life Insurance Application Action Oka
UW
Full
+ Full Application Refer to Full
+ External Data Underwriting
Full
(MVR, MIB, Rx) U Action
Poo W Okay
r Ris ,
+ Smoker? Y,N k Sc Very Issue, but cap
ore
Action at Standard
Standard Risk & Self-declared SM Risk Class
Issue as
Standard SM Risk
Action
Generally, the first approach is easier to sell to the underwriting techniques, the most common approach to underwriting deci‑
community; however, the second approach is a more objective sions had been the use of experience-based rules that resulted
way of assessing a proposed insured’s mortality risk. from several proprietary and industry-sponsored research
studies. These rules generally apply an extra loading for mortali‑
We note that when validating the predicted risk class against ty-increasing risk factors within the preferred criteria. Examples
the historical underwriter-derived risk class for an application, of such risk factors include family history of significant illnesses
the predicted risk class could be different from the underwrit‑ of either parent, participation in hazardous avocations, just to
er’s decision. The movement of applicants across risk classes is mention a few. The rules engine sums up the total risk factor
most common for those applicants whose scores are near the loading for a proposed insured, which is then compared against
borderline between two classes. However, the objective measure a table to assign a risk class. From this perspective, the external
should be the relative actuals-to-expected (A/E) mortality ratios rules engine can complement the predictive models with expe‑
for various risk classes, where the better underwriting risk is rience-based rules to further refine the risk class assigned to an
represented by a lower A/E ratio. During deployment of a risk applicant. So it is not surprising that many insurers require that
scoring solution, the choice of associating risk classes with risk decision rules for underwriting be included within their end-to-
score intervals is very much left to the insurance company but end accelerated underwriting process.
can be selected based on comparable A/E ratios for the risk class
and corresponding risk score interval. Step 7. Mortality-Risk-Based Pricing Algorithms for
Quote Generation
Step 6. External Rules Engine Although the details of mortality-based pricing models are
The data-driven predictive analytics approaches address the risk outside the scope of this article, many insurers use pricing
score prediction and tobacco usage prediction in steps 2 and 3 tables based on age, gender, risk-class and tobacco usage of an
respectively. Before the introduction of new predictive analytics individual to compute the premium for life insurance policies of
specific face amount and level term periods (for term products).
The process flow as described in Figure 4 essentially provides
these variables required by the mortality-based pricing algo‑
rithm to support a real-time quote. A useful feature can be to
compute prices for multiple combinations of face amounts and
term periods, based on historical choices made by other users,
with situations similar to the applicant. These multiple pricing
options can then be presented to the customer as described in
Step 8, to help make a life insurance buying decision that best
suits his or her situation.
T
he Society of Actuaries’ (SOA) Product Development Term Small Company Case Study
Section, Smaller Insurance Company Section, Rein‑
Figure 1 outlines the stepwise assumption changes from Phase
surance Section and the Committee on Life Insurance
1 Situation 5 to the Phase 2 small company sensitivity for term.
Research engaged Milliman to examine the impact of the new
Phase 1 Situation 5 is the pricing situation in which VM-20
reserve standard for the product development actuary. The
statutory reserves are used based on an NPR component using
research is organized in two phases. The objective of Phase
the 2017 CSO Table, and DR and SR following VM-20 require‑
1 was to investigate the changes to the product development
ments. Tax reserves are calculated as the NPR using 2017 CSO
process as a result of VM-20 through the development of case
table. The bolded item is the change for each step.
studies for term and universal life with secondary guarantees
(ULSG) products. Starting with the Situation 5 pricing results from Phase 1, Fig‑
ure 2 shows the pricing results of the stepwise implementation
Phase 2 of the research expands on the Phase 1 case studies
of each of the characteristics noted previously. We performed
and includes additional case studies focused on smaller compa‑
the study on four term product varieties—a 10-year and 20-year
nies and the impact of reinsurance. Phase 2 also discusses the
level term period on both a low band ($350k) and high band
industry’s preparedness for pricing under VM-20 and identifies
($1.2M) face amount. The results for the 20-year term, high
pricing and product design issues through interviews and dis‑
band model office are shown in Figure 2. Each row of the table
cussions with product development actuaries.
includes the changes in the preceding steps.
This article highlights some key excerpts from Phase 2 of this
Changes observed in Figure 2 include the following:
research. Phase 1 was addressed in an article in the June 2017
issue of Product Matters! For the sake of brevity, certain details 1. Step 1 drives profitability lower by introducing additional
of the research have been omitted from this article. Please Year 1 expenses. In all four term product varieties in this
Figure 1
Term Small Company Assumption Changes
Acquisition Expense Mortality Credibility and
Step per Unit Sufficient Data Period Reinsurance
Adjusted
Pretax Profit After-Tax After-Tax IRR Adjusted
Small Company 20-Year Level Term Margin1 Profit Margin2 Profit Margin3 Surplus Strain After-Tax
Step 1: Increase Per Unit Acquisition to $1.00 14.7% 8.5% 3.3% −178% 7.1%
case study, this increases surplus strain, reduces profit margin Phase 1 NPR, because mortality credibility and SDP do not
metrics and reduces IRR. impact the determination of the NPR. The characteristics
of less credible mortality experience and shorter SDP for
2. Step 2 changes the level and pattern of VM-20 statutory the smaller company increase the Step 2 DR as compared
reserves because the Deterministic Reserve (DR) is affected to the Phase 1 (and, as noted above, the Step 1 DR) higher
by the much lower credibility measurement and shorter credibility DR. In fact, under these conditions, the Step 2
SDP of the smaller company sensitivity. Because the pre-tax DR is as great as, or greater than, XXX method reserves in
profit margin is discounted at the pre-tax NIER, the pre-tax many durations for each of the four term product varieties.
