Parisian exchange options

Abstract

The option to exchange one asset for another is one of the oldest and one of the most popular exotic options. In the present article, we extend the existing literature on options to Parisian exchange options, i.e. the option to exchange one asset for the other contingent on the occurrence of the Parisian time. Thus, these options are a special kind of barrier option which is knocked out or knocked in only if the value of the first asset is worth more than the other for a certain period of time, i.e. the ratio of the assets must be above or below one (or, in general, a given barrier) for a certain period of time. We derive closed-form solutions in terms of Laplace transforms for these options, introduce new options which are automatically exercised at the Parisian time, conduct some illustrative numerical analyses and give a number of examples from structured equity products, corporate finance, M&A, risk arbitrage and life insurance where the application of Parisian exchange options can be very useful.Parisian exchange options, Exotic options, Parisian options, Exchange options,

The market pricing of the lifeboat provision in a closed-end fund

“…This study presents a realworld application on the lifeboat-provision pricing in the †There are mainly four approaches to value the Parisian option. See Chesney et al (1997) and Chen and Suchanecki (2011) for inverse Laplace transformation method, Haber et al (1999) and Vetzal and Forsyth (1999) for finite difference method, Bernard and Boyle (2011) for Monte Carlo method, and Avellaneda and Wu (1999) and Costabile (2002) for tree method. Meanwhile, Wang et al (2009) combined the Laplace transformation method and finite difference method, and devised a hybrid method to price the barrier-style option.…”

“…† Recently, the pricing of Parisian exchange option has attracted many scholars' attentions due to its widely practical applications. ‡ For instance, Chen and Suchanecki (2011) developed an inverse Laplace transformation method, while Bernard and Boyle (2011) designed a Monte Carlo method. In our study, we design a trinomial-tree method to value a Parisian exchange option.…”

Sensitivity of boundary crossing probabilities of the Brownian motion

“…Chesney et al (1997), who introduced Parisian options, derived closed form expressions for the Laplace transform of the price of Parisian contracts. Bernard et al (2005) and Chen and Suchanecki (2011) develop inverse Laplace transform methods. In order to price Parisian options, Haber et al (1999) and Zhu and Chen (2013) use a partial differential equation approach.…”

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

“…In addition, exotic types of Parisian options have been studied as well. For example, see Dassios and Wu [2011], Dassios and Lim [2014], Anderluh and van der Weide [2009], Chesney and Gauthier [2006], and Chen and Suchanecki [2011] for the pricing of double-barrier Parisian, two-sided Parisian, American Parisian and Parisian exchange options. Lastly, there is also relevant literature on the excursion times of Parisian type in the context of Lévy insurance models.…”