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average costs generated with the probability weighted deterministic projection of the assets. The connection to market consistent prices and arbitrage-free valuation is achieved by ensuring that the probability weighted deterministic projections reproduce observed market prices for some representative assets. 3.187 In most of insurance contracts the complexity of insurance options and guarantees and other features such as management actions commonly creates interdependent risk factors. Modeling risk factors when independencies are observed and estimated leads to prefer appropriate methods based on stochastic simulations, as they can deal appropriately with very complicated liability structure such as for instance pathdependent behaviour. 3.188 Therefore for less advanced undertakings closed form approach are generally more practical. However, they are only suitable in special circumstances due to the various simplifying assumptions such as the existence of complete financial markets, the stochastic dynamics of the underlying assets follow a geometric Brownian motion, use of dynamic hedging, etc. which may distort the results. 3.189 The possible simplification for financial options and guarantees is to approximate them by assuming a Black-Scholes type of environment, although its scope should be carefully limited to those cases where the underlying assumptions of such model are tested. Additionally, even stochastic modelling may require some simplifications when facing extremely complex features. This latter may be developed as part of level 3 guidance. 3.2.2.4. Investment guarantees 3.190 Some unit linked products guarantee a minimum benefit at maturity in absolute term or as an annual constant guaranteed rate of return at the issue of the contract. At maturity policyholder will receive an amount corresponding to the index but not less than the guaranteed amount. ~ 3.191 The random payout at maturity V ( T ) could be given by the formula ~ V ( T ) = max ~ ~ { S ( T ), G( T ) } 42/112 ~ { S ( T ) − G( T ); 0} ; ⎪⎧ G( T ) + max ( Calloption) ⎪⎫ = ⎨~ ~ ⎬ ⎪⎩ S ( T ) + max{ G( T ) − S ( T ); 0} ; ( Putoption) ⎪⎭ ~ where S ( T ) is the random account value at time T and G (T ) the guaranteed payment at maturity. 3.192 The time value of investment guarantees IG assuming put-call parity for European options (assuming thus implicitly Black-Scholes framework), using risk free discount rate and taking the expectation of the random payout at maturity with respect to the risk-neutral measure can be written as: ⎧Guarantee + IntrinsicValueOfExtraBenefits + OptionTimeValue ⎧Call _ option IG = ⎨ = ⎨ ⎩UnderlyingAsset + IntrinsicValueOfGuarantee + OptionTimeValue ⎩Put _ option © CEIOPS 2010
3.193 The time value of the investment guarantee shows the expected amount that should be held in addition to the underlying assets to be able to deliver the benefits due to the investment guarantee. In the call option approach the IntrinsicV alueOfExtraBenefits corresponds to the amount the call option is in-the-money if it would be exercised immediately and the OptionTime Value captures the potential to receive further extra benefits in the future due to the random fluctuations of the underlying assets. In the put option approach the IntrinsicV alueOfGuarantee corresponds to the amount the guarantee is in-the-money if it would be exercised immediately and the OptionTime Value captures the potential for the cost to change in value (guarantee to bite further) in the future, as the guarantee move (related to the variability of the underlying assets) into or out-of-the-money. 3.194 Introducing management actions and discretion into the valuation complicate valuation considerable. In practice past investment returns, decisions and especially the solvency position of the undertaking will usually have a significant impact on the management actions and decisions and create complex path-dependent processes not suitable for closed-form modelling. 3.195 The non-exhaustive list of possible simplifications for calculating the values of investment guarantees includes: • assume non-path dependency in relation to management actions, regular premiums, cost deductions (e.g., management charges,...), • use representative deterministic assumptions of the possible outcomes for determining the intrinsic values of extra benefits, • assume deterministic scenarios for future premiums (when applicable), mortality rates, expenses, surrender rates, ..., • apply formulaic simplified approach for the time values if they are not considered to be material. 3.2.2.5. Other options and guarantees 3.196 Life insurance contracts may include different types of options and guarantees. Therefore it is rather impossible to give detailed valuation approaches that would be suitable for all possible options and guarantees. 3.197 With regard to principle of proportionality as an interim approach one could ignore those options and guarantees which are not material (e.g., it could be assumed that options with low probability of being exercise – heavily out of the money - and with low impact if exercised do not exist at all). 3.198 However some of them could be valued with similar techniques as those for the surrender option and some of them can be valued with similar techniques as those for the investment guarantee. 3.199 Where the surrender options valuation approach or similar techniques as those for the investment guarantee cannot be sensibly applied for the valuation of particular type of option or guarantee a last resort for those would be a subjective ad hoc valuation. 43/112 © CEIOPS 2010
Page 1 and 2: CEIOPS e.V. - Westhafenplatz 1 - 60
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 and 40: principles. In following paragraphs
Page 41: sign ( x) = −1 if x < 0 . 3.179 E
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
Page 91 and 92: 3.5. Quarterly calculations 3.444 A
Page 93 and 94:
e to use the simplified calculation
Page 95 and 96:
Annex A. Example to illustrate the
Page 97 and 98:
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
Page 109 and 110:
“The gross-to-net proxy was used
Page 111 and 112:
where Durmod denotes the modified d
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