profit margin does not materially change, while other profit
metrics are reduced due to the additional reserve margins. • Step 3 is where 80 percent coinsurance with a $100,000
limit on retention is implemented. Because the majority
3. Step 3 reflects the implementation of a coinsurance agree‑ of the risk is now ceded away, and a coinsurance expense
ment that small companies might consider to lower surplus allowance becomes part of the DR cash flows, the level of
strain. Coinsurance changes the shape of the profit pattern
by reducing the surplus strain (increasing first year profits) Figure 3
and reducing renewal profits. For the 20-year plan $1.2M Reserve Levels—20-Year Term, High-Band
policy size, the after-tax profit margins and IRR are higher
than for Step 2 because after coinsurance is implemented, 20-Year Plan $1.2MM
the tax basis reserve is equal to the statutory basis reserve for 8000
all but the latest durations, whereas for the Step 2 situation, 7000
Dollars in Thousands
6000
the statutory basis reserve was considerably higher than the 5000
tax basis reserve. 4000
3000
In this small company sensitivity, reserve relationships change 2000
1000
from the Phase 1 case studies. This section looks at the change 0
in reserves under each of the steps implemented for the small -1000
company sensitivity. -2000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(NPR) or DR, because acquisition costs are assumed to be Phase 1 DR Phase 1 NPR Step 1* DR Step 2** DR
incurred at time of issue and are not included in the cash Step 3*** DR Step 3 NPR XXX 2017 CSO
flows for the DR forecast for the end of the first year.
* Step 1: Higher Acquisition Expenses
• Step 2 illustrates the impact of lower mortality credibility ** Step 2: Lower Mortality Credibility
and shorter SDP. The NPR for Step 2 is the same as the *** Step 3: Coinsurance
the DR changes in a material way. The NPR is affected as GUARANTEED YRT CASE STUDIES
well, because the NPR needs to allow for only the insurance The purpose of this sensitivity is to examine the potential impact
amount retained.
to pricing results should the YRT reinsurance agreement guar‑
Graphs of all the reserve streams for the 20-year plan, high band antee the YRT premium rates. The following details provide
are shown in Figure 3. In these graphs, the DR is unfloored, additional context to understand the sensitivity.
consistent with the graphical presentations of DR in Phase 1.
• The Phase 1 Situation 5 reflects nonguaranteed yearly
ULSG Small Company Case Study renewable term (YRT) reinsurance on insurance amounts in
Figure 4 shows the stepwise results from Phase 1 to the Phase excess of a $1,000,000 retention limit, with YRT premiums
2 small company sensitivity for ULSG. The small company set at 110 percent of the pricing mortality.
assumption changes are the same as shown for term except that
the acquisition expense step is not shown, because its impact was • For the Phase 1 DR and SR calculations, YRT premiums
minimal relative to the following two steps. are 110 percent of the VM-20 mortality assumption. For
the Phase 1 case studies, we did not assume any delay in the
Changes observed in the projections summarized in Figure 4
reinsurer’s premium increase.
include the following:
• We ran this Phase 2 case study for high band ($1.2M Face
• Moving from Phase 1 Situation 5 to the Step 2 small com‑
Amount), and the retained amount is assumed to be reduced
pany assumptions increases the DR, resulting in considerable
to $200,000 to better observe the impact.
additional surplus strain and noticeably lower profit margins.
• The final change made within this sensitivity is to test the
• The Step 3 reflection of coinsurance reduces surplus strain
impact of setting the guaranteed YRT rates at specified lev‑
considerably. For Step 3, the impact to IRR is noticeably
different between the low band and high band products that els. For term, we ran sensitivities assuming YRT premiums
were tested. The DR per unit of face in the high band is less equal to 115 percent and 120 percent of expected mortality.
than in the low band because the coinsurance allowance is For ULSG, we ran only a sensitivity assuming YRT premi‑
the same, while the high band has a higher ceded percentage ums equal to 120 percent of expected mortality. These are
but lower expenses to cover (as a percent of premium). As a illustrative only and not indicative of the level of rates that
result, the low band experiences only a modest IRR increase, would be available in the market.
while the high band shows a considerable increase in IRR.
Figure 5 provides the pricing result for this series of runs for the
• The impacts on profit margins in the high band and low band ULSG case study.
are more similar than the IRR impacts, indicating that the
IRR is a more sensitive profit measure at the lower retained In moving from Situation 5 from the Phase 1 report to the
amounts in these studies. Revised Baseline with $200,000 retention:
Figure 4
Pricing Results—Small Company—ULSG
Adjusted IRR
PT Profit AT Profit AT Profit Surplus Adjusted
Small Company ULSG Margin* Margin** Margin*** Strain After-Tax
Step 3: Small Company with Coinsurance 4.9% 2.5% 2.3% −31% 13.4%
• Increased investment income on the higher reserve levels Total VM-20 ULSG Reserve—Guaranteed YRT Study
helps offset the total impact, but profitability is still down
350000
across all measures due to the additional cost of ceding
300000
the business.
