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2.ContinuedPolicy Year12345 Lapse rate (%)2010543Recommend the expected lapse assumption to be used for the re-pricing ofthis term product.Commentary on Question:Candidates did well on listing factors affecting lapses; some struggled withconnecting the renewability period and shock lapses.(i) (ii)Policy Year: rates usually start high then decrease rapidly the firstseveral years and level off after 5-10 yearsPolicy Size: larger policy size generally has lower lapse ratesFrequency and Method of Premium Payment: more frequent premiumpayments have higher lapses; automatic withdrawals will have lowerlapses than directly billedClass variation: can vary by issue age, risk class, gender, tobaccoTerm products have higher lapses than Permanent ProductsCompensation: a level compensation pattern will promote persistencycompared to a heaped structure that will have more higher earlierlapsesA shock lapse rate at the end of the guaranteed renewablity period (20years)Rate of Premium Increase: The larger the increase in premium thelarger the higher the lapse rateWaiver of Premium Benefit will help decrease lapsesFor policy years 1-20 the lapse rates from the lapse study seemappropriate. Term products have a high first year lapse then grades downto an ultimate lapse rate. After year 20 because of the renewal period ashock lapse is expected; the size of the shock lapse will be in proportion tothe size of the premium increase. It can also be appropriate to split thelapse assumptions by gender, underwriting class, age or policy size.ILA LP Spring 2014 SolutionsPage 8

2.Continued(b)(i)Evaluate, and recommend ways to improve if applicable, the credibility ofbest estimate mortality rate of 0.005/year for the term policy based on a95% confidence level.(ii)Recommend changes, if any, to the best estimate mortality rate of 0.007per year for a permanent policy.(iii)Calculate the charge to be included in the pricing of the term product toaccount for the conversion feature, assuming converted policies are notincluded in the mortality experience studies, and the Net Amount at Riskis equal to the Face Amount in all yearsCommentary on Question:Part i) most candidates were able to correctly calculate the confidence intervaland recognize that because of the wide range it has low credibility.Part ii) most candidates were able to connect that because of selective lapsationthe best estimate mortality should increase. Many candidates had errors whencalculating the actual mortality rate.Part iii) wasn’t well understood by many candidates and they weren’t able tocorrectly calculate the conversion charge.(i) For a 1000 policies Expected claims nq 5/1000 * 1000 5Variance npq 1000 * (1-.005) * .005 4.97595% Confidence level of the mortality rate Expected claims /- 1.96(Var) (1/2) 5 /- 1.96 * (4.975) (1/2) 5 /- 4.37 (.63, 9.37)note: can either be per 1000 or claim amountPoor credibility due to the high variance and small amount of dataTo improve credibility: can combine company data with industry data or other internal datafrom a similar product can combine data with other internal data from a similar product Use more years of experience(ii)qdNorm 9/1000qdSelect 7/1000qwNorm 3%qwExtra .09 - 0.03 0.06SelectPct 75%qwSelect (0.09-0.03) * 75% 0.045qwNon-select 0.06-0.045 0.015ILA LP Spring 2014 SolutionsPage 9

2.ContinuedqdActual {(1-qwNorm-qwNon-Select)qdNorm-qwSelect*qdSelect} /{1-qwNorm-qwExtra}qdActual {(1-0.03-0.015)*9/1000-0.045*7/1000} / {1-0.03-0.06} 0.0091Recommend to increase best estimate mortality due to selective lapsation.(iii)qdconvterm ([x] t s) mortality rate for converted policies originallyissued at age x, converted at duration t of the term policy, inforce atduration s of the permanent policyqdperm ([x t] s) mortality rate for permanent policies issued at age[x t] and inforce at duration s.NAR(s) Net Amount At Risk at duration s for the permanent policyThe cost of extra anticipated mortality in year (s) after conversion NAR(s) * [qdconvterm([x] t s) - qdperm([x t] s)]The charge included in the pricing is the pv of the cost of extra mortality NAR(s) * [qdconvterm([x] t s) - qdperm([x t] s)] * annuity factor (.009 - .007) * 10 .02 per 1000 of Face Amount (or NAR since theyare equal)ILA LP Spring 2014 SolutionsPage 10

