Solvency II in Europe and Internal Risk Modelling N. Savelli - nino.savelli@unicatt.it Catholic University of Milan Member IAA Solvency Sub-Committee Concurrent Session: ”Update on a Global Risk Based Capital Standard” Agenda The new Solvency Regimes adopted by some European Supervisory Authorities Solvency II Project: the state-of-art Some Results of capital requirements by a Risk-Theory Simulation Model Final comments N. Savelli Solvency II in Europe and IRM 2 The new Solvency Regimes adopted by some European Supervisory Authorities N. Savelli Solvency II in Europe and IRM 3 The FSA approach Financial Services Authority (FSA) – UK: ECR (Enhanced Capital Requirement): is calculated using a standardized formula with different charges (in %) on assets (for asset risk), on liabilities (for reserving risk) and on premiums (for pure underwriting risk). ICA (Individual Capital Assessment): Insurers are additionally required to develop their own view on their capital requirements using simple Stress & Scenario testing or Internal Models. Time horizon = 1 year confidence level = 99.5% . These ICA results are submitted and discussed with regulator, and an individual capital requirement then is agreed. These tests are currently “soft”. They should become “hard” in the near future. N. Savelli Solvency II in Europe and IRM 4 The FSA Approach: the structure of ECR Total Capital Requirement (TCR) = AC + RC + UC AC = Asset charge = by applying factors to various categories of assets (Form 13 – FSA Returns) where more risky assets are attracting higher factors. Further, they include credit risks such as reinsurance recoverables. RC = Reserve charge = by applying factors to the net of reinsurance reserves for each class of business (for a total of 24 classes of business: 8 LoB for each of direct&facultative, proportional treaty and non-proportional treaty). Reserves include outstanding claims, IBNR, unearned premium reserve (undiscounted and excluding equalisation reserves) UC = Underwriting charge = by applying factors to the net premium for each class of business (the same 24 classes of business are used as for Reserve Charge). N. Savelli Solvency II in Europe and IRM 5 8 Lines of Business: - Accident & Health, - Transport - Motor - Property - Aviation - Liability - Marine - Miscellaneous & Pecuniary loss 3 different reinsurance covers: Direct & Facult. / Proportional Treaty / Non-Proportional Treaty 8 overall sets of risk factors: Timescale: T=1 and T=5 years Probability Capital Requirement to be insufficient: 1/40=2.5% 1/100=1% 1/200=0.5% 1/500=0.2% Data available: for all major UK insurers and for many of the smaller insurers (Lloyd’s not included) 1985-2001 fin. years. N. Savelli Solvency II in Europe and IRM 6 Optimised RISK FACTORS based on ALL INSURERS (T=1 year and PoF=1%) Optimised RISK FACTORS based on ALL INSURERS (T=1 year and PoF=0.5%) Asset Factors - Debt securities approved 3.4% - Land & Buildings: 7.4% - Equities: insurance dependents 0% - Equities: group&non-ins. dependents: 7.4% - Equities: other 15.5% Reserve Factors Property: 9.7% 12.1% 12.1% Liability: 14.2% 14.2% 14.2% Asset Factors - Debt securities approved - Land & Buildings: - Equities: insurance dependents - Equities: group&non-ins. dependents - Equities: other Reserve Factors Property: 8.0% 10.5% 10.5% Liability: 12.1% 12.1% 12.1% 2.8% 6.1% 0% 6.1% 12.8% (Dir./Prop./Non-Prop.) (Dir./Prop./Non-Prop.) Underwriting Factors Property: 8.6% 19.1% 45.3% (Dir./Prop./Non-Prop.) Liability: 12.4% 12.4% 12.4% (Dir./Prop./Non-Prop.) N. Savelli (Dir./Prop./Non-Prop) (Dir./Prop./Non-Prop) Underwriting Factors Property: 10.2% 23.1% 53.6% (Dir./Prop./Non-Prop) Liability: 13.9% 13.9% 13,9% (Dir./Prop./Non-Prop) Solvency II in Europe and IRM 7 The above results have been optimised using All Insurers in the market (a larger weight is placed on