Title: On the Pricing and Hedging of Discrete Dynamic Guaranteed Funds
Reference Number: 1105
Publication Date: August 2003

Eric Chang
The University of Hong Kong

Leong Kwai Li
The Hong Kong Polytechnic University

Wai-Man Tse
The University of Hong Kong

This paper investigates the possibility of hedging discrete stochastic jumps and their tradeoffs in guaranteed funds under discrete dynamic hedging. Since a guaranteed fund price process is composed of diffusion and jump process, its expected rate of return is above the risk-free rate of interest. When delta dynamic hedging occurs at discrete instants, the rate differential will be manifested in non-zero expected hedging errors. We employ the dynamic guaranteed fund as our example, whose exotic fund structure excludes the possibility of static hedge. We derive a pricing model and develop hedging formulas for discrete dynamic guaranteed funds. We show our discrete-time delta hedging formulas induce smaller hedging errors than those based on applying the continuous-time hedging formula of Gerber and Pafumi (2000) at discrete instants. Nevertheless, this discrete-time model still incurs significant negative expected hedging errors induced partly by the guarantee jumps. We introduce a gamma-adjusted delta hedging strategy. The simulation results indicate that the strategy can effectively improve the discrete hedging performance of dynamic guaranteed funds.

Last modified: 06/24/2004