Hedging options in market models modulated by the fractional Brownian motion

Boualem Djehiche; M'hamed Eddahbi

doi:10.1081/SAP-120000220

Hedging options in market models modulated by the fractional Brownian motion

Boualem Djehiche, M'hamed Eddahbi

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	753-770
Number of pages	18
Journal	Stochastic Analysis and Applications
Volume	19
Issue number	5
DOIs	https://doi.org/10.1081/SAP-120000220
State	Published - 2001

Keywords

Fractional Brownian motion
Hedging options
Stochastic calculus of variations
Stochastic volatility

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1081/SAP-120000220

Cite this

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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.",

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AB - 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.

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KW - Hedging options

KW - Stochastic calculus of variations

KW - Stochastic volatility

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Hedging options in market models modulated by the fractional Brownian motion

Abstract

Keywords

ASJC Scopus subject areas

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