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We introduce an algorithm for the pricing of finite expiry American optionsdriven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method,cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjustedalgorithm is viable for any L\'evy process whose law at an independent,exponentially distributed time consists of a (possibly infinite) mixture ofexponentials. This includes Brownian motion plus (hyper)exponential jumps, butalso the recently introduced rich class of so-called meromorphic L\'evyprocesses, cf. Kyprianou et al [16]. This class contains all L\'evy processeswhose L\'evy measure is an infinite mixture of exponentials which can generateboth finite and infinite jump activity. L\'evy processes well known inmathematical finance can in a straightforward way be obtained as a limit ofmeromorphic L\'evy processes. We work out the algorithm in detail for theclassic example of the American put, and we illustrate the results with somenumerics.

A variation of the Canadisation algorithm for the pricing of American options driven by L\'evy processes