Pricing and hedging parisian options

Abstract

A Parisian option is a variant of barrier option such that its payment is activated or deactivated only if the underlying asset has stayed below or above over a certain amount of time specified in the contract. In this paper, we provide the formulas for the sensitivities (greeks) using Laplace transform. In particular, the theta is important to understand the behavior of Parisian options and is one of reasons that dynamic hedging fails. This paper also propose static hedging strategy by decomposing a Parisian option into certain derivatives which are statically hedged. Furthermore, we compare the hedging performance of dynamic hedging and static hedging. aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa