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Vietnam Journal of Mathematics 35:3(2007) 231-245

 A Fractional Black-Scholes Model with Jumps

P. Sattayatham, A. Intarasit, and A. P. Chaiyasena

Abstract.  In this paper, we introduce an approximate approach to a fractional Black-Scholes model with jumps perturbed by fractional noise. Based on a fundamental result on the L²-approximation of this noise by semimartingales, we prove a convergence theorem concerning an approximate solution. A simulation example shows a signigicant reduction of error in a fractional jump model as compared to the classical jump model.

2000 Mathematics Subject Classification: 91B28, 65C50.

Keywords: Black-Scholes, approximate models.

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Published by Springer since January 2013