Analyzing the Impact of Time Horizon, Volatility and Profit Margins - - PDF document
28.11.2019 Analyzing the Impact of Time Horizon, Volatility and Profit Margins on Solvency Capital: Proposing a New Model for the Global Regulation of the Insurance Industry Thomas Mueller 1 Opinion Disclaimer The views and opinions
28.11.2019 1
1
The views and opinions expressed here are those of the author and do not necessarily reflect the official policy or position of the NAIC or any other agency, organization, employer or company.
2
28.11.2019 2
States of the European Union (EU)
The International Association of Insurance Supervisors (IAIS) will develop a global capital standard (ICS). It appears that ICS will incorporate the key points of European Solvency II-regulation:
3
1. The ICS is being developed with the aim of creating a common language for supervisory discussions 2. Solvency II requirement: The solvency capital must cover risks with a given shortfall probability
compared to contractual terms in traditional life insurance of several decades.
States of the European Union (EU)
The International Association of Insurance Supervisors (IAIS) will develop a global capital standard (ICS). It appears that ICS will incorporate the key points of European Solvency II-regulation:
4
1. The ICS is being developed with the aim of creating a common language for supervisory discussions 2. Solvency II requirement: The solvency capital must cover risks with a given shortfall probability
compared to contractual terms in traditional life insurance of several decades.
Solvency II provides such a common language based on a market view for the balance sheet, publicly accessible with the SFCR reports for any insurance companies.
28.11.2019 3
States of the European Union (EU)
The International Association of Insurance Supervisors (IAIS) will develop a global capital standard (ICS). It appears that ICS will incorporate the key points of European Solvency II-regulation:
5
1. The ICS is being developed with the aim of creating a common language for supervisory discussions 2. Solvency II requirement: The solvency capital must cover risks with a given shortfall probability
compared to contractual terms in traditional life insurance of several decades.
Solvency II provides such a common language based on a market view for the balance sheet, publicly accessible with the SFCR reports for any insurance companies. With a short time horizon, the business is conducted too cautiously without aiming for a higher profit margin, which only reduces the risk in the long term.
28.11.2019 4
2018 AVIVA Economic balance sheet Billion £ Description Assets 395.5 Liabilities 370.8 Stockholder equity 24.7 Capital owned by stockholder Subordinated liabilities 6.9 inter alea obligations for staff pensions schemes
Eligible capital 27.6 Capital at disposal to carry the risk SCR (Solvency Capital Requirement) 15.3 Solvency Ratio: 27.6/15.3 =180% 99.5% confidence level corresponds to 2.58 σ Minimal ratio is 100%, i.e. an eligible capital of at least 100% Volatility σ = SCR%/2.58 = 3.9%/2.58 Operating profit (OP) 3.1
2018 AVIVA Economic balance sheet Billion £ Description Assets 395.5 Liabilities 370.8 Stockholder equity 24.7 Capital owned by stockholder Subordinated liabilities 6.9 inter alea obligations for staff pensions schemes
Eligible capital 27.6 Capital at disposal to carry the risk SCR (Solvency Capital Requirement) 15.3 Solvency Ratio: 27.6/15.3 =180% 99.5% confidence level corresponds to 2.58 σ Minimal ratio is 100%, i.e. an eligible capital of at least 100% Volatility σ = SCR%/2.58 = 3.9%/2.58 Operating profit (OP) 3.1 Normalized to assets =1 27.6/395.5 = 7.0% 15.3/395.5 = 3.9% 1.5% 3.1/395.5= 0.8%
28.11.2019 5
2018 AVIVA Economic balance sheet Billion £ Description Assets 395.5 Liabilities 370.8 Stockholder equity 24.7 Capital owned by stockholder Subordinated liabilities 6.9 inter alea obligations for staff pensions schemes
Eligible capital 27.6 Capital at disposal to carry the risk SCR (Solvency Capital Requirement) 15.3 Solvency Ratio: 27.6/15.3 =180% 99.5% confidence level corresponds to 2.58 σ Minimal ratio is 100%, i.e. an eligible capital of at least 100% Volatility σ = SCR%/2.58 = 3.9%/2.58 Operating profit (OP) 3.1 Normalized to assets =1 27.6/395.5 = 7.0% 15.3/395.5 = 3.9% 1.5% 3.1/395.5= 0.8% Notations in the paper d equity σ Volatility m Profit margin
equity 7% Time (years) 5 10
15
28.11.2019 6
equity 7% Time (years) 5 10
15 0.8%+1.5%=2.3% equity 7% Time (years) 5 10
15 0.8%+1.5%=2.3% 0.8%−1.5%= − 0.7%
28.11.2019 7
equity 7% Time (years) 5 10
15 0.8%+1.5%=2.3% 0.8%−1.5%= − 0.7% 215 ≈32,000 scenarios (random walks) equity 7%
14
Time (years) 5 215 ≈32,000 scenarios (random walks) 10
