Semimartingale approximation of fractional Brownian motion and its applications

Abstract

The aim of this paper is to provide a semimartingale approximation of a fractional stochastic integration. This result leads us to approximate the fractional Black–Scholes model by a model driven by semimartingales, and a European option pricing formula is found. ... W t H , ( 2 ) ≔ ∫ 0 t ( t − s ) α d W s , α = H − 1 2 . ... Cov ( M t H , ε , M s H , ε ) = ε 2 min ( t , s ) + Cov ( W t H , ( 1 ) , W s H , ( 1 ) ) . ... However, we can see that the mixed model (1.5) contains one random source more than the original model (1.4). This means that the dynamism of (1.5) is ...