3.Learning Objectives:2.The candidate will understand the design and purpose of various product types,benefits and features.3.The candidate will understand the relationship between the product features, theirinherent risks, and the selection of appropriate pricing assumptions, profitmeasures and modeling approaches.Learning Outcomes:(2a) Describe in detail product types, benefits and features.(2c)Evaluate the feasibility of the recommended design.(3a)Identify and explain the setting of an appropriate assumption for productcharacteristics such as the following:(i)Riders(ii)Policyholder dividends(iii) Equity linked(iv)Embedded options(v)Return of premium(vi)Secondary guarantees(vii) Payout annuity benefits(viii) Crediting methodology(ix)Other non-guaranteed elements.(3b)Identify and explain the setting of an appropriate assumption for risk and otherfactors such as:(i)Available experience data(ii)The marketplace(iii) Underwriting(iv)Distribution channel characteristics(v)Reinsurance(vi)Expenses (fixed, variable, marginal)(vii) Taxes (income and premium)(viii) Investment strategy(3c)Analyze results and recommend appropriate action from an array of risk andprofit measures such as: Statutory, GAAP, Return on Equity, Market ConsistentPricing, Embedded Value(3e) Describe when a stochastic model should be used, its advantages anddisadvantages, how to build it and how to analyze its resultsILA LP Spring 2014 SolutionsPage 11

3.ContinuedSources:ILA-D116-10: Variable Annuities, Kalberer and Ravindran, Chapter 10 Overview ofCommonly Used Risk Management StrategiesHardy, Investment Guarantees, Chapter 6 Modeling the Guarantee LiabilityILA-D105-07: Life and Annuity Products and FeaturesStochastic Modeling: Theory and Reality from an Actuarial Perspective, IAA – Intro,various parts within Sections 1-4Commentary on Question:In general, candidates dumped the relevant lists on the page but failed to actually answerthe question, i.e. the specific risks of the new Vampire product. Too much effort wasspent on listing general hedging risks instead of the actual product risks. Most candidatesdid not demonstrate that they could apply what they learned in the source material to theactual question.Solution:(a)Describe risks of the new VA product. Recommend strategies to manage thoserisks.Commentary on Question: This part of the question was answered poorly bymost candidates. Many people wrote down long lists of general risks, oftenwithout any description of what they mean or how they relate back to the Vampireproduct. In order to receive full credit, candidates were expected to drawconnections between the risks described in the source material and the productinformation given in the question.The Vampire product exposes ECC to pricing risk – the risk of losses to thecompany if the GMDB and GWMB are priced too aggressively or if the risks arenot managed appropriately.The large number of funds available, especially foreign funds which are riskierand more volatile, will increase the cost of the GMDB and GMWB, dependingwhat fund allocation the policyholder chooses.The Vampire product also exposes ECC to policyholder behavior risk due thedesign features of the product. The GMWB feature allows policyholders tochoose when and how much to withdraw. The reset feature is also an impliedoption that the policyholder can use once per year, further increasing the risk ofthe product. These policyholder behavior options are risky to ECC since arational policyholder will optimize their own benefits in a given economicscenario to the detriment of ECC.ILA LP Spring 2014 SolutionsPage 12

3.ContinuedECC has the following options to manage the risks: Naked or no risk management Static or semi-static hedging Implement a dynamic hedging strategy ReinsuranceECC can also manage risk through the product design. The following productdesign changes could be made to reduce risk: Reducing the amount or number of guarantees Setting a deferral period for the withdrawals Removing the reset feature or reducing the frequency of resets Limit the number of funds available or use index funds which are easier tohedge Set constraints on asset allocation(b)(i)Describe modeling techniques for all policyholder behavior assumptionsrelevant to Vampire.(ii)Explain limitations surrounding the modeling techniques.(iii)Critique these assumptions and recommend appropriate changes.Justify your answer.Commentary on Question:This part of the question was answered poorly overall. Most candidatesrecognized that lapse rates should be modeled dynamically, but few peoplediscussed the other policyholder behavior assumptions. Some candidates alsoconfused economic assumptions with policy holder behavior assumptions.Candidates generally understood that term assumptions were not appropriate forVampire product and did a good job recognizing the differences.(i)Policyholder behavior varies with the perceived value or in-the-moneyness(ITM) of the guarantees. ITM for GMDB Guarantee Value / Account Value ITM for GMWB PV benefits / Account ValueThe following policy holder behavior assumptions need to be modeleddynamically:ILA LP Spring 2014 SolutionsPage 13

