Risk-Minimizing Hedging for Indexed Stock Options under Jump-Diffusion Processes

Abstract

With conditional mean square error of hedging cost process as risk measure, this paper presents risk-minimizing
hedging for indexed stock options under jump diffusion processes. Firstly, the cost process of hedging with
risk-minimizing criterion is testified to be a martingale. Then, the explicit optimal strategy is given using
backward recursive method. Lastly, an exemplification based on China Stock Markets is given as an example to
illuminate the relationship between underlying asset positions and option’s maturity horizon and position
adjusting frequency.