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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Kleinert, Florian¹  van Schaik, Kees¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: American options;    Optimal stopping;    Canadisation;    Levy processes;    Meromorphic;   

DOI  :  10.1016/j.spa.2015.03.003

来源: Elsevier

【 摘 要 】

We introduce an algorithm for the pricing of finite expiry American options driven by Levy processes. The idea is to tweak Can's 'Canadisation' method, cf. Can (1998) (see also Bouchard et al. (2005)), in such a way that the adjusted algorithm is viable for any Levy 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 Levy processes, cf. Kyprianou et al. (2012). This class contains all Levy processes whose Levy measure is an infinite mixture of exponentials which can generate both finite and infinite jump activity. Levy processes well known in mathematical finance can in a straightforward way be obtained as a limit of meromorphic Levy processes. We work out the algorithm in detail for the classic example of the American put, and we illustrate the results with some numerics. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free