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Exotic options under Lévy models: an overview. (English) Zbl 1089.91029

From the text: For a state of the art, we refer to A. E. Kyprianou, W. Schoutens and P. Wilmott (Eds.), Exotic Option Pricing and Advanced Lévy Models, Wiley, Chichester (2005), and the reference cited therein. Here, we give a brief overview of the literature and the different techniques to price vanilla and exotic options. We first focus on European options. We depart by pricing the vanilla call options, using i.e. (fast) Fourier transforms. Next, we move to more complicated payoff functions and will treat digital, barrier, lookback, Asian and American options using i.e., Wiener-Hopf factorization theory, numerical simulation algorithms solving partial integro-differential equation/inequalities (PIDE/PIDI) and comonotonicity theory.
This paper is organized as follows. First, we give a brief introduction to Lévy processes and the associated Lévy market models. In Section 2, we overview the pricing of European-type options. Section 3 is devoted to American options.

MSC:

91B28 Finance etc. (MSC2000)
91B26 Auctions, bargaining, bidding and selling, and other market models
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