250000
Dollars
• The long-term nature of ULSG results in considerable long- 200000
term DR and SR mortality margins (in particular, assuming 150000
no mortality improvement beyond each valuation date), 100000
which are reflected in the nonguaranteed YRT rates in Phase 50000
1. Guaranteeing the YRT rates effectively removes these 0
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
considerable margins from the DR and SR calculations, so
the IRR impact of the 10 percent increase in YRT premium Duration
compared to Phase 1 is more than offset by the reserve relief DR Baseline ($2000K retention) DR 120%*
due to the guaranteed YRT rates.
Moving from the revised baseline to YRT premiums guar‑ * 120%: Guaranteed YRT Premiums Equal to 120% of Expected Mortality
Figure 5
Pricing Results—Guaranteed YRT ULSG, High-Band
Adjusted IRR
PT Profit AT Profit AT Profit Surplus Adjusted
Guaranteed YRT ULSG Margin* Margin** Margin*** Strain After-Tax
Revised Baseline with $200,000 Retention 14.0% −2.6% −4.2% −393% 4.6%
YRT Premiums at 120% of Expected Mortality 10.1% 4.9% 3.7% −64% 13.9%
*Pretax profit margin is calculated with discount at the pretax net investment earnings rate (NIER).
**After-tax profit margin is calculated with discount at the pretax NIER.
***Adjusted after-tax profit margin includes target capital effects and is calculated with discount at the pretax NIER.
Preparedness
• There was an even mix between the pricing and valuation
areas regarding where VM-20 expertise resided, and which
area leads or led the effort to be VM-20-ready. Generally,
companies that had executed or worked on reserve financing
transactions were more prepared than companies that had
not, and at those companies, the VM-20 knowledge in the
valuation area was ahead of the pricing area. On the flip side,
at companies that were looking to roll out VM-20 products
in 2017 or early 2018, the pricing area led the learning curve.
In companies where the corporate structure was organized
across product lines rather than function, term was generally Limited Guidance
more VM-20-ready than ULSG. • There was some concern regarding limited guidance within
VM-20 and related PBR literature on appropriate assump‑
• Most of the companies had done some form of VM-20 trial tions, margin setting and covered risks (e.g., conversion
run, regardless of the company’s timeline for moving to privileges). This was true in general, and particularly regard‑
VM-20 reserves. In some cases, those were purely valuation ing assumptions for new underwriting regimes with limited
exercises, and in other cases, they were more pricing-focused. experience (e.g., accelerated underwriting).
Generally, companies expect their term business to pass the
Stochastic Exclusion Test (SET). Complexity
• More than half the participants raised concerns regard‑
• While some companies are planning to roll out products
ing the intensiveness and complexity of the computations
priced on a VM-20 basis in 2017 or early 2018, most com‑
necessary for VM-20. While most companies expressed
panies are planning to wait until the end of the three-year
satisfaction with their actuarial modeling system, it was clear
transition period. Generally, companies expected to price
that a significant effort needed to be exerted to make the
and offer a VM-20 term product before ULSG. The pricing
systems VM-20-ready, either through customized coding,
timeline is a factor in these roll-out plans; companies indi‑
learning to use the VM-20 features or upgrading systems
cated a need to reprice multiple products by the end of the
to take advantage of VM-20 capabilities. Other concerns
transition period.
around complexity included the following:
Concerns and Issues Regarding VM-20 Implementation
-- Extensive runtime, particularly for stochastic calculations
Fluctuation in Reserve Levels
• Many companies expressed concern over a now higher -- Separate assumptions for inner-loop versus outer-loop
level of unpredictability and fluctuation in their reserves projections
and anticipated profits under VM-20. This was regarding
both the impact of unlocking assumptions (in particular, the -- Auditability of projected VM-20 calculations
interest assumptions) and potential regulatory changes in
-- Coordinating between use of multiple systems (e.g., one
VM-20 methodology. There was consistent concern among
system to calculate the NPR, and another to calculate the
interviewees regarding the future definition of tax reserves.
DR and/or SR)
One participant commented on the positive side of these
fluctuation issues, in that it will allow for faster reactions or -- Moving to an asset/liability pricing approach versus a lia‑
corrections than in the past. bility-only approach
As this is a new frontier within the industry, it will be fascinat‑ • For the ULSG product, the case study indicated that a
ing to watch how pricing actuaries’ thoughts and reactions to 10-pay premium pattern is less profitable than the lev‑
VM-20 change in the next few years. el-pay situation, but the single-pay is more profitable.
The higher single-pay profitability is driven largely by
OTHER CASE STUDIES the initial strain, which is quite small in the single-pay
The Phase 2 report addresses a handful of case studies in situation. The reduced initial strain in the single-pay case
addition to those previously described. These additional case is largely due to the commission level relative to the initial
studies include: premium, which is a phenomenon not unique to a VM-20
pricing situation. n
• An attribution analysis of the margins on the Phase 1 Situa‑
tion 5 Deterministic Reserve
• Analysis of 10 years of post-level term cash flows
• A single cell of a simplified issue product Paul Fedchak, FSA, MAAA, is principal and
consulting actuary at Milliman. He can be reached
• A 30-year level premium term single cell at paul.fedchak@milliman.com.
