A Stroock formula for a certain class of Lévy processes and applications to finance | Zendy

Mhamed Eddahbi | Zendy; Josep Lluís Solé | Zendy; Josep Vives | Zendy

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A Stroock formula for a certain class of Lévy processes and applications to finance

Author(s) -

Mhamed Eddahbi,

Josep Lluís Solé,

Josep Vives

Publication year - 2005

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/jamsa.2005.211

Subject(s) - mathematics , chaotic , martingale (probability theory) , class (philosophy) , lévy process , pure mathematics , derivative (finance) , mathematical economics , finance , economics , computer science , management , artificial intelligence

We find a Stroock formula in the setting of generalized chaos expansion introduced by Nualart and Schoutens for a certain class of Lévy processes, using a Malliavin-type derivative based on the chaotic approach. As applications, we get the chaotic decomposition of the local time of a simple Lévy process as well as the chaotic expansion of the price of a financial asset and of the price of a European call option. We also study the behavior of the tracking error in the discrete delta neutral hedging under both the equivalent martingale measure and the historical probability

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