Pricing double-barrier Parisian options

Abstract

Abstract Parisian options are a useful real-option tool in risk management, particularly for corporate bankruptcy protection. However, in the past, only one barrier with the Parisian feature was studied in the literature, possibly due to the additional complication that arises with the co-existence of two barriers. In this paper, we present an analytic solution for the valuation of European-style double-barrier Parisian options by casting the pricing problem into three inter-coupled partial differential equations. These are then solved using a dimension reduction procedure and the ‘moving window’ technique. Our solution is in an explicit and analytical form that is written in terms of multiple integrals. This represents an important advantage over the purely numerical approaches previously published in the literature.