the larger insurers) Then in order to fit the factors to smaller Insurers, the optimisation has been also based on: - All Insurers except the largest 10 - All Insurers with net premium in 2001 below 10 million (GBP) Higher measures are clearly obtained for smaller Insurers (e.g. small Insurers often show a greater degree of volatility than large insurers) For T=1 and PoF = 0.5% the results show a capital requirement equal to 50-60% of net premiums. For T=1 and PoF = 1,0% the results show a capital requirement equal to 40-50% of net premiums. N. Savelli Total Capital Requirements implied by each of the three optimisation methods Solvency II in Europe and IRM 8 The PV approach Pensioen Verzekeringskamer (PV) – Netherlands: Financial Assessment Framework (it will be gradually implemented until 2008) This system consists of 2 tests: - FIRST TEST: reported liabilities > actual value of liabilities where “actual” liabilities = PV expected cash flow + risk margin. Furthermore, insurers are required to extend this test to show that in 1-year time, with 99.5% confidence level: actual value of resources > actual value of liabilities (assuming no new business) - SECOND TEST (continuity test): it concerns long-term survival of the insurer. It is performed over a 3-5 years time horizon and new business and proposed policy are considered. For both tests, a choice of methods is available, ranging from simplified versions with input by regulators to internal Models. N. Savelli Solvency II in Europe and IRM 9 The SFOPI approach Swiss Federal Office of Private Insurance (SFOPI) – Switzerland: Swiss Solvency Test (currently under consultation but due for implementation in 2006) Insurers are required to show that they hold sufficient capital to the extent that in an unlikely negative scenario (e.g. 1%), assets and liabilities can be transferred to a third party. The regulator will provide a standard model for insurance, market and credit risk, which insurers can deviate from previous authorization of the regulator. Alternatively, insurers can use internal models, if they can prove that their model reflects risks more appropriately. Assets and liabilities must be reported at their market-consistent value. N. Savelli Solvency II in Europe and IRM 10 Solvency II Project: the state-of-art (Pillar I Non-Life Working Group: Solvency II – Issues paper, February 2005) N. Savelli Solvency II in Europe and IRM 11 The Solvency II structure Who is involved in Solvency II project: Insurance Commission (IC): European Commission’s regulatory and legislative policy body ultimately responsible for drafting the new directives. IC members are appointed from the insurance supervisory authorities of the 25 member states; Committee of European Insurance and Occupational Pension Supervisors (CEIOPS): advisory body within the European Commission who advices the IC on technical aspects of Solvency II. It is composed by high-level representatives of the (insurance and pension) EU supervisory authorities Timetable: by December 2005: it is expected a proposal for framework directive key principles by December 2009: measures implementation. N. Savelli Solvency II in Europe and IRM 12 Pillar I: it focuses on quantitative aspects of solvency, mainly calculating the capital requirement (MCR and SCR) Pillar II: it is mainly concerned with qualitative measures regarding the Supervisory review Pillar III: concerns disclosure requirements. The aim is to reinforce market discipline and risk-based supervision (Note: many European insurers are not listed and then at the moment are not subject to a very high degree of public disclosure). N. Savelli Solvency II in Europe and IRM 13 Risks and Capital Measures under Pillar I In Pillar I are contained all the components of the “Insurance Risk” that can be measured quantitatively: - underwriting risk (pricing risk and reserving risk) - market risk - credit risk, - liquidity risk - operational risk Total Balance-Sheet approach: target capital and technical provisions to be covered by high quality assets N. Savelli Solvency II in Europe and IRM 14 Two capital measures likely to be introduced: - MCR (Minimum Capital Requirement) - SCR (Solvency Capital Requirement or Target Capital) and an Early Warning indicator (set above SCR and calibrated over a longer time horizon, likely to be used for supervisory intervention level) The EU Insurance Commission would like to keep a simple formula for MCR as it is now for Solvency I (roughly the maximum between 16%-18% of net premiums and 23-26% of net claims amount). It should include an absolute floor expressed in euros. N. Savelli Solvency II in Europe and IRM 15 A capital below MCR represents an unacceptable risk for policyholders and then immediate supervisory action is required Alternative options for determining MCR are: - extending present Solvency I formula to capture asset risks; - using SCR as a reference; - establishing a simple risk margin over and above liabilities N. Savelli Solvency II in Europe and IRM 16 As to SCR, it should reflect the level of capital that an insurer would need to operate with a “rather” low probability of failure for a fixed time horizon. In principle it should be calculated on a going-concern basis. This low level has not yet been defined, but at the moment the low probability might be 0.5% for 1 year time span. The Risk Measure has not yet been defined, but VaR or TVaR are good candidates (the choice will be likely linked to the desired safety level and the actual capital ratios of the market). On this matter, IAA has suggested TVaR as a more appropriate risk measure for insurers. N. Savelli Solvency II in Europe and IRM 17 Standard Formula vs Internal Model for calculating SCR The approach for calculating SCR: - Standard Formula: it should be technically feasible for all firms, but clearly no standard formula would be able to capture the complete risk profile of the company. Two main methodologies: a) Factor-Based Capital Models b) Scenario-Based Approaches. They could be combined in the SCR standard formula. - Internal Model: likely Solvency II will allow partial models initially (FSA and PV allow the use of internal models for their own new solvency regime, and SFOPI permits its use as approved alternative tool only). N. Savelli Solvency II in Europe and IRM 18 Standard Formula Factor-Based Approach: formulaic relationship between risk measures and capital requirements. The parameters in any formula can be either identical for all firms or tailored to reflect individual aspects, or a combination. The RBC in US and the Swiss Solvency Test adopt a personalised factor-based model. Criticism: - weak ability to capture interaction of risks opacity lack of dynamism low predictive power N. Savelli Solvency II in Europe and IRM 19 Scenario-Based Approach: - it can be used to analyse the impact of adverse scenarios on the firm, defined for each category of risk (underwriting, market, credit, etc. …). - Static or Dynamic scenarios (in the latter case, the assumption of management’s inertia is relaxed). Scenarios may be used to model extreme events where the factor-based approach may fail because these events may be either absent from the data or may have to be smoothed out in the calibration process; e.g. in the SST a separate treatment for catastrophic underwriting risk is made by scenarios capturing the impact of extreme events. N. Savelli Solvency II in Europe and IRM 20 In principle, a third approach might be the Probabilistic Approach (usually via Monte Carlo simulation), but it requires intensive use of data and computing power and therefore it is not useful for a standard formula. N. Savelli Solvency II in Europe