session 83 pd, modeling managing and pricing living...

Session 83 PD, Modeling Managing and Pricing Living Benefits Risk

Moderator: Sean Michael Hayward, FSA, MAAA

Presenters:

Guillaume Briere-Giroux, FSA, MAAA Sean Michael Hayward, FSA, MAAA

Eric L. Henderson, FSA, CERA, CFA, FRM, MAAA

© 2014 Oliver Wyman

Guillaume Briere-Giroux, FSA, MAAA, CFA

Modeling, Managing and Pricing Living Benefit RisksOverview of Industry Approaches

2014 Life and Annuity Symposium

Atlanta – May 20, 2014

© 2014 Oliver Wyman 11© 2014 Oliver Wyman

Overview of industry approaches

I. What living benefits?

II. What risks?

III. What scenarios and what value lenses?

IV. Industry modeling practices

After this overview, co-speakers will expand on select modeling, pricing and risk management issues with a case study focused on a fixed indexed annuity (“FIA”) with guaranteed living withdrawal benefit (“GLWB”)


What living benefits?

Sales data from LIMRA

Low

erH

ighe

rM

arke

t Ris

k

Mostly elective

Both elective and non-elective

Non-elective

Insurance risk type

Elective

Size of bubbles represents order of scale for recent new business volumes (LTC converted to single premium equivalent)

Lower HigherInsurance Risk


What insurance risks?

High

Low

Product Longevity Base lapse Dynamic lapse Withdrawals or annuitization Morbidity

VA GMAB

VA GLWB

VA GMIB

FIA GLWB*

SPIA

DIA

LTC

*With nursing home benefit

Risk level


What market risks?

Product Credit Interest rates Equity VolatilityFund

correlation / basis risk

VA GMAB

VA GLWB

VA GMIB

FIA GLWB*

SPIA

DIA

LTC

*With nursing home benefit

High

Low

Risk level


What scenarios and what value lenses?

Real World Risk NeutralValue lenses

Sim

ple

Com

plex

Dynamic policyholder behavior

Static behavior scenarios

None

Behavior “scenarios”

Size of bubbles represents order of scale for recent new business volumes (LTC converted to single premium equivalent)

Sales data from LIMRA

Det

erm

inis

tic +

se

nsiti

vitie

sS

toch

astic

Nes

ted

stoc

hast

icD

eter

min

istic

Integrated dynamic behavior scenarios

Econ

omic

sce

nario

s


Industry modeling practices

ProductStochastic

equity returns (RW)

Stochastic interest rates

(RW)

RN cost of guarantees

Behavioral cohorts

Dynamic behavior

VA GMAB ? VA GLWB VA GMIB ? FIA GLWB* SPIA ?DIA ?LTC ? ?


Key points

1 Market risks impact pricing approaches

2 Accounting and risk management practices drive “scenario layers”

3 Behavior risk drives modeling granularity and complexity

4 Assumption modeling is becoming increasingly sophisticated

Modeling, Managing and Pricing Living Benefit Risks

Modeling Considerations

Indexed Annuity GLWB Case Study

• Growing popularity of design

• Significant policyholder optionality

• Stochastic modeling is common

• Asset and liability modeling

• Interaction between assets and liabilities

9

FIA GLWBs were selected to discuss modeling considerations for living benefits

• 10 year surrender charge design

• Annual point-to-point cap crediting

• 6% compound rollup on benefit base

• Representative income rates

• No nursing home “doubler”

10

A representative FIA GLWB model was built to support the pricing and risk discussion

Next, we cover modeling considerations and use the case study to exemplify a sample of modeling practices

• Model as fixed annuity- Statutory reserves as a % of fund value

• Simple option budget approach- Assume perfect static hedge

• New product features & more computing power allowed more robust modeling

- Examples in case study

11

FIA modeling has come a long way…

1. Renewal rate setting

2. GLWB modeling

3. Dynamic policyholder behavior

4. Profit bases and metrics

5. Hedging

12

But… complex modeling issues remain

• Management has discretion in setting renewal credited rates and caps

• Typically captured using option budget approach- Assumes no unexpected gains/losses

Defaults Hedge mismatches

• Requires a portfolio earned rate to set option budget- How do we model this in liability only nested projections?

• As modelling capabilities improve, do we need to adjust management action algorithms to reflect factors other than the asset yield?

