Variable annuities: confronting points of view of insurers ... · Presentation of AXA Global Life /...

Types of guarantees offered in Variable Annuities Risk analysis and Solvency II pitfalls Confronting points of view of insurance and finance

Variable annuities: confronting points of view of insurersand bankers, with an emphasis on surrender risk

Stéphane Loisel

ISFA, Université Lyon 1

Spring School, Jena

Stéphane Loisel (ISFA, Lyon) Variable annuities March 2011 1 / 32


Table of Contents

1 Types of guarantees offered in Variable Annuities

2 Risk analysis and Solvency II pitfalls

3 Confronting points of view of insurance and finance

Stéphane Loisel (ISFA, Lyon) Variable annuities Dec. 2nd, 2010 2 / 25


Types of contracts

1 Types of guarantees offered in Variable AnnuitiesTypes of contractsGuarantees and surrender risk





Types of contracts

The ancester of VA’s in France

Garanties plancher in unit-linked life insurance contractsCorresponds to a GMDB product.Sum of payments is guaranteed for the beneficiary if policyholder dies.Used to be a compulsory guarantee in France.Usually priced by insurers thanks to la formule des puts pondérés.



Types of contracts

More sophisticated guarantees

Return of Premium: higher of total premium or account value,adjusted for withdrawalsRoll-up: premiums paid accumulated at guaranteed rate, adjusted forwithdrawalsRatchet: highest account value at contract anniversary dates, adjustedfor withdrawalsGreater of Ratchet or Roll-up: greater of annual ratchet or roll-upamount paid to successors if policyholder dies.



Types of contracts

Roll-up and Ratchet Guarantees


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Types of contracts

Guarantees can be combined


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Guarantees and surrender risk

1 Types of guarantees offered in Variable AnnuitiesTypes of contractsGuarantees and surrender risk






GMIB vs GMWB types

GMIB guarantees a minimum annual income as long as thepolicyholder is alive. After the end of deferral period, the AccountValue is converted in as a reserve on the general account of theinsurance company. This reserve is used to pay incomes. After deferralperiod, policyholder cannot exit the contract and does not ownUnit-Linked.GMWB guarantees a minimum annual withdrawal for a given period orfor life. After the end of deferral period, the policyholder still owns herAccount Value. After deferral period, policyholder can exit thecontract and recover his Account Value minus received withdrawals.




GMWB


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GMWB


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DECP - 1

More and more sophisticated products in the US

• GMDB • Fees can be

paid regularly

• 0 Penalty

• Introduction of GMIB’s

• Reduction of margins

• Sophistication of products

• Introduction of ratchet guarantees for GMDB’s

Garantees

• GMAB

• GMWB

• GMLB

Sometimes no surrender penalty

Embedded disability insurance in some VA’s

1980s 90-95 95-00 Post 2000

Start in Europe

Potential market (predicted in 2008!)

1. Source: AEGON (Analyst conference 2/3 June 2008)

Estimated market size in Europe

(AEGON – Estimated assets; €Mds)1

DECP - 3

Launched i2Live

in May 2007

First mover in UK

‘Gold’ and ‘Platinum’

Was market leader

Now withdrawn

European VA’s market

Launched in

Germany and

Luxemburg in

2008

Switzerland for

several years and

launched in 2008

in Italy

Launched ‘Champion’

in Germany in Oct

2008

European roll-out of

‘Accelerator’ plans in

Germany (‘Twinstar’),

Belgium, France, Spain,

Italy, UK Offshore (Isle

of Man), Portugal,

Switzerland

Invest4Life launched

July 2008 in Germany,

France in October 2008.

Italy in February 2008

Multiple UK launches

in Dec 2006, May 2007,

Jun 2008 & Jan 2009;

Poland in 2008

Greece Feb 09

‘5-for-life’ (GLWB)

ASLI (GLWB)

Pensions Income for Life + GMAB

Launched GMWB ‘RentaSafe’

in Switzerland in Oct-2008

Launched in Germany in

March 2009

GMAB products launched in

Spain in 2007, Hungary in

2007 and Poland in 2008

VAs in Europe

http://www.ergo.com/

http://images.google.co.uk/imgres?imgurl=http://upload.wikimedia.org/wikipedia/en/thumb/4/49/Munich_re_logo.svg/415px-Munich_re_logo.svg.png&imgrefurl=http://en.wikipedia.org/wiki/Image:Munich_re_logo.svg&h=130&w=415&sz=11&hl=en&start=1&um=1&tbnid=_UiCruNrzC9RoM:&tbnh=39&tbnw=125&prev=/images%3Fq%3Dmunich%2Bre%2Blogo%26um%3D1%26hl%3Den%26sa%3DN