and IRM 21 Internal Model Internal Models : they can be used to represent the business of an individual firm much more closely than the standard formula, with capital requirements more significantly aligned to the effective risk of the company. Internal Model could also be used as an effective risk management tool within the firm, and then it would be desirable to encourage firms to move from the standard formula to internal models through capital or other incentives. Internal models may also be a relevant tool for the capital requirements at the group level. N. Savelli Solvency II in Europe and IRM 22 Firms would only seek approval of internal models if they lead to a reduction in capital requirements compared with the standard formula The model’s approval process will require considerable effort and expertise from the supervisor Internal Models can be highly sensitive to the underlying assumptions and parameters: sensitivity testing as part of the validation process needed Cherry-picking risk: firms should not have the option of switching back to the standard formula simply because this leads to a minor capital requirement N. Savelli Solvency II in Europe and IRM 23 Potentially, internal models might be used only for some risks (or for the main lines of business) whilst the standardised formula is used for the remaining (e.g. operational risk, where less data are available) Anyhow, partial use of internal models would be a temporary solution (to avoid cherry-picking again) N. Savelli Solvency II in Europe and IRM 24 Some Results from a Risk-Theory Simulation Model see paper by Rytgaard & Savelli ”Risk-Based Capital requirements for property and liability insurers according to different reinsurance strategies and the effect on profitability”, (presented at XXXV ASTIN Colloquium 2004 in Bergen) N. Savelli Solvency II in Europe and IRM 25 General framework of the model General Insurance Casualty and Property (separately) T=3 years Compound Mixed Poisson Process Neg. Binomial distrib.for non-CAT claims Poisson distrib. for CAT claims Claim Size : LogNormal distrib. for non-CAT claims Pareto distrib. for CAT claims Dynamic Ins. Portfolio : Volume of premiums increases annually according to real growth and claim inflation Reinsurance strategy : Traditional Quota Share, Surplus, XL (and CAT XL only for Property) Investment Return : Stochastic (AR model), only 1 asset category Monte Carlo approach: 400.000 simulations Risks not considered : Reserving, Credit and Operational Risks Company Lines of Business Time Horizon Total Claim amount Number of Claims N. Savelli : : : : : Solvency II in Europe and IRM 26 The Risk-Reserve process (Ut) ~ U t Ut Bt Xt Et BRE = = = = = ~ ~ (1 j ) U t t 1 ~ ~ RE ~ RE ( B X E ) ( B X C RE ) (1 j )1/ 2 t t t t t t t ~ j LR TX DV t t 1 t t Risk Reserve at the end of year t Gross premiums in year t Aggregate claims amount Actual total expenses of year t Premiums ceded to reinsurers N. Savelli XRE CRE j LR TXt DVt = = = = = = Solvency II in Europe and IRM Claims amount recovered by reins Reinsurance Commissions Investment return (annual rate) Loss Reserve amount Taxation amount Dividends of the year 27 Total Claims Amount (Xt) ~ kl , t ~ k cat , t l 1 k 1 k 1 L ~ ~ ~ X t Z l ,k ,t Wk ,t non-CAT claims CAT claims (for Property only) kl,t = non-CAT Claim Number of year t (for the line l) is assumed to be Negative Binomial distributed (i.e. Poisson distribution with a stochastic parameter n*q, where q is a multiplicative random structure variable with mean 1 and distributed as a Gamma(h,h) - only short-term fluctuations and no systematic changes are assumed). The expected number of claims is increasing with the real rate of growth: nt=n0*(1+g)t kCAT,t = CAT Claim Number of year t (affecting only property lines) is assumed to be Poisson distributed. The Poisson parameter is