Option-Like Nature of Variable Annuities

Andrew D. Rallis

Senior Vice President &

Global Chief Actuary

Presented at CBOE RMC Europe 2013

October 1, 2013

2

VA Riders

GMxB = Guaranteed Minimum Benefit

GMIB I = Income

GMWB W = Withdrawal

GMDB D = Death

GMAB A = Accumulation

3

GMxBs - Key Features

Benefit Guarantee

GMDB Death Benefit

Return of Premium

Annual Step-up (a.k.a. Ratchet)

5%-6% Roll-up (a.k.a. compounding)

GMWB Withdrawal

Benefit

105% of Deposit

7% Maximum Withdrawal Rate

GMAB Accumulation

Benefit Return of Premium

GMIB Income Benefit

Maximum of

(a) Annual Step-up, or

(b) 5% - 6% Roll-up

@ Contractual GMIB Payout Rates

4

Hypothetical Account Value TIME

Highest Anniversary

Income Base

Accumulation 10-Year Waiting

Period Pay-Out

Client

provided

whichever

produces

greatest

income

Guaranteed Minimum Income Benefit – What is it?

- An optional feature designed to provide a predictable level of future

retirement income regardless of investment performance

5

Which GMxB is Which?

GMIB Greeks

(Excludes Travelers Business)

(Based on 7/31/05 Inforce and 8/1/05 Capital Market Data)

Option value of the net

liability (option value of

claims less option value

of fees).

Sensitivity of the liability

option value to a

sumultaneous shock

in all equity indices.

Sensitivity of the liability

option value to a parallel

shift in the yield curve.

Sensitivity of the Delta to a

simultaneous shock in all

equity indices.

GMIB Option value = OV Claims - OV Fees

-400

-350

-300

-250

-200

-150

-100

-50

0

-25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

Shock, %

$mil

lio

n

G M IB Delta = Delta F ees -D elta Cla im s

4 .0

5 .0

6 .0

7 .0

8 .0

-25% -20% -15% -1 0% -5% 0% 5% 10 % 15% 20% 2 5%Shock, %

$m

illi

on

G M IB R h o

0 .0 0

0 .5 0

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

- 1 0 0 - 8 0 -6 0 - 4 0 - 2 0 0 2 0 40 6 0 8 0 1 0 0

S h o ck , %

$M

illi

on

s

G M IB G amma

-8 0,00 0

-6 0,00 0

-4 0,00 0

-2 0,00 0

0

2 0,00 0

4 0,00 0

-25 % -2 0% -15% -10 % -5% 0% 5% 10% 15 % 2 0% 25 %

Sh ock , %

$D

oll

ars

GMWB Greeks

(Excludes Travelers Business)

(Based on 7/31/05 Inforce and 8/1/05 Capital Market Data)

Option value of the net

liability (option value of

claims less option value

of fees).

Sensitivity of the liability

option value to a

sumultaneous shock

in all equity indices.

Sensitivity of the liability

option value to a parallel

shift in the yield curve.

Sensitivity of the Delta to a

simultaneous shock in all

equity indices.

