Study Notes and Published Refences - Note SN 8I-202-00 - VARIABLE ANNUITY MINIMUM DEATH BENEFITS

Study Notes and Published Refences - Note SN 8I-202-00 - 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 B-S 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

B-S 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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