• A short-pay ULSG single cell study
• When we analyzed the factors contributing to the excess of Jackie Keating, FSA, MAAA, is principal and
the DR over a best estimate gross premium reserve for the consulting actuary at Milliman. She can be reached
at jackie.keating@milliman.com.
Phase 1 VM-20 case studies (Situation 5), we found that for
both term and ULSG, moving from anticipated experience
mortality to VM-20 mortality assumptions had the most
significant impact on the level of reserve.
• Under the case study of specified post-level term assump‑ Karen Rudolph, FSA, MAAA, is principal and
tions, the post-level term period cash flows are clearly consulting actuary at Milliman. She can be reached
at karen.rudolph@milliman.com.
beneficial to the profitability metrics.
• For the 30-year term single cell, the tax impacts together Andrew Steenman, FSA, MAAA, is a consulting
actuary at Milliman. He can be reached at andrew.
with the reduction in reserve requirements and material steenman@milliman.com.
surplus relief make for a significant increase in profitability
under VM-20.
New Insurance Products the SOA. The survey findings provide an effective tool for insur‑
ers to benchmark performance, identify common challenges and
The following are just a handful of insights from the over 200-
Five Insights from the Society of page analysis; readers can access the overview and full report on
Actuaries Product Development Survey the SOA website.1
P
Figure 1.
ast success doesn’t guarantee ongoing success, partic‑
ularly when it comes to insurance product portfolios. Many insurers acknowledge they do not have a clearly defined
Today’s evolving insurance landscape has made new strategy for product development, but this does not necessarily
product development vital to insurers’ financial strength and hinder the entire product development process. For example,
business growth. At a time of changing customer demand, reg‑ the undefined strategy companies do not report launching
ulatory standards, and market pressures, how do insurers bring fewer products. Those companies with a defined strategy
successful new products to market? most frequently embraced fast-follower or niche approaches.
Fast followers avoid the investment and risk of first-to-market
After two years in the making and more than 3,700 data points innovation, but must work quickly to react to changes in the
analyzed, a far-reaching product development survey conducted market and seek to improve on the design being followed.
by RGA and LIMRA on behalf of the Society of Actuaries (SOA) Fast follower companies may not consider themselves highly
sheds new light on how individual life and annuity insurers are innovative, nor do they make disruptive innovation a measure
evaluating this question. RGA and LIMRA collaborated on this for success.
Figure 1
Which of the following best describes the primary focus of your organization’s life insurance product development strategy?
Cost leadership
Faster companies are able to shave off weeks, even months, from While currently used more in the marketing space, almost 70
certain product development efforts (pp. 133–154). Insurers percent of companies indicated they are exploring predictive
that navigate the development process faster tend to begin steps modeling in the area of automated, simplified or accelerated
much sooner and alongside other steps, without waiting for com‑ underwriting. This highlights the link to increased customer
pletion of one task to move on to potential dependent tasks. For satisfaction, and where market leaders and fast followers are
them, items like rider development and reinsurance start earlier spending a great deal of time. Blending with marketing plans
in the overall process than at other providers. However, the most based on predictive modeling’s ability to identify consumer
Figure 2
How important are the following to your organization’s current product development strategy?
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
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Figure 3
For which steps of the product development process is your company currently using predictive modeling
(PM) or beginning to explore the use of predictive modeling?
100%
90% 16%
80% 36%
47%
70% 59% 59%
60% 75%
88% 77%
50% 68%
40% 28% 42%
30% 24% 31%
20%
25% 19% 20%
10% 21% 18% 16% 13% 9% 6%
0% 3%
Marketing Plan Assumption In-Force Underwriting Other Product Product Product
(Target Market/ Development Analysis Pricing Concept And Planning And
Cross Sell) Feasability Design
(+) Currently Using (–)
Figure 4
Duration and Timing of Product Development Steps
Idea Generation
Product Concept/Feasibility
Underwriting Guidelines All
Assumption Development Fastest
Product Planning & Design
Traditional Rider Development
Living Benefit Rider Development
Product Pricing
Reinsurance
State/regulatory Filings
Update Business Procedures
Marketing Plans
Update It - Day 1
PRODUCT DEVELOPMENT COMPLETE
Update IT - Day 2
0 10 20 30 40 50 60 70 80
Weeks
25
15 5 5
10 8 9 3
9 2
13 6
2 3
5 9 7 1 1
4 3 1
6 2 3 1
4 4 4 2
2 1 2 1 2 1 2
0
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As
needs and propensity to buy, disruptive underwriting can lead to new valuation manual that will likely increase travel times for
compelling products with the right value proposition. product development until the process becomes more ingrained
in companies.
5. HOT TRENDS AREN’T ALWAYS HIGH PRIORITIES.
One trend is the wearables idea in the underwriting process (can Administration is identified as an issue, and just because the
and how data could be used). I think another one would just answer is simple, it does not make it easy. The cost and time to
be in general what we here refer to as an “e-initiative,” so an effectively overhaul various processes/systems are too much for
electronic application, electronic signatures and the electronic most companies and as legacy systems increase, the burden will
continue to grow. Use of certain changes in process (e.g., Agile)
underwriting. See Figure 5.
may alleviate some time constraints.
