Pricing and Hedging of Discrete Dynamic Guaranteed Funds

We derive a risk‐neutral pricing model for discrete dynamic guaranteed funds with geometric Gaussian underlying security price process. We propose a dynamic hedging strategy by adding a gamma factor to the conventional delta. Simulation results demonstrate that, when hedging discretely, the risk‐neutral gamma‐adjusted‐delta strategy outperforms the dynamic delta hedging strategy by reducing the expected hedging error, lowering the hedging error variability, and improving the self‐financing possibility. The discrete dynamic delta‐only hedging not only causes potential overcharge to clients but also could be costly to the issuers. We show that a naive application of continuous‐time hedging formula to a discrete‐time hedging setting tends to worsen these possibilities.