In this paper, we assume that the log return of the underlying asset follows a semi-Markov process, then from the knowledge of the kernel we derive an explicit expression for the value of the option and for the bare risk in the case of the European call (put) option and, by means of a recursive system, we derive the value and the bare risk in the case of the American option. The prices and risks we obtained depend explicitly on the waiting-time distributions of the asset and they are duration dependent. The link with models based on Markov Chains and Continuous Time Random Walks is debated. (C) 2009 Elsevier B.V. All rights reserved.
European and American options: The semi-Markov case / Guglielmo, D'Amico; Jacques, Janssen; Manca, Raimondo. - In: PHYSICA. A. - ISSN 0378-4371. - STAMPA. - 388:15-16(2009), pp. 3181-3194. [10.1016/j.physa.2009.04.016]
European and American options: The semi-Markov case
MANCA, Raimondo
2009
Abstract
In this paper, we assume that the log return of the underlying asset follows a semi-Markov process, then from the knowledge of the kernel we derive an explicit expression for the value of the option and for the bare risk in the case of the European call (put) option and, by means of a recursive system, we derive the value and the bare risk in the case of the American option. The prices and risks we obtained depend explicitly on the waiting-time distributions of the asset and they are duration dependent. The link with models based on Markov Chains and Continuous Time Random Walks is debated. (C) 2009 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