In recent years, the industry has put a great deal of attention
The research does not have all the answers, but mainly gives
and research on emerging trends, such as wellness programs and
companies a chance to look at certain parts of the product
the use of wearable devices to collect consumer data. Yet when
development process to benchmark and think through how to
it comes to actual product development, bottom-line concerns
potentially improve. n
such as low interest rates and meeting regulatory requirements
remain the most important considerations. Interestingly, accel‑
erated underwriting and in-force management are the only
considerations out of 20 choices to be considered at least “some‑ Donna Megregian, FSA, MAAA, is vice president
what important” by all survey respondents. & actuary at RGA. She can be reached at
dmegregian@rgare.com.
SUMMARY
There are many items to take away from the research. Com‑
panies that seek to understand travel time from idea to launch ENDNOTE
will most keenly focus on Section D of the report. Considering
1 https://www.soa.org/research-reports/2017/product-development-process/
that the survey asked about 2014 actions, product development
in 2017 has already been impacted by regulatory changes of a
Indexed UL Current
sum of recurring premiums plus 10 percent of single premiums.
Relative to prior survey results, fewer participants reported sig‑
R
to YTD 9/30/16 from 71 percent to 79 percent of total cash
esults of Milliman’s 10th annual survey of leading univer‑ accumulation UL/IUL sales. IULSG also increased from 5 per‑
sal life (UL) and indexed UL (IUL) products have been cent to 8 percent of total combined ULSG/IULSG sales over
compiled, revealing reactions to the various dynamics of the survey period. CAIUL sales, as a percent of total combined
this market. Thirty-two carriers submitted responses to the sur‑ CAUL/CAIUL sales, decreased from 32 percent to 30 percent
vey related to product and actuarial issues such as sales, profit over this period. Similar to responses in the past, overall survey
measures, target surplus, reserves, risk management, underwrit‑ statistics suggest that in the future participants plan to focus
ing, product design, compensation, pricing and illustrations. more on IUL products, especially AccumIUL, and on CAUL
products.
The scope of the Milliman survey included UL with second‑
ary guarantees (ULSG), cash accumulation UL (AccumUL), The graph in Figure 2 illustrates the IUL product mix and the
current assumption UL (CAUL), and the indexed UL (IUL) significance of AccumIUL products within the IUL market.
counterparts of these products. The definition of these product
types is shown as follows: LIVING BENEFIT RIDER SALES
Seven of the 12 participants that reported UL/IUL sales with
• UL/IUL with Secondary Guarantees: A UL/IUL product chronic illness riders provide a discounted death benefit as
designed specifically for the death benefit guarantee market an accelerated benefit. Under the discounted death benefit
that features long-term no-lapse guarantees (guaranteed to approach, the insurer pays the owner a discounted percentage
last until at least age 90) either through a rider or as a part of of the face amount reduction, with the face amount reduction
the base policy. occurring at the same time as the accelerated benefit payment.
This approach avoids the need for charges up front or other
• Cash Accumulation UL/IUL: A UL/IUL product designed
specifically for the accumulation-oriented market where Figure 1
efficient accumulation of cash values to be available for dis‑
Ul Product Mix by Year
tribution is the primary concern of the buyer. Within this
category are products that allow for high-early cash value
accumulation, typically through the election of an acceler‑
80%
Percent of Total Individual UL Sales
Figure 3
Chronic Illness Rider Sales As A Percent Of Total Sales
Calendar Year Total Individual UL ULSG Cash Accumulation UL Current Assumption UL
Calendar Year Total Individual IUL IULSG Cash Accumulation IUL Current Assumption IUL
IUL Sales With Chronic Illness Riders As A Percent Of Total IUL Sales
2013 30.3% 10.2% 34.4% 15.9%
Figure 4
LTC Rider Sales as a Percent of Total Sales by Premium
Calendar Year Total Individual UL ULSG Cash Accumulation UL Current Assumption UL
Calendar Year Total Individual IUL IULSG Cash Accumulation IUL Current Assumption IUL
9/30/16, sales of policies with LTC riders as a percent of total (PBR) may be implemented as early as Jan. 1, 2017, and 27 survey
sales by premium were 24.0 percent for UL products and 9.8 participants reported they expect to implement PBR for all of
percent for IUL products. Figure 4 shows sales of LTC riders as their UL/IUL products gradually over the three-year phase-in
a percent of total sales (measured by premiums, and weighting period allowed. Resource issues, time needed, financial impact/
single-premium sales at 10 percent) for UL and IUL products cost/benefits, clarification/finalization of PBR/IRS regulations
separately by product type. and PBR implementation of other product first were cited as
factors impacting the rationale for implementation plans.
