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.
展开▼
