Risk Analysis and Hedging of Parisian Options under a Jump‐Diffusion Model

Abstract

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 jumpdiffusion 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.

Integral Equation Based Approach for Static Options Replication

“…Chung and Shih (2009); Ruas et al (2013) used calendar-spread approaches for American options whereas Chung et al (2013a,b); did for American barriers and for double barriers. Parisian options, which are classified as occupation time derivatives in Broadie and Detemple (2004), are added to the list (Kim and Lim, 2016). More recently, Kim and Lim (2019) proposed a recursive method for autocallable structured products based on the results developed in this paper.…”