PROFIT MEASURES
Similarly, the earliest effective date for the use of the 2017
The predominant profit measure reported by survey participants
Commissioner’s Standard Ordinary (CSO) mortality table was
is an after-tax, after-capital statutory return on investment/internal
rate of return (ROI/IRR). This is consistent with what has been Figure 5
reported in past surveys. The average ROI/IRR target reported
Actual Results Relative to Profit Goals for 2015
by survey participants was 9.9 percent for ULSG, 11.1 percent
for AccumUL, 10.5 percent for CAUL, 10.1 percent for IULSG,
12.3 percent for AccumIUL and 12.8 percent for CAIUL. 100%
6% 13%
90%
29% 27%
The charts in Figures 5 and 6 shows the percentage of survey 80% 33%
50%
participants reporting that they fell short of, met or exceeded 70%
their profit goals by UL product type for calendar year 2015 and 60% 72% 63%
YTD 9/30/16, respectively. Of note is the percentage of partici‑ 50% 47%
pants that fell short of their profit goals for ULSG products: 50 40% 62%
31% 67%
30%
percent in 2015 and 63 percent during YTD 9/30/16. As in the
20%
past, the primary reasons reported for not meeting profit goals 27% 25%
10% 19% 22%
were low interest earnings and expenses. 10%
0%
ULSG Cash Current IULSG Cash Current
PRINCIPLE-BASED RESERVES AND THE 2017 CSO Accumulation Assumption
UL UL
Accumulation Assumption
IUL IUL
Results from the survey indicate a staggered approach in imple‑ Exceeded Met Fell Short
menting recent regulatory changes. Principle-based reserves
100%
10% 13%
90%
30% 33% 33%
80%
70% 63%
60%
74%
50% 75%
40%
40% 60% 50%
30%
25%
20%
27% 21%
10% 17% 13%
13% 10%
0%
ULSG Cash Current IULSG Cash Current
Accumulation Assumption Accumulation Assumption
UL UL IUL IUL
Jan. 1, 2017. The 2017 CSO is the new valuation mortality table in Figure 7. More participants believe PBR will be effective
to be used in the determination of CRVM (Commissioners rather than ineffective in making reserve financing arrange‑
Reserve Valuation Method), net premium reserves, tax reserves, ments obsolete.
minimum nonforfeiture requirements and so on. Twenty-two
survey participants reported that they would implement this UNDERWRITING
table for all of their UL/IUL products gradually over the The use of predictive modeling in the life insurance industry has
three-year phase-in period allowed. Ten participants reported recently gained attention. Predictive modeling utilizes statisti‑
implementation of the 2017 CSO would be product dependent; cal models that relate outcomes/events to various risk factors/
implementation will be immediate for some products and over predictors. Scoring models in life underwriting are an example
the three-year phase-in period for others. of predictive modeling used in the life insurance space. Eleven
survey participants use scoring models to underwrite their UL/
It is not surprising that these regulatory changes are not being IUL policies. Eight of the 11 use scoring models for fully under‑
implemented immediately, given the complexity of the regula‑ written policies, one uses them for simplified issue business, and
tions, the potential impact on pricing and the bottom line, and the final two use them for both fully underwritten and simplified
the strain on resources, especially for smaller carriers. issue business. Eight participants reported using scoring models
with automated rules.
In addition, 21 participants provided a rating of how effective
they believe PBR will be in making reserve financing arrange‑ The types of scoring models were reported by 10 of the 11
ments (e.g., captives) obsolete. Ratings are shown in the table survey participants that use scoring models. In total, seven use
lab scoring models, four use credit scoring models and five use
Figure 7 scoring models relative to motor vehicle records (MVR).
Effectiveness Ratings of PBR Making Reserve Financing
Arrangements Obsolete ILLUSTRATIONS
The credited rate used in IUL illustrations for participants’
Rating # Of Responses most popular strategies decreased relative to the illustrated
rate of one year prior for 10 of 21 survey participants. One
Very Ineffective 0
participant reported no change in the illustrated rate, and
Ineffective 4 eight reported increases in the illustrated rate. The median
illustrated rate reported was 6.69 percent and the average was
Average 9 6.58 percent.
Effective 6 The survey has included a number of questions relative to IUL
Very Effective illustrated rates and rates calculated under Actuarial Guide‑
2
line 49 (AG 49) Section 4A and Section 4C. A new question
CONCLUSION
In future years, the implementation Trends in the UL/IUL market in recent years generally have
of PBR, the 2017 CSO table, and been due to the popularity of indexed UL and continuing low
interest rates, with some reaction to regulatory actions. In future
new underwriting approaches years, the implementation of PBR, the 2017 CSO table, and
new underwriting approaches will likely have a more significant
will likely have a more significant impact on the UL/IUL market than seen in recent years. To
impact on the UL/IUL market remain competitive, and even to survive, in this market, it is crit‑
ical for carriers to address the issues and opportunities that arise.
than seen in recent years.
A complimentary copy of the executive summary of the May
2017 Universal Life and Indexed Universal Life Issues report
that was included in the survey this year asked participants
may be found at: http://us.milliman.com/insight/2017/Univer-
to report the maximum illustrated rate that was allowed for
sal-life-and-indexed-universal-life-issues--2016-survey/. n
the most popular strategy/investment choice within their
IUL portfolio, both immediately pre-AG 49 and immediately
post-AG 49. The pre-AG 49 rates ranged from 5.60 percent to
8.50 percent, with an average of 7.38 percent and a median of Sue Saip, FSA, MAAA, is a consulting actuary
7.65 percent. The post-AG 49 rates ranged from 5.02 percent at Milliman. She can be reached at sue.saip@
milliman.com.
to 7.75 percent, with an average of 6.69 percent and a median
of 6.86 percent.
