Hedging Cost Analysis of Put Option with Applications to Variable Annuities

Variable annuities (VA) are equity-linked annuity contracts which provide the opportunity for policy-holders to benefit from financial markets appreciation and at the mean time provide protection from the downside risks of the markets. They have been overshadowing traditional fixed annuities to become the leading form of protected investment worldwide. However, the embedded guarantees in VA can bring significant downside risks to the insurer and need to be hedged. Among different hedging strategies, move-based discrete hedging strategies are widely adopted in practice but the cost analysis for move-based discrete hedging strategies are mathematically complex. In this thesis, we first examine various move-based hedging strategies and show that a two-sided underlier-based hedging strategy is desirable for the return of premium guarantee. Then we assume a GBM model for the sub-account to develop a semi-analytic framework for the hedging cost analysis of this strategy and thereby propose a modified "Percentile Premium Principle", which imposes a significant "loading" on top of the regular charge to cover the costs arising from the discrete re-balances under the two-sided underlier-based strategy. We apply the modified "Percentile Premium Principle" to the pricing of various VA designs, including GMMB, annual ratchet VA, structured product based VA with both buffered and contingent protection. Finally, we advance the algorithm towards a more general model-GBM with regime switching-to allow a better representation of the VA sub-account.Ph