13

1. Renewal Rate Setting

• Option budget = net asset yield - spread

• Solve for cap using closed-form solution

• Consider volatility strike skew

14

1. Renewal Rate Setting – Case Study Approach

• GLWB elections impact the illustration of policyholder balances- “Haircut” does not work, need to model cohorts of election

• Elections are just that… elective! Do we need to model them dynamically?

- Implications on model memory usage and distributed processing

• Statutory reserve impacts- Model every possible election point in CARVM?

• GAAP reserve impacts- SOP 03-1, but any FAS 133 considerations?

15

2. GLWB Modeling

16

2. GLWB Modeling – Simplified Cohort Approach

• Dynamic lapses need a credited rate and competitor rate- Difficult to compare caps across crediting strategies

• Option budget serves as a proxy

• Inclusion of riders changes dynamics- In-the-moneyness will impact lapses- Does inclusion of guarantees or different fee structures impact the

competitor comparison?

• Do we have credible experience as product designs keep changing?

17

3. Dynamic Policyholder Behavior

• Interest-sensitive lapses on base contract- Option budget serves as a proxy

• In-the-moneyness of riders dampens lapses- “S curve like” schedule of lapse multipliers

• Therefore, product reacts to both index credits and the interest rate environment

- Magnifies impact of hedge or ALM mismatches

18

3. Dynamic Policyholder Behavior – Case Study Approach

• Pricing exercises often focus on statutory based metrics- IRR, profit margin- Accurate CARVM reserves

• Integrated GAAP projections “nice to have”- GLWB riders require SOP 03-1 liabilities in addition to FAS

133 reserve

• Embedded value- Important for European based companies- Supplement to statutory based metric or replacement?

19

4. Profit Bases and Metrics

• Several layers of complexity

• Base product credit hedging- Static call spreads- Dynamic hedging

• GLWB rider hedging- Futures - Delta- Call options - Gamma/Vega- Net exposure against credit hedge?

20

5. Hedging

Valuationdate

Month 3 Month 5Month 4Month 2Month 1

∆Γνρ ∆Γνρ ∆Γνρ ∆Γνρ ∆Γνρ ∆Γνρ

5. Hedging – Case Study Approach

• Dynamic hedging for GLWB• Additional inner loop computations for Greeks

22

Case Study – Reasonableness checks using simple deterministic scenarios

Case Study Pricing IRRs - Sample Deterministic Scenarios

Scenarios

Base only, hedge credits

GLWB included, hedge credits

GLWB included, hedge credits and GLWB

Slow increase in yields, 2.5% index credit 12.7% 13.6% 13.8%Slow increase in yields, 3.5% index credit 13.6% 17.1% 13.4%Slow increase in yields, 1.5% index credit 11.7% 9.9% 13.6%Low rates/low index returns 9.7% 6.7% 11.9%

• More exposure to low rates and low equity returns when GLWB is present, magnified by dynamic behavior

• More stable results with GLWB dynamic hedge

Modeling, Managing and Pricing Living Benefit Risks

Pricing and Risk Considerations

Indexed annuity GLWB case study

• Setting the stage• Case study results and discussion• Product management considerations• Concluding remarks

Agenda

24

• Interest rate risk is material for FIA income riders- This risk does not materially impact average pricing result

• Equity risk is smaller and muted by the 0% floor- Equity risk premium can have a large impact on profit metrics

• Start with case study to make the point

25

Setting the stage… Large risks vs. large risk premiums

• Reduction in range of profit margin (“PM”) outcomes per goal of hedge program

• Risk/reward tradeoff of hedge less compelling

• Remaining interest rate risk material

26

Impact of Living Benefit Hedge

‐2.00%

‐1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

1 101 201 301 401 501 601 701 801 901 1001

Profit Margin

Interest Credit Hedge Economic Hedge

Interest Credit Hedge PM

Economic Hedge PM

Mean 2.97% 1.65%

Std Dev 1.14% 0.76%

1. Equity risk premium lead call options to produce excess returns

2. This can improve pricing results if the hedge notional is greater than the economic hedge

What explains this result?