GMWB Option value = OV Claims - OV Fees

-10

-8

-6

-4

-2

0

-25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%Shock, %

$mil

lio

n

G M W B Delta = D elta F ee s -Delta Claim s

0.0 0

0.1 0

0.2 0

0.3 0

-25 % -2 0% -1 5% -10 % -5% 0% 5 % 1 0% 1 5% 20 % 25 %Sho ck, %

$m

illi

on

G M W B R h o

0

1 0 ,0 0 0

2 0 ,0 0 0

3 0 ,0 0 0

4 0 ,0 0 0

5 0 ,0 0 0

6 0 ,0 0 0

- 1 0 0 - 8 0 -6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0

S h o ck , %

$D

oll

ar

s

G M W B G am ma

-7,00 0

-6,00 0

-5,00 0

-4,00 0

-3,00 0

-2,00 0

-1,00 0

0

1,00 0

-2 5% -20 % -15 % -1 0% -5% 0 % 5% 10 % 1 5% 2 0% 25 %

Sho ck , %

$D

oll

ar

s

Option

Value

Delta

Rho

Gamma

6

GMIB versus European Put

GMIB

risk free rate

volatility

income base/AV adjusted

by Guaranteed/Current rates

waiting period

Basket transfers

Total return

European Put

risk free rate

volatility

in-the-moneyness

Tenor

Price return

7

Why Accounting Matters

Economic vs GAAP vs Stat

Economic gain or loss

GAAP income volatility

Statutory solvency

Small product variations can drive big changes in

strategy

8 8

GMDB GMIB GMWB/GMAB

Accounting Guidance SOP 03-1 FAS 133 / FAS 133

SOP 03-1

Balance Sheet Additional Embedded/ Embedded

Liability Add. Liability Derivative

Accounting Correlation Low Moderate High

Hedging Instruments Reinsurance/ Derivatives/ Derivatives

Derivatives Reinsurance

US GAAP Accounting Influence on Risk Management

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Challenges to Hedging Programs

VA writers would normally use the following risk mitigation

techniques:

9

Strategy Market Risk Exposure

Dynamic Hedging Realized volatility of equities and

interest rates

Underhedging, e.g. due to

SOP 3-01

Direction and realized volatility of

equities, level and volatility of interest

rates - tail risk

Static Hedging with vanilla

Puts

High cost, basis risk, cross-effects

Managed volatility funds were designed as a response to address

these issues

10

Lapse Assumption Lowered to Fully Reflect

Post-Crisis Experience

0%

5%

10%

15%

20%

25%

30%

35%

40%

-80% -60% -40% -20% 0% 20% 40% 60% 80% 100% 120%

“In the Moneyness”

Prior Curve

Current Curve

Lapses

Lapse Function Relative to “In the Moneyness (ITM)”

10 Note: In-the-Moneyness = Adjusted GMIB Benefit Base ÷ Account Value - 1. Adjusted GMIB Benefit Base = GMIB Benefit Base x Guaranteed Payout % ÷ Current Payout %.

11

Cross Greeks

Delta vs. parallel shift in Int Rates

Delta: sensitivity to 1% shift in all equity indices simultaneously

2

4

6

8

10

12

14

-150 -100 -50 0 50 100 150

Yield Curve Shifts

Total GMIB Delta

Euro Put

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Why Volatility Matters

Vega = Sensitivity of Economic Value to equity volatility

movements

SOP liabilities not as sensitive to these movements

– SOP 03-1 Paragraph 31

– implied vol versus historic vol

Balance hedging of Economic Value to GAAP income

volatility

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Tradeable Indices

S & P 500 (SPX)

NASDAQ 100 (NDX)

Russell 2000

Morgan Stanley EAFE

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Constructing an Implied Volatility Surface

Step 1 : SPX

– Incorporate market traded long dated vol

– SPX 15yr implied vol level higher than 10yr implied vol

– Apply historical vol starting at 20yr point

– Grade down forward vol to historical vol between 15yr and 20yr

Step 2 : Other Indices

– Generate other curves based on dealer indications to 10yr

– Apply SPX vol slope between 10yr and 15yr points

Step 3 : Apply Skew Adjustments

– e.g. 3% of ATM spot implied vol per 10% in/out moneyness

– Adjust overall vol surface or make policy level adjustments

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Key Rate Vega

1

4

7

10

13

16

19 0.70

1.00

1.300.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

Vega,

% Total

Maturity Bucket, years

ITM

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DEALER L 2%

DEALER K 2%

DEALER J 16%

DEALER I 5%

DEALER H 13%

DEALER G 11%

DEALER F 13%

DEALER E 24%

DEALER D 2%

DEALER C 0%

DEALER B 2%

DEALER A 10%

Distribution of Vega by Dealer Counterparty

VA Hedging Program – Distribution by Dealer

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