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Measuring the effectiveness of static hedging strategies for a guaranteed minimum income benefit. (English) Zbl 1291.91244

Summary: A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase. This paper analyzes the effectiveness of static hedging strategies for the GMIB. Using Monte Carlo simulation, the effectiveness of a static hedging strategy is measured by the empirical hedging loss distribution, where each hedging loss is defined as the difference between the GMIB payoff and the hedging portfolio payoff at the maturity date. Hedging portfolios are constructed by minimizing the Conditional Tail Expectation of the hedging loss distribution or minimizing the mean-squared hedging loss. The positions in the hedging portfolio instruments are determined at the outset from solving either portfolio optimization problem and are held fixed until the maturity date. Our results suggest which instruments are most important to achieve the best results. We backtest the performance of static hedging strategies for the GMIB over the period 1961 to 2012.

MSC:

91G70 Statistical methods; risk measures
91B30 Risk theory, insurance (MSC2010)
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