OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS IN LÉVY MODELS

Amina Bouzguenda Zeghal () and Mohamed Mnif ()
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Amina Bouzguenda Zeghal: ENIT-LAMSIN, B.P. 37, 1002 Tunis-Belvédère, Tunisie
Mohamed Mnif: ENIT-LAMSIN, B.P. 37, 1002 Tunis-Belvédère, Tunisie

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 08, 1267-1297

Abstract: In this paper, we extend the results of Carmona and Touzi [6] for an optimal multiple stopping problem to a market where the price process is allowed to jump. We also generalize the problem of valuation swing options to the context of a Lévy market. We prove the existence of multiple exercise policies under an additional condition on Snell envelops. This condition emerges naturally in the case of Lévy processes. Then, we give a constructive solution for perpetual put swing options when the price process has no negative jumps. We use the Monte Carlo approximation method based on Malliavin calculus in order to solve the finite horizon case. Numerical results are given in the last two sections. We illustrate the theoretical results of the perpetual case and give the numerical solution for the finite horizon case.

Keywords: Multiple optimal stopping; Snell envelop; American option; Lévy processes; Malliavin calculus (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S0219024906004037

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