P
Although actuaries have tested two extreme cases, it is difficult
ricing an insurance product requires assumptions, to reflect profitability with the actual sales level. This fight is
actuarial models and professional judgments; the pric‑ usually resolved in front of the CEO and/or CFO with a reason‑
ing results are usually accomplished by a set of finite
able balance between profitability and growth for the company.
numbers deemed as the best estimate of certain profitability
measures, and they are also accompanied by a list of sensitivity Cross-terms among the pricing variables are usually
testing results to help actuaries better understand any poten‑ ignored.
tial deviation from the pricing target due to misestimates, Sensitivity tests are commonly performed at one dimension (or
misjudgments or other uncertainties. one variable) and one dimension only. The interactions between
two pricing variables (or cross-terms) are usually ignored. For
This paper suggests expanding the current approach by con‑
some products, the cross effect can be significant, especially at
structing a pricing surface, or capturing the joint distribution
the tail. For example, for single premium immediate annuity
of interested pricing measure driven by pricing variables. In this (SPIA) product pricing, the company performs sensitivity tests
paper, we will discuss why we use pricing surface, how to con‑ on interest rate and longevity, respectively, but did not test the
struct the surface and what the benefits of using pricing surface combined changes of interest rate and longevity at the same
are; we also provide an example to illustrate the idea and draw a time. Some actuaries found that the impact of the cross-term can
conclusion based on the discussion. be greater than the two individual sensitivity results combined
at the tail. The reason is that the change of one pricing variable
WHY PRICING SURFACE magnifies the impact of the change on the other variable. In this
The pricing results are driven by pricing variables. What case, the longevity extends the duration and makes the profit‑
value we assign to a variable is based on the assumption. Some ability more sensitive to the interest rate. Although the effect
assumptions can be obtained directly from the market such as may not be significant with moderate changes of assumptions,
interest rate or from a company’s experience of similar products it should not be overlooked until tested. Of course, some cross
(such as mortality or lapses). Other assumptions may require effects can go the opposite way, where the changes of two pric‑
professional judgment if the experience is relevant but not ing variables can be off-set to each other to certain extent. This
directly applicable. would be good news for the company. When this is observed,
pricing actuaries or risk managers need to know as well.
Due to various degrees of uncertainty of the assumptions, a
point estimate (usually labeled as best estimate) is not sufficient More sensitivity tests may not be enough.
to provide the complete picture of pricing results even with a list To price an innovative product, it is a challenge to get comfort‑
of sensitivities, let alone to support the decision-making process. able with actuarial assumptions because of lack of experience (if
Here are a few examples. we assume experience is relevant). Actuaries usually rely on the
experience of similar products, or competitors’ experience (usu‑
It is a challenge to reflect economy of scale. ally indirectly from consulting firms), or simply rely on their
For an insurance company, it is common to see a fight between own professional judgment. No matter where the assumptions
sales force and pricing actuaries. The sales force wants to lower landed, they are still actuaries’ best guess. The high level of
the price to make the product more competitive or easy to sell; uncertainty leads to more sensitivity tests to help understand
they argue that as long as the marginal profitability (where only the results that could potentially deviate significantly from
policy-driven expenses are included, no overhead expenses) is the mean. However, these sensitivity tests may not be enough
positive, additional policies sold will make a positive contribu‑ to cover all possibilities for certain assumptions, especially at
tion to the company. On the other hand, pricing actuaries feel the extremes, where human judgement has its limitations. As
that pricing should reflect the true cost to the company. an example, when interest rates were above 10 percent the in
One approach is the so-called curve fitting, which requires mul‑ VM+ = the ending value when mortality increased by ∆M
tiple point estimates to help look for a statistical distribution
that best fits these points. Once the distribution is identified, VR+M+ = the ending value when interest rate and mortality
actuaries can use the distribution to find other pricing points increased
they are interested in.
VR+M− = the ending value when interest rate increased and mor‑
Another approach is to apply multiple-variate Taylor expansion tality decreased
using a few observed points. Here we use Taylor expansion to
illustrate the process. VR−M+ = the ending value when interest rate declined and mor‑
tality increased
Step 1: Define Pricing Variables and Sensitivity Levels
Taking SPIA pricing as an example, we assume the pricing result VR−M− = the ending value when interest rate and mortality
is a function of two pricing variables, namely interest rate and decreased
mortality rate, because we assume they drive the pricing results.
To calculate first order of derivatives with respect to interest
We also assume that function meets the certain mathematical
assumptions such that we can apply Taylor series to this function. rate, we have the following formula:
We then define the sensitivity levels so that we calculate the first For rate up, the formula becomes
and second orders of the derivatives. In Table 1, we choose the VR+ / V0 - 1
following: ( ∂V
∂R )+
=
∆R
Table 1
Similarly, for when the rate goes down, we have
Sensitivity Levels of Pricing Variables
VR- / V0 - 1
Pricing Variables Changes of Pricing Variable # of Tests ( ∂V
∂R ) _
=
∆R
Best Estimate None 1 The first order of derivatives with respect to mortality can be
done in the same fashion.
