rising interest rates, lapse risk, and the stability of ... · rising interest rates 15 1510 105 0...

Motivation Results References

Rising interest rates, lapse risk,and the stability of life insurers

Elia Berdin, Helmut Grundl, Christian Kubitza

International Center for Insurance Regulation (ICIR)

Goethe-University Frankfurt

Assicurazioni Generali S.p.A.

Frankfurt, May 24, 2018

13th Talk on Insurance and Regulation

Berdin, Grundl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 0/13


Disclaimer

The findings, views and interpretations expressed herein are those of the authors and shouldnot be attributed to Assicurazioni Generali S.p.A.



Motivation

Since 2009, esp. German life insurers struggle with low interest rates:Large annual guaranteed rates vs. small return on assets

In the EU: 59% of legacy contracts with guarantees between 2% and 4%

⇒ Deteriorating solvency (Berdin and Grundl (2015))

2016: Solvency II came into force⇒ Market-consistent valuation + risk-based capital⇒ Low discount rates + high capital requirement for guarantees

⇒ Rise in interest rates beneficial for solvency level?



Rates are currently increasing...



Our Approach

Simulate HGB + Solvency II balance sheet of average German life insurer in 2015

Interest rates: (1) low (10Y rf rate = 0.5%),(2) sudden increase to 6% in 2 years, (3) gradual increase by 0.3% p.a.

Assets: Mainly sovereign + corporate bonds;calibrated according to EIOPA Stress Test 2014

Liabilities: Portfolio of endowment life (saving) contracts with guaranteed interest rate(=Hochstrechnungszins, 1.25% in 2015) and 30 yrs to maturity

Lapse risk: Policyholders can lapse contracts and receive surrender value(=99% of accumulated funds); calibrated to German market



Benchmark Interest Rates

−15 −10 −5 0 5 10 15 20

0%

2%

4%

6%

8%

10%

Year

(1) Low interest rates



Rising Interest Rates

−15 −10 −5 0 5 10 15 20

0%

2%

4%

6%

8%

10%

Year

(2) Sudden increase

−15 −10 −5 0 5 10 15 20

0%

2%

4%

6%

8%

10%

Year

(3) Gradual increase



Calibration

Parameter Initial ValueSolvency ratio (standard model; no transitionals) 120%Average guarantee in force 3.4%HGB Equity / Assets 10%Modified duration (Assets) 8.3Modified duration (Liability; scaled to assets) 11.4

⇒ Calibration matches representative German life insurer in 2015



Increasing lapse rates...

1 5 9 13 170%

5%

10%

15%

20%

25%

30%

35%

40%

Year

(2) Sudden increase.

1 5 9 13 170%

5%

10%

15%

20%

25%

30%

35%

40%

Year

(3) Gradual increase.

Figure: Lapse rate across cohorts in each year.

Median lapse rate increases from 2.7% (2015) to 7.5% upon sudden increase⇒ High surrender payments to policyholders

Note: 7.5% much more conservative than 2018 EIOPA stress test (lapse rate = 20%)Berdin, Grundl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 7/13


...result in liquidity need

1 5 9 13 17

−0.02

0

0.02

0.04

Year

(1) Low

(2) Sudden Increase

(3) Gradual Increase

Figure: Free cash flow / Assets0.

⇒ Roughly 20% of initial assets sold over time in case of sudden increase (2)(≈ total debt security holdings of German life insurers in 2017)⇒ Substantial market impact⇒ Fire sales + liquidity spirals?



HGB Own Funds

Niederstwertprinzip: Assets but not liabilities depreciate under HGB

1 5 9 13 170%

10%

20%

30%

40%

50%

60%

70%

80%

Year

(1) Low

(2) Sudden Increase


(a) HGB own funds / total assets.

1 5 9 13 17

0%

5%

10%

15%

20%

Year

(1) Low

(2) Sudden Increase


(b) ZZR / Liabilities.

⇒ Interest rate rise worse than low interest rates on HGB balance!⇒ Zinszusatzreserve exacerbates adverse effect and increases even after interest rate rise!



SII Own Funds and Surrender PaymentsSolvency II: market-consistent valuation⇒ Assets + Liabilities depreciate ⇒ Own Funds / Assets increase due to duration gap

BUT: Best estimate might fall below surrender value⇒ Each contract lapsed can cost own funds ⇒ Reduction of own funds

1 5 9 13 17-20%

-10%

0%

10%

20%

30%

40%

Year

∆MCV

Figure: Surrender return upon a gradual increase (3):Relative difference between best estimate and surrender value.

