Quadratic Risk Minimization Hedging Strategies for Ratchet Options in Equity-indexed Annuities

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This study proposes a quadratic risk minimization (QRM) hedging strategy for the compound annual ratchet (CAR) design in Equity-index Annuities. Compared to hedging strategies under the Black and Scholes framework, the advantage of QRM is that the QRM simultaneously considers the capital gain (or loss) and the extra hedging cost, from the practical constraint of discrete hedge trading, and minimizes this hedging cost via the Least Square Method. A recursive algorithm is developed from the CRR tree model to overcome the path dependency of the ratchet option and to improve the efficiency of the original QRM hedging strategy. A Monte Carlo simulation method is used to compare the effectiveness of the QRM hedging strategy with the delta hedging strategy, based on three criteria: initial hedging cost, hedging cost, and transaction cost. The numerical result shows that QRM outperforms the delta hedging strategy in terms of hedging cost and transition cost, although QRM has a higher initial cost than the delta-hedge strategy has. Furthermore, empirical investigation based on the recent bearish Taiwan stock market indicates that the recursive QRM yields lower capital loss and hedging cost than delta-hedge does.