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• the economic cycle affecting policyholders’ ability to pay further premiums; • the personal circumstances of policyholders and whether they can afford premiums 3.176 A non-exhaustive list of possible simplifications for modelling surrender rates, which could be used in combination includes: • assume that surrenders occur independently of financial/ economic factors, • assume that surrenders occur independently of biometric factors, • assume independency in relation to management actions, • assume that surrenders occur independently of the undertaking specific information, • use a table of surrender rates that are differentiated by factors such as age, time since policy inception, product type,..., • model the surrender as a harzard process either with a non-constant or constant intensity. 3.177 Some of these simplifications convert the hazard process in deterministic function which implies independency between the surrender time and the evaluation of economic factors, which are obvious not a realistic assumptions since policyholder behaviour is not static and is expected to vary as a result of changing economic environment. 3.178 Other possible surrender models 63 where the surrender rate SR t for a policy at time t also depend on economic variables include the following: • Lemay’s model FVt SRt = a ⋅α + b ⋅ GV • Arctangent model = a + b ⋅ arctan( m∆ − n) • Parabolic model • Modified parabolic model SRt t SR = a + b ⋅ sign ∆ MRt • Exponential model SR = a + b ⋅ e SR t t t 40/112 t 2 ( ∆ t ) ⋅ t = a + b ⋅ sign( ∆ ) ⋅ ∆ ⋅ k + c CRt m⋅ t t ( CRt −1−CRt ) FVt −CSVt • New York State Law 126 SR = a + b ⋅ sign( ∆ ) ⋅ ∆ ⋅ k − c ⋅ ( ) t where a , b, c, m, n, j, k are coefficients, α denotes underlying (possible time dependent) base laps rate, FV denotes the fund/account value of the policy, GV denotes the guaranteed value of the policy, ∆ equals reference market rate less crediting rate less surrender charge, CR denotes the credit rate, MR denotes the reference market rate, CSV denotes the cash surrender value and sign ( x) = 1 if x ≥ 0 and 63 Models giving surrender rates above 100 % are not relevant. t t FVt © CEIOPS 2010
sign ( x) = −1 if x < 0 . 3.179 Even after a model has been selected there is a great challenge to estimate the parameters. The policyholder behaviour may change over time and the current observed surrender pattern could be a poor prediction of future behaviour. 3.180 Undertakings could also assume that mortality is independent of the financial market. A questionable but practical simplification is to assume stochastic independency between surrender rate and financial markets and between surrender rate and mortality rate. 3.181 For with profit contracts the surrender option and the minimum guarantees are clearly dependent. Furthermore, management actions will also have a significant impact on the surrender options that might not easily be captured in a closed formula. 3.2.2.3. Financial options and guarantees 3.182 Life insurance contracts usually have besides classical pure insurance elements also implicitly or explicitly built in different kinds of financial options and guarantees (see CEIOPS’ advice DOC-21-09 and DOC-33-09 for a wider reference to these guarantees). 3.183 The benefits of with-profit contracts usually consist of a guaranteed benefit and of variable extra benefit that is based on the profits the undertaking has been able to generate and that is often added to the guaranteed benefits as reversionary extra benefit or a variable terminal extra benefit that is not guaranteed until maturity. 3.184 As discussed in CEIOPS-DOC-33-09, financial options and guarantees can generally be valued accordingly to two main techniques: • use observed market price if the risk factor is hedgeable on deep, liquid and transparent market • use mark-to-model if the risk factor is non-hedgeable i.e.: • stochastic simulation technique, • deterministic approach, o closed form estimate derived from an arbitrage-free model with parameters calibrated to market prices of similar options (e.g. Black-Scholes formula). 3.185 Valuing financial options and guarantees with stochastic simulation techniques (Monte Carlo or appropriate numerical partial differential equation approaches) considers a range of future stochastically varying economic conditions (e.g. interest rates) calibrated to a market consistent assets model. The connection to market consistent prices and arbitrage-free valuation is achieved by ensuring that the asset model reproduces observed market prices for some representative assets. 3.186 Deterministic approach made series of deterministic projections of the values of the underlying assets. Deterministic projection corresponds to a possible economic scenario together with the associated probability of occurrence. The cost of the financial options and guarantees equal to the 41/112 © CEIOPS 2010
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Page 3 and 4: 1. Introduction 1.1. In its letter
Page 5 and 6: 2.2.2. The following recitals provi
Page 7 and 8: “[…]Where, in specific circumst
Page 9 and 10: 3.6 It is noted that in the recital
Page 11 and 12: have in place internal processes an
Page 13 and 14: not be appropriate to reduce this v
Page 15 and 16: 3.36 Hence where an (re)insurance u
Page 17 and 18: Scale 3.46 Assigning a scale introd
Page 19 and 20: “scale” that will apply in all
Page 21 and 22: circumstances of its omission or mi
Page 23 and 24: 3.81 Under these circumstances, it
Page 25 and 26: • the level of certainty i.e. the
Page 27 and 28: 3.105 All in all, at least the foll
Page 29 and 30: the chosen valuation method. If it
Page 31 and 32: development, so that it is likely t
Page 33 and 34: • As part of supervisory guidance
Page 35 and 36: case the threshold is not exceeded.
Page 37 and 38: if the threshold is not exceeded th
Page 39: principles. In following paragraphs
Page 43 and 44: 3.193 The time value of the investm
Page 45 and 46: distribution to policyholders as th
Page 47 and 48: • assume independency between ass
Page 49 and 50: company or new line of business, al
Page 51 and 52: easonable be supposed proportional
Page 53 and 54: incurred when the method is applied
Page 55 and 56: 3.261 The general rule for calculat
Page 57 and 58: • the loss absorbing capacity of
Page 59 and 60: 3.285 As a consequence of this, the
Page 61 and 62: SCR for the individual lines of bus
Page 63 and 64: • the loss absorbing capacity of
Page 65 and 66: OPRU,lob,>0 = an approximation of t
Page 67 and 68: Life insurance 3.323 With respect t
Page 69 and 70: 3.330 With respect to health insura
Page 71 and 72: eing applicable for life insurance
Page 73 and 74: 3.351 The structure of the health u
Page 75 and 76: ∆rn = the absolute decrease of th
Page 77 and 78: the methods to be used for projecti
Page 79 and 80: CEIOPS’s draft advice on the valu
Page 81 and 82: 3.392 In this context, the technica
Page 83 and 84: clearly the present difficulties of
Page 85 and 86: • Even if the undertaking’s rei
Page 87 and 88: information regarding the RBNS-clai
Page 89 and 90: CEIOPS’ Advice Simplifications re
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3.5. Quarterly calculations 3.444 A
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e to use the simplified calculation
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Annex A. Example to illustrate the
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Annex B. Some technical aspects reg
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is accurate because the payment of
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C.6. The individual elements sketch
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UMRU,lob,≥0 = max{∑ ≤ t Durmo
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E.5. The considered proxies based o
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E.14. The following criteria should
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“The gross-to-net proxy was used
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where Durmod denotes the modified d
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