15 15% Expected value for the equity after 10 years 0.8%−1.5%= − 0.7% 0.8%+1.5%=2.3%
28.11.2019 8
equity 7%
15
Time (years) 5 215 ≈32,000 scenarios (random walks) 10
15 15% Expected value for the equity after 10 years 0.8%−1.5%= − 0.7% 0.8%+1.5%=2.3% equity 7%
16
Time (years) 5 215 ≈32,000 scenarios (random walks) 10
15 15% Expected value for the equity after 10 years 0.8%−1.5%= − 0.7% 0.8%+1.5%=2.3%
# random walks with given equity after 15 years for a depleted equity after 10 or 14 years 4 10 10+9 15 1 1
28.11.2019 9
equity 7%
17
Time (years) 5 215 ≈32,000 scenarios (random walks) 10
15 15% Expected value for the equity after 10 years 0.8%−1.5%= − 0.7% 0.8%+1.5%=2.3%
# random walks with given equity after 15 years for a depleted equity after 10 or 14 years 4 10 10+9 15 1 1 50(=34+16)/32,000=1.55‰ probability of ruin within 15 years
equity 7%
18
Time (years) 5 215 ≈32,000 scenarios (random walks) 10
15 15% Expected value for the equity after 10 years 0.8%−1.5%= − 0.7% 0.8%+1.5%=2.3%
# random walks with given equity after 15 years for a depleted equity after 10 or 14 years 4 10 10+9 15 1 1 16/32,000 ≈ 0.5‰ probability of shortfall after 15 years 50(=34+16)/32,000=1.55‰ probability of ruin within 15 years
28.11.2019 10
19
20
Current strategy Volatility σ 1.5% Profit margin m 0.8%
28.11.2019 11
21
Current strategy Volatility σ 1.5% Profit margin m 0.8% Seemingly riskier strategy Volatility σ 2.0% Profit margin m 1.5%
Analytical models for stochastic development
deviations are Brownian motions
𝑞 𝑞
probability equity
𝑒
28.11.2019 12
After a few years
Analytical models for stochastic development
deviations are Brownian motions
𝑞 𝑞
probability equity
𝑒
After a few years After a few more years
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
28.11.2019 13
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
28.11.2019 14
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
28.11.2019 15
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑞 𝑞
probability equity
𝑒 𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
28.11.2019 16
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
28.11.2019 17
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑞 𝑦, 𝑢 𝑦 𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑞 𝑦, 𝑢 𝑦
Probability of shortfall at time t ⇔ Probability of a negative equity at time t ⇔ area of the surface in green, if the whole surface in grey and green is normalized to 1
28.11.2019 18
𝑞 𝑞
probability equity
𝑒
Analytical models for stochastic development
deviations are Brownian motions
After several decades
𝑞 𝑦, 𝑢 𝑦
Probability density of a scenario leading to an equity x, regardless the previous development.
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑞 𝑞
probability equity
𝑒
A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑞 𝑦, 𝑢 𝑦
Probability of shortfall at time t ⇔ Probability of a negative equity at time t ⇔ area of the surface in green, if the whole surface in grey and green is normalized to 1 That needs to be corrected by introducing a function 𝑞 such that 𝑞 0,𝑢 − 𝑞 0, 𝑢 = 0.
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
36
28.11.2019 19 Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
37
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
38
𝑞 𝑞
28.11.2019 20 Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
39
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑦
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
40
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 : 𝑦
28.11.2019 21 Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
41
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion
𝑦
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
42
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion
𝑦
28.11.2019 22 Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
43
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion probability equity
𝑒 −𝑒 𝑦
After a few years
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
44
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion probability equity
𝑒 −𝑒
28.11.2019 23
After a few years
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
45
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion After a few more years probability equity
𝑒 −𝑒
After a few years
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
46
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion After a few more years probability equity
𝑒 −𝑒 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦 𝑦
28.11.2019 24
After a few years
Correcting Brownian motion for the subtracted term 𝒒 𝒚, 𝒖
𝑦
probability equity
𝑒 −𝑒
47
𝑞 𝑞
Probability density of a scenario leading at an equity x with crossing the zero line at least once.
