Pricing derivatives in Hermite markets

TL;DR

This paper introduces a new framework for Hermite fractional financial markets, addressing arbitrage issues by applying a strategy-specific tax, thus enabling arbitrage-free trading within these complex models.

Contribution

It generalizes existing fractional market models by incorporating a novel arbitrage tax mechanism to eliminate arbitrage opportunities.

Findings

Hermite markets can be transformed into arbitrage-free markets with the proposed tax.

The framework extends fractional Brownian motion models to more general Hermite processes.

The approach applies to both pure and mixed Hermite market models.

Abstract

We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion and fractional Rosenblatt markets. Considering pure and mixed Hermite markets, we introduce a strategy-specific arbitrage tax on the rate of transaction volume acceleration of the hedging portfolio as the prices of risky assets change, allowing us to transform Hermite markets with arbitrage opportunities to markets with no arbitrage opportunities within the class of Markov trading strategies.