⇒ Best estimate < surrender value if interest rates are highBerdin, Grundl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 10/13


SII Own Funds

1 5 9 13 170%

10%

20%

30%

40%

50%

60%

70%

80%

Year

(1) Low

(2) Sudden Increase


Figure: SII own funds / total assets.

a) Interest rate rise generally positive

b) Surrender payments make (2) sudden rise less favorable than (3) gradual rise in first years



Solvency Ratio

1 5 9 13 170

100%

200%

300%

400%

500%

Year

(1) Low

(2) Sudden Increase


Figure: Solvency II ratio: OF/SCR.

SCR increases as absolute interest rate shock increases with rates (rdown = (1− δ)r)⇒ Sudden increase detrimental for solvency⇒ Gradual increase beneficial



Conclusion

Rising interest rates...

result in liquidity need of up to 20% of total assets ⇒ fire sales (?)

are beneficial on SII but not HGB balance sheet ⇒ accounting frictions!

jeopardize solvency if increase is too fast.



Thank you.



References

Berdin, E. and Grundl, H. (2015). The Effects of a Low Interest Rate Environment on Life Insurers. GenevaPapers on Risk and Insurance - Issues and Practice, 40:385–415.

European Insurance and Occupational Pensions Authority (EIOPA) (2014). Technical specification for thesolvency ii preparatory phase. available at https://eiopa.europa.eu/regulation-supervision/

insurance/solvency-ii/solvency-ii-technical-specifications.


https://eiopa.europa.eu/regulation-supervision/insurance/solvency-ii/solvency-ii-technical-specifications

https://eiopa.europa.eu/regulation-supervision/insurance/solvency-ii/solvency-ii-technical-specifications


Appendix



Calibration of lapse rates

Average lapse rate in year t based on German environment:

λt = log (λt − a)

= c + log

(1∑h n

ht

)+ log

(∑h

nht e−ed1∆rht +d2∆Th

t

)∼ N

(µt , σ

2t

)Observations: Log excess average German lapse rates L1, ..., Ln.

1) Repeat until convergence of µc and σc (c ∼ N (µc , σ2c ):

a) d1 = arg min∑

t

(λt − Lt

)2

b) Update µc and σc via ML estimators

2) If λ2015(model) < 0.0286− ε, increase d2 and go to 1).Else: Return.



Calibration (1/2)

Asset weights based on avg German insurer in 2015 (EIOPA (2016)):

Asset Portfolio WeightsSovereigns wsov 56.7%Corporate wcorp 34.3%Stocks wstocks 5.6%Real Estate wreal estate 3.4%

Revolving portfolio with 20 sovereign bonds, 10 corporate bonds that mature int = 0, 1, 2, ...⇒ Duration = 8.26 years (≈ GDV (2013), EIOPA (2016))



Calibration (2/2)

Back book with contracts that mature at times t = 0, 1, ..., 29⇒ Liability duration = 11.4 (≈ GDV (2013), EIOPA (2016))

Average guarantee outstanding at t = 0: 3.4% (≈ EIOPA (2016))

Lapse penalty 1− ϑ = 1%



Solvency Capital Requirements

Standard model of Solvency II: SCR = OFt − OFshocked

Market risk: interest rate, equity, property, spread

Lapse risk: down/up/mass shock of lapse rates

Solvency ratio: OF/SCR (without LTGM or ERM)

Initial Solvency Ratio = 120% (≈ BaFin (2016))⇒ OF/MV (Assets) ≈ 8% (≈ EIOPA (2016))



1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year

Bonds FVCouponsPremiums

(1) Low interest rates.

1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year



1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year



Figure: Composition of median cash inflows over time scaled by the market value of assets at timet = 0. Bonds FV are face-value payments of maturing bonds. Coupons consists of bond coupon, rent,

and dividend payments. Premiums are the annual premiums of policyholders.



1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year

Lump-sum benefitSurrender payments


1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year



1 5 9 13 170

0.02

0.04

0.06

0.08

0.1

Year



Figure: Composition of median cash outflows over time scaled by the market value of assets at timet = 0. Lump-sum benefit are payments to policyholders at contract end. Surrender payments are

payments to policyholders lapsing their contract before maturity.



1 5 9 13 17-20%

-10%

0%

10%

20%

30%

40%

Year

∆MCV


1 5 9 13 17-20%

-10%

0%

10%

20%

30%

40%

Year

∆MCV


1 5 9 13 17-20%

-10%

0%

10%

20%

30%

40%

Year

∆MCV


Figure: MCV surrender return, ∆MCVlapse = MCV−SVMCV

, in different interest rate environments.∆MCVlapse reflects the return on market-consistent value of a life insurance contract (MCV) that the

insurer earns upon the contract lapsing. The figure shows the distribution of the median surrenderreturn for each cohort over time. The straight and thick line depicts the median (across cohorts)

median (within cohorts) lapse rate over time. If ∆MCVlapse < 0, the insurer makes a loss on the MCVbalance sheet upon contract’s lapsing.



