- EIA - fixed annuity w non-traditional method of interest crediting
- int credited a function of some well-known index (generally)
- have a guarantee designed to meet DA SNFL to avoid being categorized as a security

- GMAV - guar min acct val - designed to satisfy SNFL
- GMAV(t) = 90%*single prem *(1.03^t) (essentially old DA SNFL min CV)

- Index Acct Value (IAV)
- IAV(t<=index period) = 100%*singleprm*prod(1+indexbasedInterest(i)) from i = 1 to t
- IAV(T') = max(GMAV(T),IAV(T)) where T' is one moment after time T and T is lenght of index period

- Components involved in calc of Index-Based Interest
- index
- index period
- index growth%
- participantion rate
- margin
- cap/Floor

- Index - equity proxy used to calc level of interest credited to IAV
- S&P 500 most common
- DJIA also used

- Index Period - similar to SC period
- usually 7-10 years
- some desings do not continue Index-based int crediting after index period
- some have rolling index periods w/ new SC periods

- Index Growth % - two main categories
- point-to-point growth % - uses only 2 close levels
- IndexGrowth% = (FinalClosingLevel / InitialClosingLevel) - 1

- average Index Growth % - based on average closing level over a peroid of time - typically 1 year
- IndexGrowth% = ([sum(daily closing levels) / # trading days] / initial closing level) - 1
- daily averaging has tendency to keep indiv volatility minimized
- typically will produce 55-60% of unaveraged calc
- can also do monthly averaging - more volatile than daily, less than annual
- still provides 55-60% of unaveraged

- IndexGrowth% = ([sum(daily closing levels) / # trading days] / initial closing level) - 1
- can also have ratcheting - means returns locked and connot be countered by poor future indexes

- point-to-point growth % - uses only 2 close levels
- Participation Rate - percentage factor applied to raw index growth %
- early plans had up to 125% participation
- if doing daily averaging, still < 100% of point-to-point growth

- Floor Return - usually 0%, can be higher
- floors on index-based int calc guar IAV never lower than SP and IAV will never decrease

- Margin - similar to participation rate < 100%, decreases index-based int relative to index growth %
- can be applied before or after participation rate
- cannot reduce int < 0%

- Cap - can be applied before or after margin
- Margin and Cap - ways to "stunt" growth measurement and allow purchase of less expensive options
- high equity volatility can be a problem for insurers funding multi-year guar EIA products
- index-based int in EIA funded by call optoin on the index
- longer period until maturity, more higher volatility affects option prices

- another strain on EIA funding when rates are low
- GMAV generally funded w/ fixed income bonds w/ remainder of prem income (after expenses) use to fund index-based int
- w/ lower int rates, not much $ left over after funding GMAV

- when int rates low and equity volatility high, if yverything has been adjusted as much as possible (w/in mktg constraints), then participation rate needs to be adjusted

- need to design products that have less restrictive SNFL min requirements
- Annual Reset EIAs - resettable components still have min guar attached to them with ability to change index-based int components as often as annually, EIA writers have a way to manage high index volatilities
- Flexible Premium EIAs - allows writers to reduce GMAV from 90% of prem @3% to as low as 65% @3%
- common => 75% of initial prem and 87.5% of additional prem
- lowers cost of funding guar, leaving more to spend on int-based index

- Lower GMAV Int Rates
- SNFL being updated to allow 1.5% as min int

- Index Growth Measurement
- averaging - smooths volatility and dampens return
- daily averaging not very common in EIA design
- monthly avg and point-to-point prevalent

- innovative return methods
- binary returns - if index increases, credit x%, 0% otherwise
- or might have tiers 0%, 3%, 6% if [0,5%) -> 3% [5%,infinite) ->6%

- highwater mark - instead of using two end points, use starting point and highest point during period

- binary returns - if index increases, credit x%, 0% otherwise
- Customer Choice
- index choice - client chooses index to participate in
- index growth measurement - client chooses avg or point-to-point
- fixed int - client chooses fixed rate rather than indexed rate
- fund transfer - client can have several options elected adn move money between them

- Inducements to Purchase
- premium bonuses, sometimes spread over index period

- GMAV alternatives
- instead of 90% @ 3%, 100% @ 2% w/ SC
- designed w/ mktg in mind
- example w/ SC = 10%-0 over 10 yrs, 100%@2% w/SC >= 90% @ 3% so SNFL not a problem

- averaging - smooths volatility and dampens return

- EIA Funding
- 1st - how will product be funded
- traditional annuity - credited rate = inv earning rate - margins for expenses and profits
- EIA funding - premium = GMAV costs + PV expenses/profits + index-based Int budget
- credited rate - two elements - GMAV adn Index-based int component
- for s/t guarantees, GMAV funding can be rolled into pricing spread
- rather than managing option program w/ budget determined up-front, application of traditional spread pricing to EIAs is more realistic
- Net Earned Rate - Pricing spread = hedging budget
- actual option purchase = notional * option cost
- notional for 1st year is prem, for future years, IAV

- several factors can affect ability of hedge budget to fund significant index-based int levels for future years
- reinvestment rates cound incr/decr teh net earned rate which would change the hedge budget
- actual Index-based Int credited affects future levels of IAV
- high int means budget has to cover higher amounts

- high future equity volatility causes higher option costs
- high future risk-free rates cause higher option costs
- high option costs in any year during an index period can strain option budget

- Funding Index-Based Interest
- early EIA writers used OTC equity options to exactly match index-based int they were giving to customers
- designs evolved and OTC deals no longer absolutely necessary
- two major forms of hedging - static and dynamic
- static hedging - synonymous w/ buy and hold and ofter involves OTC options
- most common static hedge today: purchase of a call spread option on teh index
- actually 2 trx - puchase plain vanilla call option adn sale of call option w/ strike = cap rate of liability being hedged

- B/S call option pricing formula: call option price = S(0) - N(d(1))-k*e^(-r(f)*t)*N(d(2))
- d(1) = (ln(S(0)/k) + (R(f)+ (sd^2)/2)*T) / (sd*sqrt(T))
- d(2) = d(1) - sd*sqrt(T)
- S(0) - Initial Security Price
- k - strike price
- r(f) - risk free rate
- sd - volatility
- N() cumm PDF for std Normal dist

- decide on funding ratio
- usually < 100% b/c lapses (assuming not vested @ surr)
- assume too low a lapse rate, stuck w/ extra options
- too high - not enough

- economies of volume necessary on OTC b/c high fixed cost

- most common static hedge today: purchase of a call spread option on teh index
- Dynamic (delta) hedging
- involves monitoring the delta of the liab portfolio and holding a changing position in index via futures or other instruments
- disadvantages:
- higher trx costs b/c of frequent position changes
- no downside protection

- static hedging - synonymous w/ buy and hold and ofter involves OTC options
- Other EIA pricing Considerations
- customer choice - might not have enough in each option to offer economies of scale in hedging program
- index return method complexities
- no guarantees that any dealers willing to price deals w/ complex return designs

- policy guarantees - multi-year guarantees currently not attractive
- might be attractive if future int rates increase and volatility decreases and option dealers willing to sell l/t options

- GMAV funding
- necessary to fund GMAV w/ fixed int rate bond fund
- evaluate risks of default and int rate risk

- int rate risk important to consider w/r to lapses

- necessary to fund GMAV w/ fixed int rate bond fund

- Reserving

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