The Guaranteed Minimum Withdrawal Benefits (GMWBs) are optional riders provided
by insurance companies in variable annuities. They guarantee the policyholders' ability to get the initial investment back by making periodic withdrawals regardless of the
impact of poor market performance. With GMWBs attached, variable annuities become more attractive. This type of guarantee can be challenging to price and hedge.
We employ two approaches to price GMWBs. Under the constant static withdrawal
assumption, the first approach is to decompose the GMWB and the variable annuity
into an arithmetic average strike Asian call option and an annuity certain. The second
approach is to treat the GMWB alone as a put option whose maturity and payoff are
random.
Hedging helps insurers specify and manage the risks of writing GMWBs, as well
as find their fair prices. We propose semi-static hedging strategies that offer several
advantages over dynamic hedging. The idea is to construct a portfolio of European
options that replicate the conditional expected GMWB liability in a short time period,
and update the portfolio after the options expire. This strategy requires fewer portfolio
adjustments, and outperforms the dynamic strategy when there are random jumps in
the underlying price. We also extend the semi-static hedging strategies to the Heston
stochastic volatility model.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/4990 |
| Date | January 2010 |
| Creators | Liu, Yan |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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