27

1 9 17 25 33 41 49 57 65 73 81 89 97 105

113

121

129

137

145

153

161

169

177

185

193

201

Scenario

Option Payoff OC

• As shown below, economic hedge ratios* vary across product types

• Base FIA product: Time value of money and surrender charges

• Presence of guarantees: Certain benefit streams are insensitive to index credits (e.g., high rollup GLWB)

Product Type FIA no rider FIA w/fixed roll-up income rider

FIA with indexed roll-up income rider

Economic Hedge Ratio* at issue ~80% ~55% ~70%

*Economic hedge ratio defined here as % of account value hedged that results in stable level of accumulated surplus at end of projection 28

What is the economic hedge?

• Impact on profit margin dependent on:

- Expected option return- Option budget- Liability duration

• If not passed through the product design, the over-hedge can be considered a capital-efficient surplus investment

Equivalent Yield and PM Contribution from the Equity Risk Premium

% “Over‐hedge” (% of AV) 40%

Option ROI 30%

Current yield 5.0%

Option cost (% of AV) 2.0%

Over‐hedge pre‐tax yield contribution (% of AV) 0.20%

Liability duration 8.0

Over‐hedge profit margin contribution 1.04%

29

Understanding the pricing impact without “hitting the grid”

Product management consideration #1: Static or dynamic hedging strategy?• Building on the prior example, we show that the pricing impact of hedging the GLWB can depend on the choice of the hedging strategy

• Dynamic Delta hedging replication strategy gets “paid” less than selling the option, leading to a higher cost of hedging the GLWB

• Careful to not distort benefits from dynamic hedging in pricing. The result is highly dependent on economic inputs.

30

Estimating cost of hedging GLWB Static Hedge Delta Hedge

Reduction in notional (% AV) to hedge guarantee 40%

Option cost saved (or replication cost received) 2% 1.8%

Option payoff foregone 2.6% 2.6%

Option ROI 30% 45%

Current yield 5%

Pre‐tax yield contribution foregone (% of AV) 0.20% 0.29%

Liability duration 8.0

“Cost” of hedging (lost profitmargin) 1.04% 1.48%

• Consider a product with rollup rate = index credit + 3% (as opposed to guaranteed 6%)• Traditional pricing approaches disadvantage this design:

- When already hedging the account value, the modeled cost of adding the feature is the expected value of benefits (high cost since long the risk premium)

- When already hedging the GLWB, the modeled cost of adding the feature is the cost of hedging the benefit (i.e., less than the expected benefit)

• Even with AG 33 reserving and risk benefits, the resulting design and customer value proposition is uneven (see chart)

7,000

8,000

9,000

10,000

11,000

12,000

13,000

GuaranteedIncome Rider

Participating IR(PV of Non‐guaranteedincome)

Participating IR(Cost offunding)

Mon

thly In

come

Guaranteed High Expected

31

Product management consideration #2: Typical hedging / pricing practices explain the pull toward strong guarantees

• Higher equity option ROI increases real world pricing metrics

• Increase is greater when guaranteed elements are greater

• Calibrating ERP without monitoring the option ROI can result in different option budgets by hedge strategy and other inconsistencies

- On approach is an option ROI calibration for pricing that reflects the “opportunity value” of making this investment, not its expected return

32

IRR 10% ROI 30% ROI ∆ IRR

Sample base policy 16.48% 17.23% 0.75%

Sample GLWB 15.07% 17.14% 2.07%

Product management consideration #3: Calibrating the equity option ROI

• Desire to maintain aggregate pricing targets• Individual products equally share company over-hedge gains by adjusting product specific pricing targets

- Guaranteed benefit products (with associated high over-hedge) receive a smaller share of index option gains

- Base product and participating rider benefit design receive more

FIAPortfolio

Base Product

Fixed Income Rider

Over‐hedge (% of AV) 40% 23% 46%

Option ROI 30% 30% 30%

Option cost (% of AV) 2% 2% 2%

Current Yield 5% 5% 5%

Over‐hedge pre‐tax yield contribution (% of AV) 0.24% 0.14% 0.28%

Duration 8.0 6.8 8.2

Over‐hedge contribution to PM 1.2% 0.6% 1.5%

PM adjustment from current +0.6% ‐0.3%

33

Product management consideration #4: Adjusting pricing return targets

• Risk management impact on pricing differs by risk

• Complement complex modeling with top-down analysis

• Be a thoughtful advisor when pricing and managing through these issues

34

Concluding Remarks

session 83 pd, modeling managing and pricing living...

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