On the fractional Black-Scholes market with transaction costs

TL;DR

This paper analyzes the impact of proportional transaction costs on hedging strategies in a fractional Black-Scholes market, deriving errors and asymptotic behaviors as the Hurst parameter approaches 1/2.

Contribution

It introduces a novel analysis of hedging errors under fractional market dynamics with decreasing transaction costs as trading frequency increases.

Findings

Derived a non-trivial hedging error for European options with convex payoffs.

Studied the asymptotic behavior of hedging errors as the Hurst parameter approaches 1/2.

Provided insights into the effect of transaction costs on hedging in fractional markets.

Abstract

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the case when the transaction costs coefficients decrease as $n^{-(1-H)}$. We study the expected hedging error and asymptotic behavior of the hedge as $H \to 1/2$