http://www.allianz.com/

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DECP - 4

Emergence of the Irish platform

2006

Q1 Q2 Q3 Q4

2007

Q1 Q2 Q3 Q4

Twinstar – Germany

5 for LifePlatinum i2Live

UK

Eu

ro

pe C

on

tin

en

tale

Accumulator – Italy

Accumulator –Spain

Riley bond

Capital Resources –

France

Generation F– Spain

Secure Retirement

Twinstar – Belgium

in Ireland

Estate planning bond

SafetyNet

2008

Q1 Q2

Global TopReturn – Germany

Active Rispamio – Italy

Q4Q3

Q4 – Germany

Q4 – France

Q4 – UK

Q4 – UKQ1 – UK

– Spain

– France

Accumulator -Retraite –

France

Investment Control

Income for Life

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http://www.allianz.com/en/index.html

http://www.swisslife.com/slcom/en/home.html

http://www.swisslife.com/slcom/en/home.html

http://www.aig.com/gateway/home/1-67-0-0-index.htm

The effect of the crisis

Some players withdraw some products (like AXA in Germany)

Some others stop their VA business (Hartford in Europe)

Regulators (Ireland, France, Germany,…)

2010: the VA market restarts as if nothing happened?DECP - 5

45 50

70

8899

121128

107 112 114

128 131

155

177

125

152

500560

700

1,400

1,300

750

900

1,200 1,200

1,100

1,2001,250

1,3501,450

900

900

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

E

VA

ne

w b

us

ine

ss

($

bn

)

S&

P 5

00


Some key risks associated to VA’s


2 Risk analysis and Solvency II pitfallsSome key risks associated to VA’sRisk aggregation in Solvency II internal formula




Some key risks associated to VA’s

VA’s key risks

Volatility, interest rates, Gamma, exchange ratesBasis riskArbitrage (investment choices made by policyholders)Policyholders’ behavior risk (surrender, arbitrage)LiquidityCounterparty, Key-Person, operationalTransaction costs, cost of capital...



Risk aggregation in Solvency II internal formula


2 Risk analysis and Solvency II pitfallsSome key risks associated to VA’sRisk aggregation in Solvency II internal formula



Solvency Capital Requirement (SCR)

SCR

Standard formula:

Lognormal loss distribution assumption

1-Year Time Horizon

Modular Structure of SCR

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Risk aggregation

The are correlation parameters given by QIS4 matrices.

Advantage of the above formula:

it takes diversification effect into account: the global SCR is always

smaller than the sum of the SCR per LoB

Some obvious drawbacks:

-multi-level risk aggregation problems

-Gap with internal models

Incentive to develop internal risk models.

Multi-level risk aggregation: exercise

1) Compute the risk capitals for A+B, for C+D and for A+B+C+D.

2) Derive the implicit correlation coefficient between (A+B) and (C+D).

Multi-level risk aggregation: solution

1) Compute the risk capitals for A+B, for C+D and for A+B+C+D.

2) Derive the implicit correlation coefficient between (A+B) and (C+D).

Multi-level risk aggregation: exercise

1) Recompute the risk capitals for A+B, for C+D and for A+B+C+D.

2) Derive the new implicit correlation coefficient between (A+B) and (C+D).

Multi-level risk aggregation: solution

1) Recompute the risk capitals for A+B, for C+D and for A+B+C+D.

2) Derive the new implicit correlation coefficient between (A+B) and (C+D).

Multi-level risk aggregation: conclusion*

*Suggested post-reading: Multi-level risk aggregation by D. Filipovic, ASTIN Bulletin (2009).


Surrender risk

Surrender riskWhat’s new?Best estimates assumptions instead of prudential assumptions definedtoday by the Code des Assurances (in France);What does it change?Today, estimated surrender rate is 100% in technical reserves: theinsurer is forced to reserve at least the mathematical reserve of thecontract. (the policyholder can surrender her contract whenever shewants)In Solvency II, the reserves may be adapted to the observed surrenderrate. The insurer is allowed to reserve only what corresponds to theobserved / modeled surrender probability.Thus, surrender assumptionsNowadays : impacts ALM predictions and EEV;In the future : will entirely take part in Accounting of the company!



Surrender risk

SCR requirements

SCR stress tests: QIS 5 report suggests closed formulas to modelsurrenders (depending on guarantees, credited rates, indexperformance)but this has to be calibrated with the portfolio;Lapse risk is part of the underwriting risk module (50% correlated withthe SCR linked to management fees drift...);In the last technical pre-specifications, the insurer should compute theimpact on the SCR of

I a constant drop by 50% of the lapse rate (limited to an absolute dropof 20%),

I a constant rise by 50% of the lapse rate (limited to 100%),I massive surrenders of 30% of the population-at-risk (absolute increase).