3.ContinuedLapsesLapse rates vary by ITM of the guarantees and, therefore, require dynamicmodeling. Lapse rates should decrease when ITM increases, and lapserates should increase when ITM decreases. Start with a base lapse rateand apply a dynamic lapse adjustment factor.Dynamic lapse base lapse * λwhere λ min [ cap , max { floor, 1 - sensitivity * ( GV / AV - triggerpoint ) } ]The dynamic lapse adjustment factor can be one sided or two sided One sided is capped at 1 (i.e. Only serves to decrease base lapse rate) Two sided can increase lapse rate beyond base lapse (considered lessconservative)Withdrawal AmountWithdrawal amount can be modeled with 2 methods (or a combination ofboth): Dynamic modelingo Withdrawal is based on ITM, age, qualified / non-qualified status,distribution channel and product incentiveso A single dynamic formula is usually not sufficient Cohort modelingo Policies are split into different cohortso Withdrawal behavior varies by cohort, e.g. Cohort A withdraws0%, B withdraws 100% and C withdraws 80%Withdrawal TimingWithdrawal timing can be modeled in one of 2 ways: Can assume that the policyholder withdraws right away or when firstavailable (if there is a waiting period) Can model using cohorts similar to cohort modeling described forwithdrawal amount (i.e. each cohort has a different withdrawalschedule)Asset AllocationAssume a static asset allocation as it would be too complicated to modeltransfers across 200 different funds.Reset UsageResets can be modeled in one of 3 ways: an optimal reset usage, i.e. reset at the best possible time (conservativeassumption) reset on a fixed schedule, e.g. reset on policy anniversaryILA LP Spring 2014 SolutionsPage 14

3.Continued reset whenever reset is available, i.e. whenever AV 1.05 GV andreset has not been utilized for the year Dynamic formulas may break down due to unforeseen policyholderreactions and irrational behaviorLack of credible data (dynamic models have not been validated)Experience studies need to be done on a regular basisLife events will play a role regardless of market performance, e.g. alapse / withdrawal may be driven by need instead of ITM of theguaranteeDynamic modeling relies on adequate stochastic modelso ITM drives dynamic formulas and ITM depend on economicscenarioso It is important to choose a good interest / equity modelo Simplifications such as cell grouping may distort dynamic models(ii) (iii)Mortality Tables Vampire will not require underwriting T10 policyholders will have different mortality rates due to differentunderwriting criteria T10 mortality tables will be split into different categories: M/F,premium bands, smoker / non-smoker etc It is not adequate to use T10 mortality tables, adjustments have to bemade.Renewal Expense VAs have higher administrative expenses than Term products due too Daily calculation of unit valueso Infrastructure required for timely processing of all transactiono Service cost e.g. customer service centre, frequent updates onaccount balance, etc Using the same unit expense as Term 10 is not adequate It is not adequate to use T10 renewal expenses. Need to increase theT10 expenses reflect the higher administrative expenses of VAs.Inflation Rate Inflation will determine future increases in renewal expenses. It isadequate to use the same inflation rate since this is not a productspecific assumption.ILA LP Spring 2014 SolutionsPage 15

3.Continued10% Annual Return Stochastic modeling is required since ITM of the guarantees varies byeconomic scenario. An Economic Scenario Generator (ESG) should be used to forecastreturns The ESG may involve the joint simulation of many variablecombinations such as:o multiple equity indices,o several points on the yield curveo currency exchange rateso inflation rateso yield curves in multiple countrieso historical and implied volatilities(c)With respect to projecting underlying stock returns:(i)Evaluate the use of both lognormal and Wilkie models.(ii)Recommend a more appropriate model. Justify your recommendation.(iii)Describe other steps for implementing a stochastic modeling process.Commentary on Question:This part of the questions was generally answered well. Many candidates wereable to list the pros and cons of both the lognormal and Wilkie models. Toreceive full credit, the candidate needed to relate the pros and cons back to theVampire product described in the question, and most candidates failed to do this.The majority of candidates received full credit for recommending the RSLN modelas a more appropriate model, and for listing the steps required for implementinga stochastic modeling process.(i)The lognormal model is simple and tractable. It provides reasonableapproximations over short time intervals, but is less appealing for longerterm applications. Vampire’s GMDB and GMWB features are long termin nature, making the lognormal model inappropriate.Also, empirical studies indicate that the lognormal model fails to captureextreme price movements and that a distribution with fatter tails should beused. The model also fails to capture volatility bunching and doesn't allowfor autocorrelation of the data.ILA LP Spring 2014 SolutionsPage 16

