Hedging options in market models modulated by the fractional Brownian motion
Authors:
Boualem Djehiche a;
M'hamed Eddahbi b
| Affiliations: | a Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden |
| b Faculty of Sciences and Technics, Department of Mathematics and Computer Sciences, Cadi Ayyad University, Marrakech, Morocco |
DOI:
10.1081/SAP-120000220
Publication Frequency:
6 issues per year
Published in:
Stochastic Analysis and Applications,
Volume
19,
Issue
5
October
2001
, pages 753
- 770
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Abstract
We use the stochastic calculus of variations for the fractional Brownian motion to derive formulas for the replicating portfolios for a class of contingent claims in a Bachelier and a Black-Scholes markets modulated by fractional Brownian motion. An example of such a model is the Black-Scholes process whose volatility solves a stochastic differential equation driven by a fractional Brownian motion that may depend on the underlying Brownian motion.
|
| Keywords: Fractional Brownian motion; Stochastic volatility; Stochastic calculus of variations; Hedging options |
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