Pricing and Hedging of Discrete Dynamic Guaranteed Funds

Abstract

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.