- Introduction
- examples of models taht use expereince assumptions
- pricing adn repricing studies
- product design studies
- determination of reserve adequacy
- financial reporting (DAC)
- financial projections or forecasts
- actuarial appraisals

- examples of models taht use expereince assumptions
- categories of experience assumptions
- cash flow view
- 3 broad categories
- obligation or liability assumptions - mort, lapse, admin exp, taxes, div and int crediting strategies
- asset assumptions - earnings rates, default, inv expenses, inv strategy
- scenario assumptions - scenario(s) being analyzed

- 3 broad categories
- degree of conservatism
- best estimate or include PAD - depends on how used
- acctg rules may require w/ or w/o PADs
- acctg/regulatory rules may prescribe assumption (may or may not be conservative)

- best estimate assumptions represents actuary's judgement as to most likely outcome
- if in doubt - pick more conservative choice
- in fin reporting context - conservative assumption means w/ higher liability or smaller asset
- in pricing context - lower benfit or higher charge to customer

- PAD should consider degree assumption is at risk in total and by duration
- adjusting a PAD shoudl make result more conservative
- prescribed assumptions usually contain implied PAD
- if doesn't seem conservative, test w/ realistic assumptions

- best estimate or include PAD - depends on how used

- cash flow view
- Establishing Experience Assumptions
- steps necessary to develop assumptions
- identify assumptions req'd
- determine structure of each assumption
- analyze experience and trends in experience for each assumption
- review and adjut set of all assumptions for reasonableness, consistency, and appropriateness
- document assumptoins
- monitor experience and update assumptions

- Identify Assumptions Req'd
- depends on model - different simplifying assumptions based on model purpose
- common assumptions
- obligation (liab) assumptions
- mort/morb rates tax rates
- lapse rates incidence and level of prem payments
- expense rates reins results

- Asset Assumptions
- inv earnings rate default rates
- capital gains rates inv expenses

- Scenario Assumptions
- specified set of deterministic int rate scenarios
- stochastically generated int rate scenario
- set of possible economic scenarios
- set of sensitivity tests

- obligation (liab) assumptions

- Determining Structure of Each Assumption
- can be very simple or very complex depending on model and purpose and materiality
- assumptions determined for particular experience class
- purpose of grouping - establish homogenous groups for analysis expected to generate similar experience
- experience class consists of all contracts that
- similar type (UL/Term/WL/etc)
- same structure of charges/benefits
- issued over continuous time period
- similar mktg objects

- different assumptoins might have different classifications
- experience class used for pricing shoudl remain in tact - OK to merge w/ another class, but not split
- key principles to decide on complexity of assumption structure
- differences in exp assumptions shoudl reflect differences in experience
- ok to vary mort by IA/sex/smoker/dur
- ok to vary lapse by mode of payment

- if no differences in an assumption, don't split
- definition of class s/b objective and easily understood
- # class s/b practical and cost effective
- balance between precision and expense

- differences in exp assumptions shoudl reflect differences in experience

- Analyze Experience adn Trends in Expereince for Each Assumption
- evaluate credibility of data
- homogenity of data - ex. split out substd from std for mort
- reasonability of methods and results

- Evaluate quality of data
- understand the data and how it will be used
- possible alternate sources of data - balanced w/ practicality
- can it be obtained in a reasonable time at a reasonable cost

- appropriateness of data - recent? limitations? biases?
- reasonableness and comprehensiveness of data - internally and externally consistent

- possible alternate sources of data - balanced w/ practicality

- understand the data and how it will be used
- Use Actual or similar experience
- s/b that of class of business assumption applies to, provided experience is determinalbe, available, and credible
- aka actual experience

- if actual experience not determinable, available, or credible, base assumptions on
- "similar expereince" from same company
- similar business other cos
- other sources
- in this order

- s/b that of class of business assumption applies to, provided experience is determinalbe, available, and credible
- Reflect Trends in Exp as Appropriate
- evaluate trends and make judgemenet whether trends will continue
- ok to ingore trends if doing so is conservative or not permitted in regs

- Reflect Company and external Factors
- review company business practices and reflect in assumptions
- esp true if company practices changed recently or will shortly or if relying on other co data w/ diff business practices
- mort rates shoudl reflect selection criteria for each rating class
- freq of u/w exceptions, reinstatement reqs, etc

- inv assumptions shoudl be consistent w/ limits on asset type, quality, duration, convexity
- different assumptions for each segment if appropriate

- Sensitivity Test Assumptions
- test to show impact of probable deviations that could have material financial effects
- standard stat tests or historical exp for likely range

- evaluate credibility of data
- Review & Adjust Set of all assumptions for Reasonableness, Comsistency, & Appropriateness
- generally not a single assumption but a range fo assumptions that are consistent w/ underlying data
- set of assumptoins s/b comprehensive and internally consistent
- consistency checks
- inflation assumptions for expenses consistent w/ inv earning assumptions
- mort anti-selection assumptions consistent w/ lapse assumptions
- u/w exense and mort rates consistent w/ u/w practices
- inv expenses and returns consistent w/ inv policy

- model validation chekcs
- does model produce aggregate reserves consistent w/ most recent valuation
- does model produce cahnge in reserve in future years consistent w/ past trends in actual reserves

- Document Assumptions
- Documentation of experience assumptions should cover
- what the assumption is
- data underlying the assumption
- how assumption was developed
- how to use the assumption

- Documentation of experience assumptions should cover
- Monitor Experience and Update Assumptions
- need ot be reviewed and updated on a regular basis
- just because you reviewed doesn't mean you have to change it

- steps necessary to develop assumptions

- normally of form of table of rates varying by IA and duration since issue
- q(x,t) = q(y,s) if x+t = y+s adn t>n and s > n (ultimates s/b in sync)
- q(x,t) <= q(y,s) if x+t = y+s and t<s and t<= n (same AA, qx for one closer to issue)
- ANB <=> ALB - normally just average rates @ adjacent ages
- q_ALB(x) = 1/2*(q_ANB(x) + q_ANB(x+1))
- q_ANB(x) = 1/2*(q_ALB(x-1) + q_ALB(x))

- M/F smoker/nonsmoker have signficantly different mort rates and relationship si NOT a simple multiple
- other distinctions usually just expressed as a multiple or other simple mod
- credibility of data plays role in whether experssed as multiple or completely different table
- common variations in mort class
- risk selection class
- selection process - simplified/guar iss blood/no blood
- size of policy - usually lower mort for higher face
- misc - mktg method, plan type, policy provisions, other

- Analyzing Experience
- Credibility
- confidence intervals - convenient way to judge credibility of co's experience
- 95% conf interval (of expected claims) E+/-1.96(VAR^.5)
- E = expected = nq
- Var = npq (for claims)
- 95% conf interval of mort rate [E+/-1.96(VAR^.5)]/n

- confidence intervals - convenient way to judge credibility of co's experience
- Risks Covered
- normally studies done on "std" issues and exclude
- policies not subject to normal u/w stds (GIO/group conv/term conv/simpl/guar iss)
- substd policies
- policies inforce under ETI/RPU
- multple life policies
- sep studies for excluded policies
- then use a multiple or other mod to std table

- multiple life mort generally derived from single life mort assumptions

- normally studies done on "std" issues and exclude
- Mortality Studies
- anniv to anniv studies and calendar year studies
- ways into study - A-inforce @ BOP and N - new entract (age x+ r)
- ways out - B - inforce EOP W - w/d (age x+s) D- death
- use Balducci assumption for dist of deaths
- q(x) = D / [A + (1-r)N - (1-s)W]
- exposure for a cell - seriatim or aggregate
- if aggregate, use mid-year assumption for entry/w/d
- 6 ways to get through study and their exposure
- (A,W) s
- (A,B) 1
- (A,D) 1 <- no deduction for deaths)
- (N,W) s-r
- (N,D) 1-r
- (N,B) 1-r
- sum up indiv exposure to get total exposure
- aggregate - exposure = 1/2[P(x,z) + P(x,z+1) + D(x,z)]
- using calendar year-end inforce data and deaths

- Other Aspects of Mortality Studies
- need to look at several years for credibility concerns
- too long a study might not be representative of recent experience
- usually 5 years of data
- usually policy count or amt (or both ) study basis
- count basis
- distorted by multiple policies by same insured
- if overall # pols in large, s/b not an issue

- amount basis
- shows financial impact
- generally preferred
- credibility not as high as count (b/c of variation in amts of ins)

- Enhancing Credibility
- grouping IA & durations together can enhance credibility
- similar to adding years to study
- grouped results smoothed
- A/E analysis can also help credibility

- Credibility of A/E Ratios
- Var(expected # claims) = sum(pq)
- 95% conf interval of claims (CIC)
- E[# claims] +/-1.96*sqrt(var(# claims))

- 95% Conf Interval of mort ratio = CIC / E[# claims]
- Var(amt claims) = sum(A(i)^2*q(i)*p(i)) where A is Amt of ins
- E[amt claims] = sum(A(i)q(i)
- conf interval - amt of claims E[amt claims]+/-1.96*sqrt(var(amt claims))
- variation in policy size can increase size of confidence interval

- Adjusting Mortality Tables for Special Situations
- some mort assumptions derived from mort tables, not developed by study
- multiple life/substd
- Term conversions
- expected mortality is higher than regular u/w polices and needs to be accounted for in pricing and other models
- include term conv in regular mortality study and have all permanent policies share extra mort cost
- include charge in term pricing for PV of cost of extra anticipated mort on perm policy
- (q_c([x]+t+s) - q_s([x+t]+s)*NAR(s) <- cost of extra mort in year s after conv

- can do sep study on converted policy mortality if enough data
- extra mort can be estimated by making assumption about degree of anti-selection

- Anti-Selection
- several situations when PO can be expected to antiselect
- when ART rate @ renewal is higher than newly u/w policy
- if healthy enough to qualify for new policy, they can be expected to do so & those that cna't will keep policies

- when ART rate @ renewal is higher than newly u/w policy
- conservation of deaths
- A - portion of policies that lapse @ dur r to buy new policy @ x+r
- A*q(x+r,t-r) + (1-A)q_AS(x,t) = q(x,t)
- A(s) - portion of policies that lapse @ s to buy new @ x_s
- q_AS(x,t) = [q(x,t) - sum(A(s)q(x+s,t-s))] / [1 - sum(A(s))] where sum are s=1 to t

- several situations when PO can be expected to antiselect
- Blending Tables
- sometimes necessary to combine two tables to get a single blended table (ie Unisex)
- usually better to blend survival table (lx) instead of mort tables (qx)

- Adjusting Similar Experience
- factors to consider if using similar experience b/c actual not credible
- quality fo co u/w relative to experience underlying other experience
- distribution channels - more antiselection in brokerage than career
- anti-selectin from excessive lapses
- u/w reqs for preferred or substd risk classes
- reins quotes on the business

- if need a table in a country where no study of insured lifes mortality exists
- also consider
- starting w/ general population mortality studies
- quality of data
- cause of death info
- abiltiy to do medical u/w
- ability to contest claims
- liklihood of wars, epidemics, or natural disasters

- also consider

- factors to consider if using similar experience b/c actual not credible

- Credibility

- Stucture
- generally by duration since policy issue
- may also vary by
- IA
- freq of prem payment
- policy size
- plan type (term/WL/UL/annuity)
- mktg method
- market
- for perm, 1st year usually higher than renewal
- term and annuity - often shock lapse tied to product design
- annuity - when SC expires
- term - when level prem period ends

- lapse rates often vary by scenario for CFT or option pricing b/c of different interest rates
- expressed as a formula that adjusts base rate to reflect
- delta mkt and credited rate
- size of SC

- expressed as a formula that adjusts base rate to reflect
- Lapses assumed to occur on prem due dates
- "lapse skew" might be appropriate depending on distribution of business

- Analyzing Experience
- Credibility
- generally less of an issue for lapses than for mort
- generally less refined assumptions than for mort (helps w/ credibility of data)
- lapse rates generally higher (helps w/ credibility of data)
- confidence intervals - calced same as mort