Interest rate (“R”) +/−1% parallel shift 2
Similarly, for second order of derivatives, we take the calculated
Mortality (“M”) +/−10% of base mortality table 2
first order of derivatives and calculate them using the following
Interest rate × +/−1% parallel shift × +/−10% formulas:
4
Mortality Mortality
For interest rate move,
VR+ / V0 - 1 - ( ∂V
) ∆R The change of the steepness of the slope tells us that the cross
( )
∂2V ∂R +
= ×2 effect is not even across the spectrums, because it would be, oth‑
∂R2 + (∆R 2) erwise, a flat surface tilted at an angle.
the benefits:
Step 3: Estimate the Impact Using Taylor Series • The pricing surface helps monitor the profitability of sales
that may derivate from initial pricing target. Ideally, once
When the derivatives are calculated, we estimate the final move‑
priced, the profitability of a product does not change. In real‑
ment in the target value that is driven by pricing variables using
ity, this may not always be the case; the market environment
the following formula. As an example, if we want to estimate the
changes over time. Assumptions change as the experience
final value with a rate increase of ∆r and a mortality increase of
emerges. A company’s pricing team or in-force management
∆m, we will have
team cannot afford to keep up with the changes and conduct
repricing exercise as frequently as they want to, or to monitor
∆V
++
= ( ∂V
∂R )+
× ∆r + (
∂M )+
∂V
× ∆m the actual profitability of the new sales bring to the table due
to real-time changes at point of sale from original pricing.
+
1
2 [( ∂∂RV )(∆r) + ( ∂M
2
2 )
∂ V (∆m) + 2
2
×(
2
∂R∂M )
∂V
2 × ∆r × ∆m ]
2
2
++
With pricing surface, one can either confirm the pricing
results for recent sales, or quantify the gap between the actual
and pricing results, and pinpoint the drivers. This helps the
Other combinations of moves will be estimated in similar company make the right decision with respect to encouraging
fashion. sales when the environment is favorable or put a limit of sale
when otherwise. For example, using the preceding chart and
We then apply the Taylor expansion formula to construct a pric‑
taking SPIA, when experiencing persistent low interest rate
ing surface so that we can estimate the pricing results for any
(e.g., 0.5 percent lower than pricing) and seeing mortality
combination of mortality and interest rate changes.
improves overtime (e.g., mortality is reduced by 5 percent),
To illustrate, the pricing surface in Figure 1 was plotted to show the pricing surface would tell us that the profitability would
the joint distribution of profitability (as percentage of baseline be reduced by 55 percent. If the company feels they are
or best estimate) by interest rate and mortality changes (relative missing pricing target by a margin, they may choose to slow
to best estimate assumptions). down or stop the sales or conduct repricing if the market
demand persists. On the other hand, if the interest rate and
Here we not only see the relationship between profitability and mortality movement are exactly opposite, the pricing surface
each individual pricing variables while holding the other vari‑ shows the profitability would increase by 71 percent. This
able constant, but also see the cross effect of the two variables. better-than-expected profitability could make the company
Ending Pricing Result Movement (by %)
400%
M +20% 300%
Mortality Movement
M +10% 200%
M +0% 100%
M −10%
0%
M −20% R +0.5% R +1%
R +0% −100%
R −0.5%
R −1%
−200%
Interest Rate Movement
−200%–100% −100%–0% 0%–100% 100%–200% 200%–300% 300%–400%
create additional incentive to encourage sales or consider with fields or senior management by bringing everything
reducing the premiums (one could build the surface with to the table. If a certain sales goal is met by the sales force,
premium as a variable) to boost sales. Nevertheless, when it marginal expense assumption can be achieved, the product
comes to repricing, if there is no change in product design, can be cheaper, on the other hand, if sales are lagging, the
the surface should contain all the results already, no repricing product has to be expensive to meet the profitability target.
exercise is necessary. This tool could also help the company to communicate with
regulators or rating agencies if used properly.
• Finally, the pricing surface can facilitate communications
both within and outside a company. If a number of policies CONCLUSION
sold is selected as a pricing variable and pricing surface is con‑ While current best estimate pricing results provides information
structed accordingly, it will capture the relationship between for decision making, a pricing surface offers a comprehensive
the pricing results and number of policies sold. As a result, view of the pricing results throughout the spectrum of each
there is no need to argue between using marginal expense driver that might alter the pricing results. Although construct‑
pricing or using fully allocate expense assumptions, because it ing the joint distribution is a challenge, there are simplified
is baked in pricing and the surface will show how the pricing approaches to make it happen. Furthermore, it is worth the
results vary as number of policies sold change. If only one effort to obtain the pricing surface. It helps make an informed
policy is sold, the surface will tell us the product is expensive decision and facilitate the pricing conversation within and out‑
or the profitability is low because all the overhead expense side a company. n
has to be allocated to one policy. At the other extreme, if
huge amount of policies are sold (up to certain extent or
high end of economy of scale under current service capacity),
the surface will say that the profitability is close to the one Feng Sun, FSA, CERA, MAAA, is AVP & actuary at
when marginal expense assumption is used under traditional MassMutual Financial Group. He can be reached at
fsun@massmutual.com.
pricing. The actuals profitability is probably somewhere in
between. This surface would facilitate the communication
Secondary Guarantees
some of which is explained by product design differences.
T
for these important product lines.
hrough its Policyholder Behavior in the Tail workgroup,
the Society of Actuaries has published a new report1 Anyone interested in more information or learning about how
summarizing the results of its most recent assumption to participate in future surveys should contact Barbara Scott at
survey for Universal Life Insurance with Secondary Guaran‑ bscott@soa.org. n
tees. Highlights are as follows: