Study Notes and Published Refences  Note SN 8I20200  VARIABLE ANNUITY MINIMUM DEATH BENEFITS  A MONTE CARLO PRICING APPROACH
Overview
 generous min DB designs, harder to understand risks in providing MGDB
 benefit costs little (if anything) usually
 could be very costly in certain events
 Monte Carlo approach
 large # scenarios b/c > 1/2 trials result in 0 or minimal cost
 but very long tail (sd > mean typically)
 results similar (but slightly higher) than BS approach
 first tests using 3.75% base return assumption
 historical returns consistenly above that.
 author uses 8% remainder of note
 cost of MGDB drops drastically as assumed yield increases
 base return assumption is a CRITICAL ASSUMPTION
 distribution has large kurtosis
 large number of outliers
 sd > mean demonstrated volatility of results
Pricing
 approach pricing through an asset charge
 problem  charge collected over longer time frame than claims
 creates reserving problem and insurer exposed to lapse risk
 one approach  study point in each scenario where insurer is in worst position
 if distribution of results is unsatisfactory, try again w/ higher/lower asset charge
Enhanced DB Definitions
 enhanced DB provisions included in many contracts
 "Ratchet 5 to 70" increases (never decreases) min DB on every 5th anniv to then current policy value (if it is higher than prior min db)
 no increases after age 70
 "Increase 5% to 200%"  prems accumulated at 5% subject to 200% max, no age limit
 "combined to age 70"  combines ratcheted formula w/ int formulat  greatere DB under either formula, but no increases after 70
 enhanced formulas add signficantly to cost
Ratcheting Frequency
 resets are most important cost factor
 frequency of reset also significant cost factor
Summary  Volatile Results
 actual costs highly sensitive to
 base underlying yield assumption
 issue age
 mkt volatility
 lapse rate
 benfit provisions
Evaluation of Methodology
 BS easily produces sensible, quick calcs of values for min DB for simpler cases
 complex for ratcheted formulas
 Monte Carlo  requires many trials, but easy enough w/ current spreadsheets

Copyright © 2004 Steve Welander.
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