- Lapse Studies
- mechanics same as mort - except lapses & deaths switch spots in calcing claims and exposures

- Factors Affecting Lapse Rates
- product design
- policy size
- dist channel - brokerage higher lapses than career due to shoping
- effectivness of company conservation programs
- if lapse rates expressed as formula that varies by int rate scenarios
- significant judgement involved in setting parameters
- sensitivity of lapse to int rate usually varys by
- product type - DAs more sensitive than trad life
- dist channel - stock broker business more sensitive than agent sold

- Types of Lapses
- usually include
- termination w/o value b/c failure to pay prems
- cash surrenders
- transfers to ETI/RPU

- others that depend on study or purpose of assumptions
- term conversions
- if term conv charges attributable to term policy, need a sep study
- if cost absorbed by new policy, count as lapse

- partial w/d - usually included in lapse rate unless product design has provision for free partial w/d
- premium persistency - actual to target/billed from flex
- termination w/o value b/c policy loan > CV

- term conversions

- usually include

- Credibility

- Structure
- deterministic models generally use one of two appraoches
- portfolio avg
- Inv generation method (IYM)

- for IYM
- fixed prem policies grouped by issue year
- flex prem polices group prems by mo rec'd

- nv income assumptions generally net (after expenses & defaults)
- Policy loans can be asset CF or liab CF
- for deterministic models - generally aggregated w/ other investments
- therefore also need assumptions for
- policy loan int rate
- policy loan expenses
- policy loan utilization rate

- therefore also need assumptions for
- if model has multiple int rate scenarios, policy loans generally modeled as liab CF w/ utilization rate that varys by scenario
- how many?
- specified by client/regulation?
- generated by stochastic model
- # scenarios depends on relative importance of asset risk and practical concerns (such as model runtime)
- for each scenario, int rates can vary by
- time
- asset class
- asset quality
- credit risk

- Inv returns can be measured on a book ro mkt value basis
- also need assumptions for
- mix of existing assets by asset class and maturity
- reinvestment and disinvestment strategy

- for deterministic models - generally aggregated w/ other investments

- deterministic models generally use one of two appraoches
- Analyzing Experience
- int rate determined as inv income from block / avg assets in block
- i = 2*I/(A+B-I)

- for "new money" rate - usually some benchmark rate + spread
- total returns on a mkt value basis - needs to realized and unrealized g/l
- r = (B-A-C)/(A+C/2) - C is net cash flows, A&B - mkt values

- mutual funds often calc daily and if assume that all CF @ end of day
- r = (B-A)/A

- if evaluating rates of return over time
- time-weighted return - geometric mean of rates of return
- dollar-weighted return - level rate of return earned taking into acct timing of CF

- int rate determined as inv income from block / avg assets in block

- Structure
- generally split between direct (aka marginal) expenses and indirect expenses
- certain expenses can be direct or indirect depending on model and purpose of model
- also split between acq, maint and overhead

- Analyzing Experience
- Units
- unit expense assumption = expenses / # untis
- experience study looks @ expenses by calendar year
- pricing
- policy year expenses
- usually charge expenses @ either BOY, EOY or midYear
- need appropriate unit count based on when expense is charged
- expenses charged BOY -> count = (A+B+N)/2
- midyr -> (A+B)/2

- expenses charged BOY -> count = (A+B+N)/2

- Expense ALlocation
- important to understanc how co allocates expenses to LOB
- some expenses clearly associated w/ particular product or LOB
- other not so clearly - several methods to allocate
- first need to split total expenses into major components
- once categorized, allocate
- transaction or item counts
- transfer costs
- employee time allocations
- indexed based allocations (allocated by policy count or prems)

- Projecting Expenses
- future unit expenses depend on estimating of total level of expenses an dcount on which unit expenses based
- projection shoudl reflect
- historic trends
- expected future volumes of business
- expected inflation rates
- how expenses vary w/ changes in business volume (fixed/varaible/step rate)
- impact of any planned business changes

- Units

Copyright © 2004 Steve Welander.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled 'GNU Free Documentation License'.