3.ContinuedTherefore, it would not be appropriate for ECC to use a lognormal modelto project stock returns underlying the Vampire product.The Wilkie model is a multi-variate model and was developed for longterm applications. The problem with this model is that it was designedand fitted as an annual model and is an unsatisfactory approximation forcontracts with monthly cash flows. This is important for the Vampire VAsince there are reset opportunities for the policyholder to increase theguarantee any time during the year. Also, annual models are tooinfrequent to use for dynamic hedging strategies.Therefore, it would also not be appropriate for ECC to use a Wilkie modelto project stock returns underlying the Vampire product.(ii)Recommend the Regime-Switching Lognormal Model (RSLN). This model maintains the attractive simplicity of the lognormal modelsuch as mathematical tractability, but more accurately captures themore extreme observed behavior. It is also one of the simplest ways to introduce stochastic volatility andallow you to reflect the fact that the market may switch betweenstable, low-volatility periods and more unstable high-volatility periods. The RSLN model also provides a good fit to the data relevant toequity-linked insurance.(iii) Describe the goals and all of the intended uses of the model.Decide if stochastic modeling is necessary or if an alternative approachwill yield equally useful results.Determine which of the projection techniques should be used, if astochastic model is deemed appropriate.Decide on the risk metrics (VaR, CTE, etc.) to use.Establish which risk factors need to be modeled stochastically.Determine the approach for modeling these risk factors in terms ofwhich distributions or models should be used, and how to parameterizeor fit the distributions.Determine the number of scenarios necessary to reach the point atwhich additional iterations provide no additional information about theshape of distribution.Calibrate the model.ILA LP Spring 2014 SolutionsPage 17

3.Continued Run the model.Validate the model and review output.Conduct a peer review.Communicate results.ILA LP Spring 2014 SolutionsPage 18

4.Learning Objectives:2.The candidate will understand the design and purpose of various product types,benefits and features.3.The candidate will understand the relationship between the product features, theirinherent risks, and the selection of appropriate pricing assumptions, profitmeasures and modeling approaches.Learning Outcomes:(2a) Describe in detail product types, benefits and features.(3a)Identify and explain the setting of an appropriate assumption for productcharacteristics such as the following:(i)Riders(ii)Policyholder dividends(iii) Equity linked(iv)Embedded options(v)Return of premium(vi)Secondary guarantees(vii) Payout annuity benefits(viii) Crediting methodology(ix)Other non-guaranteed elements.(3e)Describe when a stochastic model should be used, its advantages anddisadvantages, how to build it and how to analyze its results.Sources:Stochastic Modeling: Theory and Reality from an Actuarial Perspective, IAA – Intro,various parts within Sections 1-4ILA-D102-07: Equity Indexed Annuities: Product Design and Pricing ConsiderationILA-D102-07: Equity Indexed Annuities: Product Design and Pricing Consideration(LO#3)Commentary on Question:Commentary listed underneath question component.Solution:(a)Calculate the percentage growth in the Index Account Value at the end of threeyears.Commentary on Question:Most candidates understood the calculations. Some candidates did not calculatethe GMAV, so full marks were not given as they failed to demonstrate the need tocompare GMAV and IAV.ILA LP Spring 2014 SolutionsPage 19

4.ContinuedGMAV0 90% (by definition)GMAV1 GMAV0 x 1.03 92.70%GMAV2 GMAV1 x 1.03 95.48%GMAV3 GMAV2 x 1.03 98.35%Index Based Interest1 Greater of 0% and Min({[(S&P1/S&P0) x ParticipationRate ] - Margin }, Cap) 5.75%Index Based Interest2 Greater of 0% and Min({[(S&P2/S&P1) x ParticipationRate ] - Margin }, Cap) 8.00%Index Based Interest3 Greater of 0% and Min({[(S&P3/S&P2) x ParticipationRate ] - Margin }, Cap) 0.00%IAV0 100.00%IAV1 IAV0 x (1 Index Based Interest1) 105.75%IAV2 IAV1 x (1 Index Based Interest2) 114.21%IAV3 IAV2 x (1 Index Based Interest3) 114.21%The percentage growth in IAV at the end of three years is 14.21%(b)Describe the criteria that must be met to use a book value valuation method on ablock of EIA business in the U.S.Commentary on Question:Not many candidates answered this part correctly. Some knew “Hedged asRequired” must be met, but failed to explain/describe the concept correctly.To use book value valuation (Type I Method, Enhanced Discounted IntrinsicMethod):"Hedged as Required" criteria must be met. Must provide ensurances that no matter how the market value of the optionsor liabilities behave, the Index-Based Interest is actually being hedged by theoptions. the market value of the options being held as hedges should also move in thesame direction and at the same magnitude as the market value of the liabilities The appointed actuary has to be able to show that any Index-Based Interest isaccounted for in some sort of hedging instrument & that no matter what theIndex Returns are, the Index Account Value is funded adequately.(c)Describe the practical considerations an actuary s

Using actual number of claims instead of expected in calculating the blended expected claims, and 3. Normalizing the expected claims using the inverse of the step 2 / step 3 . Experience Assumptions for individual Life Insurance and Annuities ILA-D106-07: Gross Premiums for Dis