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Approximation of non-Lipschitz SDEs by Picard iterations

Baptiste, Julien; Grepat, Julien; Lépinette, Emmanuel (2018), Approximation of non-Lipschitz SDEs by Picard iterations, Applied Mathematical Finance, 25, 2, p. 148-179. 10.1080/1350486X.2018.1507749

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01397399
Date
2018
Journal name
Applied Mathematical Finance
Volume
25
Number
2
Publisher
Taylor & Francis
Pages
148-179
Publication identifier
Metadata
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Author(s)
Baptiste, Julien cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Grepat, Julien
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g. solutions to non-Lipchitz SDEs. An application to the pricing of Asian-style contingent claims in the CEV model is presented and compared to other methods of the literature.
Subjects / Keywords
Pricing; European Options