On the valuation of Paris options: foundational results

英文摘要：

This paper adresses the valuation of the Paris barrier options proposed by Yor, Jeanblanc-Picque, and Chesnay (Advances in Applied Probability, 29(1997), 165-184) using the Laplace transform approach. Based on suggestions by Pliska the notion of Paris options is extended such that their valuation is possible at any point during their lifespan. The Laplace transforms derived by Yor et al. are modified when necessary, and their basic analytic properties are discussed.