kept constant over the chosen time horizon N. Savelli Solvency II in Europe and IRM 28 Zl,k,t = non-CAT claim Size for the k-th non-CAT claim of year t (for the line l): is assumed to be LogNormal distributed, with values increasing annually according to the deterministic claim inflation (i) only. Wk,t = CAT claim Size for the k-th CAT claim of year t (affecting only property lines): is assumed to be Pareto distributed, with values increasing every year according to the joint (deterministic) effect of real growth (g) and claim inflation (i) rates. N. Savelli Solvency II in Europe and IRM 29 For each line, non-CAT claim size random variables Z are here assumed to be i.i.d.; In case of a CAT claim, the CAT claim sizes affecting each line are clearly not independent Here random variables Xt are assumed time independent. In reality, however, long-term cycles are present and therefore auto-correlation might be significant (especially for medium/long-term analyses). N. Savelli Solvency II in Europe and IRM 30 General assumptions Real growth rate (g): 5% (for every line) Claims inflation rate (i): Liability 5% Property 2% Loss reserve ratio (LR/B): Liability 120% Property 30% Expenses loading coefficient (c): 25% Risk loading coefficient (λ): 1 tx E ( X~ ) E ( ~j ) LR b X~ Motor Liability: λ = 2.1 % Commercial Liability: λ = 14.7 % Property (Homeowners, Agriculture, Commercial): λ = 17.5 % (having fixed b=35%) Investment return process (j): expected rate 4% and std 2% (approx.) Taxation flat rate (tx): Dividends flat rate (div): N. Savelli 35% 20% gross profit of the year net profit of the year Solvency II in Europe and IRM 31 Liability multi-line insurer (most relevant input parameters) LoB 1 Motor LoB 2 Commercial TOTAL 18.000 2.000 20.000 Variance structure variable 0,02 0.03 Skewness structure variable + 0.28 + 0.35 Initial expected claim size (Eur) 6.000 16.000 7 16 Initial Risk Premium (mill Eur) 108,0 32,0 140,0 Initial Gross Premiums (mill Eur) 147,0 48,9 196,0 Initial expected number of claims Variability coefficient of claim size 7.000 NOTE: Parameters as Var(q), E(Z) and CV(Z) are derived from the IAA-SWP Report (2004) N. Savelli Solvency II in Europe and IRM 32 Property Multi-line Insurer (most relevant input parameters) LoB 1 Homeowners 200.000 200.000 LoB 2 Agriculture 40.000 400.000 LoB 3 Commercial 20.000 1.200.000 Exp. loss frequency per risk losses 8.0 % 16.0 % 8.0 % Initial expected number of claims Variance structure variable q Skewness structure variable q Initial expected claim size (EUR) Variability coefficient of claim size 6.000 0,04 + 0.40 8.000 4 2.000 0.04 + 0.40 12.000 8 2.000 0.04 + 0.40 24.000 12 10.000 80,0 128,0 48,0 256,0 1 Initial Number of policies Sum Insured per policy (EUR) Catatrophe PML (mill EUR) Exp. n. of catastrophe claims TOTAL 260.000 12.000 Catastr. claims – Pareto param 1.2 Cumulation factor 0.5 Initial Risk Premium (mill EUR) - hereof single risk losses - hereof cat losses Initial Gross Premiums (mill EUR) N. Savelli 49,3 44,7 4,6 77,2 27,5 20,6 7,0 43,2 Solvency II in Europe and IRM 43,2 40,4 2,7 67,6 120,0 105,7 14,3 188,0 33 Simulation steps 1. 2. 3. 4. Start simulations with u0=0 Calculate risk measure rbc for a time horizon T=1,2,3 (gross and net of reinsurance) Use u0=rbc(TVaR; 99%,T=1) as initial capital ratio Compute expected RoE N. Savelli Solvency II in Europe and IRM 34 Alternative Reinsurance Strategies At the moment we consider the only reinsurance strategies available on the market, which are: Liability Multil. Insurer 1. No reinsurance 2. Q/S 10% with commission 25% (cRE=c) Property Multil. Insurer 1. No reinsurance 2. Q/S 40% with commission 27% (cRE=c+2%) and Cat XL protecting retention N. Savelli Solvency II in Europe and IRM 35 Results of 400.000 simulations No reinsurance (Strategy 1) Risk Measures (% Total Gross Premiums at T=0) Liability Multi-line Insurer Property Multi-line Insurer T=1 T=2 T=3 T=1 T=2 T=3 99.0 % 19.9 25.1 27.4 125.8 149.6 159.3 99.5 % 26.6 32.9 37.2 152.7 175.4 186.4 99.9 % 55.0 75.0 77.9 204.4 226.1 252.6 99.0 % 33.4 41.3 46.0 161.4 184.7 200.3 99.5 % 44.0 54.3 60.4 184.2 209.0 230.0 99.9 % 85.7 94.7 96.6 235.7 263.2 313.6 rbc (VaR) rbc (TVaR) N. Savelli Solvency II in Europe and IRM 36 Results of 400.000 simulations With reinsurance (Strategy 2) Risk Measures (% Total Gross Premiums at T=0) Liability Multi-line Insurer (QS 10%) Property Multi-line Insurer (QS 40% + CAT XL) T=1 T=2 T=3 T=1 T=2 T=3 99.0 % 17.9 22.6 24.7 10.5 12.9 14.5 99.5 % 24.0 29.6 33.5 12.5 15.4 17.7 99.9 % 49.5 67.5 70.1 17.4 22.4 25.7 99.0 % 30.0 37.2 41.4 13.6 16.9 19.3 99.5 % 39.6 48.8 54.3 15.9 19.9 22.5 99.9 % 77.1 85.2 86.9 22.7 27.4 30.8 rbc (VaR) rbc (TVaR) N. Savelli Solvency II in Europe and IRM 37 Alternative Reinsurance Strategies (Liability Multiline Insurer) Now we assume that the following reinsurance strategies are available on the market: 1. No reinsurance 2. Q/S 10% with commission 25% (cRE=c) 3. Q/S 20% with commission 25% (cRE=c) 4. Unlim. xs 730.000 @ 7.57% N. Savelli Solvency II in Europe and IRM 38 Alternative Reinsurance Strategies (Property Multiline Insurer) 1. No reinsurance 2. Q/S 40% with commission 27% (cRE=c+2%) and Cat XL protecting retention 3. Surplus treaty after € 300.000 (i.e. retention = 100% for househ., 75% for agric. and 25% for comm.) with commission 26% (cRE=c+1%) and Cat XL protecting retention. This coverage corresponds approx. to cede the same amount of premiums as QS 40%. 4. Risk XL € 840.000 xs 360.000 @ 7.51% and Cat XL protecting retention 5. Cat XL only (XL 369,9 mill xs 14,1 mill - RoL 6.27%) N. Savelli Solvency II in Europe and IRM 39 rbc(TVaR 99%) according to different retentions T = 1 year Liability Property Strategy 1 50% 50% Strategy 1 40% oo 30% RBC RBC 40% 20% Strategy 2 10% 30% 20% o 10% Strategy 2 0% 0% 0% 20% 40% 60% 80% 100% 0% N. Savelli XL 40% 60% 80% 100% Ceded premiums Ceded premiums QS 20% QS & Cat XL Solvency II in Europe and IRM Surplus & Cat XL Risk and Cat XL 40 Liability Multi-line insurer – Results (400.000 simul.) u0 = rbc (TVaR - 99%, T=1) Reinsurance strategy 1. No reinsurance 2. Net of QS 10% 3. Net of QS 20% 4. Net of risk XL N. Savelli T=1 T=2 T=3 rbc (TVaR - 99%) 33.4 41.8 46.9 Exp. RoE (%) 19.32 40.88 (in [0;2]) 65.00 (in [0;3]) rbc (TVaR - 99%) 30.1 37.6 42.2 Exp. RoE (%) 19.33 40.89 65.00 rbc (TVaR - 99%) 26.7 33.4 37. 6 Exp. RoE (%) 19.32 40.88 65.00 rbc (TVaR - 99%) 23.5 30.9 36.4 Exp. RoE (%) 12.75 26.81 42.49 Solvency II in Europe and IRM 41 Property Multi-line insurer - Results (400.000 simul.) u0 = rbc (TVaR - 99%, T=1) Reinsurance strategy 1. No reinsurance 2. Net of QS 40% 3. Net of Surplus 4. Net of risk XL 5. Net of CAT XL N. Savelli T=1 T=2 T=3 rbc (TVaR - 99%) 161.4 187.3 205.3 Exp. RoE (%) 7.45 15.28 23.76 rbc (TVaR - 99%) 13.7 17.1 19.5 Exp. RoE (%) 18.08 37.71 59.13 rbc (TVaR - 99%) 19.3 25.5 30.1 Exp. RoE (%) 7.52 15.64 24.48 rbc (TVaR - 99%) 26.7 36.6 44.6 Exp. RoE (%) 0.92 1.72 2.53 rbc (TVaR - 99%) 24.2 31.1 36.3 Exp. RoE (%) 12.79 26.61 41.69 Solvency II in Europe and IRM 42 Final Comments Prominent role of Internal Modelling in the future Quantitative Tools are strongly necessary for this task (with special reference to extreme events and dependencies) Nowadays the minimum EU solvency ratio for a P&C Insurers is roughly 16-20% of net premiums, and the results of many studies show how the minimum capital ratio should be significantly increased (at least 35-40% of premiums) Attention must be paid to excessive capital requirements with undesirable effects on a higher cost of capital for the insurance market N. Savelli Solvency II in Europe and IRM 43 Questions and Comments ? N. Savelli Solvency II in Europe and IRM 44