1 5 9 13 170%

10%

20%

30%

40%

50%

60%

70%

80%

Year

(1) Low

(2) Sudden Increase


(a) Market-consistent valuation.

1 5 9 13 170%

10%

20%

30%

40%

50%

60%

70%

80%

Year

(1) Low

(2) Sudden Increase


(b) Historical cost accounting.

Figure: Own funds ratio: Own funds relative to total assets at (a) market-consistent values and (b)historical cost accounting values. Median and 90% confidence interval over time for the three interestrate environments (1) low interest rates, (2) sudden increase in interest rates, and (3) gradual increase

in interest rates.



1 5 9 13 17

0%

2%

4%

6%

8%

10%

Year

RoA (without depreciation)Depreciation


1 5 9 13 17

0%

2%

4%

6%

8%

10%

Year



1 5 9 13 17

0%

2%

4%

6%

8%

10%

Year



Figure: Insurer’s return on assets and depreciation of HCA book values. The figures compare the bookvalue of assets at time t with time t − 1 with respect to the pure asset return (including coupon,

dividend, and rent payments) and depreciation of book value (upon a decline of at least 10% of marketvalues compared to face values). We show the median and 90% confidence at each point in time.



1 5 9 13 17

0%

5%

10%

15%

20%

Year

(1) Low

(2) Sudden Increase


(a) Interest rate reserve.

1 5 9 13 170%

10%

20%

30%

40%

50%

60%

70%

80%

Year

(1) Low

(2) Sudden Increase


(b) HCA own funds - respective IRR.

Figure: Impact of interest rate reserve. (a) Size of the German interest rate reserve (IRR; German:ZZR) relative to the book value of liabilities including the IRR, (LIRR

t − LBVt )/LIRR

t . (b) HCA value ofown funds when accounting for the IRR as a liability.



0 2 4 6 8 10 12 14 16 18 200%

1%

2%

3%

4%

Year

rG (constant lapse)

rG (sensitive lapse)


0 2 4 6 8 10 12 14 16 18 200%

1%

2%

3%

4%

Year

rG (constant lapse)



0 2 4 6 8 10 12 14 16 18 200%

1%

2%

3%

4%

Year

rG (constant lapse)



Figure: Average guarantee in force (weighted by the MCV of insurance contracts). Sensitive lapse refersto the baseline situation with lapse rates being sensitive to interest rates and contract age. Constant

lapse refers to a situation with constant probability of lapsing for each policyholder, λ = 0.0286.



Solvency Capital Requirement

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year

SCR LapseSCR Interest RatesSCR Remaining Market + Div.


0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year



0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year



Figure: Solvency II capital requirement (SCR) / liabilities.

⇒ Interest rate risk drives SCR⇒ SCR increases although guarantee decreases:Absolute shock is larger with higher interest rates: rdown10 = r10 − |r10|0.31



0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year



0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year



0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

Year



Figure: Solvency II capital requirement (SCR) as a share of the MCV of liabilities. SCR Lapse refers tothe capital requirement for lapse risk; SCR Interest Rates refers to the capital requirement for interestrate risk; SCR Remaining Market + Div. to the capital requirement for remaining market risks (equity,

property, and spread risk) and accounts for diversification effects between SCRs for different risksaccording to the correlation coefficients given by the European Insurance and Occupational Pensions

Authority (EIOPA) (2014).



1 5 9 13 170

100%

200%

300%

400%

500%

Year

(1) Low

(2) Sudden Increase


Figure: Solvency II ratio as own funds to solvency capital requirement (SCR). Median and 90%confidence interval over time for the three interest rate environments (1) low interest rates, (2) sudden

increase in interest rates, and (3) gradual increase in interest rates.



−10 0 10 20 30 40 502 %

2.5 %

3 %

3.5 %

4 %

4.5 %

Year

Pro

fit

Par

tici

pat

ion

ObservedrPrP : βt,1=-0.0015

(a) In year 9.

−10 0 10 20 30 40 502 %

2.5 %

3 %

3.5 %

4 %

4.5 %

Year

Pro

fit

Par

tici

pat

ion

Observed rPrP ; βt,1=0.0038

(b) In year 20.

Figure: Environment (2): Observed and predicted profit participation for calculating themarket-consistent value (MCV) of life insurance contracts.


rising interest rates, lapse risk, and the stability of ... · rising interest rates 15 1510 105 0...

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