The biggest SCR is then inserted into the correlation matrix.



Surrender risk

4 main approaches to model surrender rates

Financial approach: pricing the surrender option, no behavioral model.Policyholders are assumed to behave like optimal investors. Hugeamount of papers.Statistical approach: collective. Empirical data enables one tocalibrate the following surrender function;Economical approach: individual. Microeconomy, expected utilitytheory.Probabilistic / econometric approach: individual. Segmentationmodels, to define risk classes on a given population in the classicalmodel (GLM, CART and others, see Milhaud, L. andMaume-Deschamps (2010)).



Pricing methodologies



3 Confronting points of view of insurance and financePricing methodologiesOptimal behavior vs lapse ratesSurrender risk


Confronting points of view of insurance and finance


Actuarial vs financial

In general,Actuaries tend to price insurance contracts as (Best Estimate ofLiabilities + Risk Margin).The Risk Margin is theoretically supposed to be computed thanks to acost of capital approach.The Risk Margin should be different from one company to the other(depends of the overall risk profile and objectives in principle).In finance, one often uses risk-neutral pricing, indifference pricing, ...Concepts are similar: a risk premium is present in both cases.But insurers too often forget that risk neutral pricing required that therisk is hedged!


Confronting points of view of insurance and finance


Actuarial and financial pricing may be mixed

Basic example: Guaranteed Minimum Death BenefitInsurers typically use the so-called Weighted Put Formula.Correlation between pandemic risk and market risk is ignored.Pricing method is subject to caution (risks cannot be duplicated).



Optimal behavior vs lapse rates


Optimal behavior (financial approach): Quanto-Asian options (seeMilevsky’s paper: Why your grandmother purchases Quanto-Asianoptions)Complex problems, in particular some of them are related to exercisefrontier computations of American optionsin real-world, policyholders do not behave like that. But what ifconsultants start to train policyholders in the future?The most important question: are investment decisions made by thepolicyholders, or are they strongly suggested by contract vendors?



Surrender risk

References on general VA pricing and hedging framework

Bauer, Kling and Russ [2008]: A universal pricing framework.Mortality risk: Schrager[05], Plat[09]; Moller[98,01], Milevsky andPosner[01], Biffis et al. [01, 05, 09].Stochastic volatility: Ballota and Haberman[03], Chu and Kwok[07],Haastrecht, Plat and Pelsser[09].Stochastic interest rate: Bacinello and Ortu[94], Nielsen andSandmann[95], Miltersen and Persson[99], Coleman, Li andPatron[04].



Surrender risk

References on risk management of VA’s

Milevsky and Salisbury [06]: financial valuation of GMWB’s.Taksar and Hunderup [07]: optimal proportional reinsurance strategies.Dai, Kwok and Zong [08]: optimal withdrawal strategies in GMWB’sForsysth et al. [02,05,07]: Numerical methods.Kling, Ruez and Russ [10]: the impact of stochastic volatility onpricing, hedging and hedge efficiency of variable annuity guarantees.For detailed mathematical framework, please see T.-L. Nguyen’s slides(Cours Bachelier 2011).




Who makes the decision?

Kanheman-Tversky paradoxDifferent views: arbitrage and surrender vs surrenderAn example of fallacious conclusion


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Surrender risk



3 Confronting points of view of insurance and financePricing methodologiesOptimal behavior vs lapse ratesSurrender risk



Surrender risk

How can independent risks become suddenly stronglycorrelated?

Endogenous uncertainty:Uncertainty is generated/modified by response of individual entities toeventsFeedback loop: outcomes → forecasts → decisions → outcomes →revised forecasts → revised decisions → . . . (Millennium Bridge)Statistical relationships are endogenous to the model, and mayundergo structural shifts (Goodhart’s Law: Any observed statisticalregularity will tend to collapse once pressure is placed upon it forcontrol purposes)Relevant when individual entities are similar in terms of forecasts andlikely reactions to eventsRelevant when outcomes are sensitive to concerted actions



Surrender risk




Surrender risk

Analogy with LTCM

This analogy is drawn from Danielsson and Shin (2003).Potential massive surrenders (Loisel and Milhaud (2010), Arnal et al.(2010)) in life insurance, link with Paul Embrechts’s ICA 2010 talk.


Presentation of AXA Global Life / 2010 – V1.0 (2010, june the 29th)The data used in this presentation are the property of AXA Global Life and cannot be reused without the prior written consent of AXA Global Life.

Distribution change

36 Lyon - 22/07/2010

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Presentation of AXA Global Life / 2010 – V1.0 (2010, june the 29th)The data used in this presentation are the property of AXA Global Life and cannot be reused without the prior written consent of AXA Global Life.

Illustration

41 Lyon - 22/07/2010

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