Risk Analysis and Hedging of Parisian Options Under a Jump-Diffusion Model

A Parisian option is a variant of a barrier option such that its payment is activated or deactivated only if the underlying asset remains above or below a barrier over a certain amount of time. We show that its complex payoff feature can cause dynamic hedging to fail. As an alternative, we investigate a quasi-static hedge of Parisian options under a more general jump-diffusion process. Specifically, we propose a strategy of decomposing a Parisian option into the sum of other contingent claims which are statically hedged. Through numerical experiments, we show the effectiveness of the suggested hedging strategy