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Arbitrage with fractional Gaussian processes

Xili Zhang and Weilin Xiao

Physica A: Statistical Mechanics and its Applications, 2017, vol. 471, issue C, 620-628

Abstract: While the arbitrage opportunity in the Black–Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black–Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black–Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann–Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

Keywords: Arbitrage opportunities; Fractional Gaussian processes; Black–Scholes model; Self-financing; Long-range dependence (search for similar items in EconPapers)
Date: 2017
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