A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes

Abstract

We introduce an algorithm for the pricing of finite expiry American options driven by Lévy processes. The idea is to tweak Carr’s ‘Canadisation’ method, cf. Carr (1998) (see also Bouchard et al. (2005)), in such a way that the adjusted algorithm is viable for any Lévy process whose law at an independent, exponentially distributed time consists of a (possibly infinite) mixture of exponentials. This includes Brownian motion plus (hyper)exponential jumps, but also the recently introduced rich class of so-called meromorphic Lévy processes, cf. Kyprianou et al. (2012). This class contains all Lévy processes whose Lévy measure is an infinite mixture of exponentials which can generate both finite and infinite jump activity. Lévy processes well known in mathematical finance can in a straightforward way be obtained as a limit of meromorphic Lévy processes. We work out the algorithm in detail for the classic example of the American put, and we illustrate the results with some numerics.