𝑞 𝑦, 𝑢 : 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
Probability density of a scenario leading to an equity x without crossing the zero line before.
𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 :
No m𝑏𝑠𝑗𝑜 (𝑛=0) → horizontal motion A positive m𝑏𝑠𝑗𝑜 (𝑛>0) → upwords motion After a few more years After several decades probability equity
𝑒 −𝑒
48
Formula and geometric meaning for the probability of ruin
28.11.2019 25
equity
𝑞 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦
Probability
𝑞 𝑞 𝑞
49
Formula and geometric meaning for the probability of ruin
equity
𝑞 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦
Probability
𝑞 𝑞 𝑞
Probability of shortfall at time t
𝛸 − 𝑒 + 𝑛𝑢 𝜏 𝑢
50
Formula and geometric meaning for the probability of ruin
28.11.2019 26
equity
𝑞 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦
Probability
𝑞 𝑞 𝑞
Probability of shortfall at time t
𝛸 − 𝑒 + 𝑛𝑢 𝜏 𝑢
51
Formula and geometric meaning for the probability of ruin
Probability of falling short before time t and then recovering up to an equity x>0 at time t > 0
𝑓
𝛸 −𝑒 + 𝑛𝑢
𝜏 𝑢
+
equity
𝑞 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦
Probability
𝑞 𝑞 𝑞
Probability of shortfall at time t
𝛸 − 𝑒 + 𝑛𝑢 𝜏 𝑢
52
Formula and geometric meaning for the probability of ruin
Probability of falling short before time t and then recovering up to an equity x>0 at time t > 0
𝑓
𝛸 −𝑒 + 𝑛𝑢
𝜏 𝑢
+
Probability of going ruin up to time t
=
28.11.2019 27
equity
𝑞 𝑞 𝑦, 𝑢 − 𝑞 𝑦, 𝑢 𝑦
Probability
𝑞 𝑞 𝑞
Probability of shortfall at time t
𝛸 − 𝑒 + 𝑛𝑢 𝜏 𝑢
53
Formula and geometric meaning for the probability of ruin
Probability of falling short before time t and then recovering up to an equity x>0 at time t > 0
𝑓
𝛸 −𝑒 + 𝑛𝑢
𝜏 𝑢
+
Probability of going ruin up to time t
=
Scaling factor area
1 10 20 30 40 Probability
Shortfall 0.00001% 0.090% 0.037% 0.010% 0.003% Ruin =proposed model 0.00003% 0.54% 0.74% 0.78% 0.78%
Corresponding Solvency II ratio
Shortfall 180% 109% 118% 129% 141% Ruin=proposed model 175% 89% 85% 84% 84% Business Management according Solvency II Volatility σ 1.5% Profit margin m 0.8%
Eligle capital or equity d
7.0% Business Management according proposed model Volatility σ 2.0% Profit margin m 1.5%
1 10 20 30 40 Probability
Shortfall 0.0011% 0.025% 0.002% 0.0001% 0.00001% Ruin =proposed model 0.0027% 0.50% 0.53% 0.53% 0.53%
Corresponding Solvency II ratio
Shortfall 148% 121% 144% 166% 185% Ruin=proposed model 141% 90% 89% 89% 89%
28.11.2019 28
1 10 20 30 40 Probability
Shortfall 0.00001% 0.090% 0.037% 0.010% 0.003% Ruin =proposed model 0.00003% 0.54% 0.74% 0.78% 0.78%
Corresponding Solvency II ratio
Shortfall 180% 109% 118% 129% 141% Ruin=proposed model 175% 89% 85% 84% 84% Business Management according Solvency II Volatility σ 1.5% Profit margin m 0.8%
Eligle capital or equity d
7.0% Business Management according proposed model Volatility σ 2.0% Profit margin m 1.5%
1 10 20 30 40 Probability
Shortfall 0.0011% 0.025% 0.002% 0.0001% 0.00001% Ruin =proposed model 0.0027% 0.50% 0.53% 0.53% 0.53%
Corresponding Solvency II ratio
Shortfall 148% 121% 144% 166% 185% Ruin=proposed model 141% 90% 89% 89% 89%
1 10 20 30 40 Probability
Shortfall 0.00001% 0.090% 0.037% 0.010% 0.003% Ruin =proposed model 0.00003% 0.54% 0.74% 0.78% 0.78%
Corresponding Solvency II ratio
Shortfall 180% 109% 118% 129% 141% Ruin=proposed model 175% 89% 85% 84% 84% Business Management according Solvency II Volatility σ 1.5% Profit margin m 0.8%
Eligle capital or equity d
7.0% Business Management according proposed model Volatility σ 2.0% Profit margin m 1.5%
1 10 20 30 40 Probability
Shortfall 0.0011% 0.025% 0.002% 0.0001% 0.00001% Ruin =proposed model 0.0027% 0.50% 0.53% 0.53% 0.53%
Corresponding Solvency II ratio
Shortfall 148% 121% 144% 166% 185% Ruin=proposed model 141% 90% 89% 89% 89%
28.11.2019 29
1 10 20 30 40 Probability
Shortfall 0.00001% 0.090% 0.037% 0.010% 0.003% Ruin =proposed model 0.00003% 0.54% 0.74% 0.78% 0.78%
Corresponding Solvency II ratio
Shortfall 180% 109% 118% 129% 141% Ruin=proposed model 175% 89% 85% 84% 84% Business Management according Solvency II Volatility σ 1.5% Profit margin m 0.8%
Eligle capital or equity d
7.0% Business Management according proposed model Volatility σ 2.0% Profit margin m 1.5%
1 10 20 30 40 Probability
Shortfall 0.0011% 0.025% 0.002% 0.0001% 0.00001% Ruin =proposed model 0.0027% 0.50% 0.53% 0.53% 0.53%
Corresponding Solvency II ratio
Shortfall 148% 121% 144% 166% 185% Ruin=proposed model 141% 90% 89% 89% 89%
Solvency II forces insurers to invest in safe government bonds and not in more suitable corporate bonds with a safer long-term perspective. Or to reinsure a higher proportion of the business than would be appropriate in the long term.
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
58
28.11.2019 30
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
59
Opons for acons − two ends of the spectrum: Nation-state policy: Stick to the reasonable U.S. RBC standard for variable annuities Acceptance of the future worldwide standard based on Solvency II; use workarounds to avoid the disadvantages.
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
60
Opons for acons − two ends of the spectrum: Nation-state policy: Stick to the reasonable U.S. RBC standard for variable annuities Acceptance of the future worldwide standard based on Solvency II; use workarounds to avoid the disadvantages.
28.11.2019 31
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
61
Opons for acons − two ends of the spectrum: Nation-state policy: Stick to the reasonable U.S. RBC standard for variable annuities Acceptance of the future worldwide standard based on Solvency II; use workarounds to avoid the disadvantages.
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
62
Opons for acons − two ends of the spectrum: Nation-state policy: Stick to the reasonable U.S. RBC standard for variable annuities Acceptance of the future worldwide standard based on Solvency II; use workarounds to avoid the disadvantages.
28.11.2019 32
Problems of the European Solvency II-Standard became hopefully more transparent. The legislator decides; the regulators can influence the legislation and have considerable room for manoeuvre in implementing the laws. Remarks:
63
Opons for acons − two ends of the spectrum: Nation-state policy: Stick to the reasonable U.S. RBC standard for variable annuities Acceptance of the future worldwide standard based on Solvency II; use workarounds to avoid the disadvantages.
64
28.11.2019 33
UK life insurance market reveals major differences even in one country itself:
In Solvency II, future payments are generally discounted at the risk-free interest rate. However: This leads to a longer time horizon through the back door by some kind of workaraoud,
standard.
Traditional participating policies Future market Products Endowment policies with bonus Annuities and pensions. Risk mitigation Enormous discretion to reduce maturity value, see JIR article 38-04 Matching Adjustment exemption of Solvency II If the insurer holds certain long-term assets with cash flows that match the liabilities Upward shift of risk-free interest rate to reflect that insurer is not exposed to spread movements due to its long time horizon. Matching Adjustment exemption of Solvency II
65
positive m𝑏𝑠𝑗𝑜 𝑒>0
area
Left Gaussian bell curve right Gaussian bell curve
𝑓
A smaller area on the left side is sufficient to neutralize the normal distribution distances on the right side.
𝑓
can be understood as a scaling factor, since it is independent of t and depends only on the model parameters.
66
28.11.2019 34
𝜔 ∞ = 𝑓
in business at time t Probability of going out
Probability of going out of business at any time
= = − −
Probability of being in business at time 0 Probability of going ruin up to time t
Patchwork-calculation
Whole picture:
67
From a presentation by the Italian Insurance Association Ania
68
28.11.2019 35
From a presentation by the Italian Insurance Association Ania:
69