PRICING DERIVATIVES IN HERMITE MARKETS

We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion (FBM) 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. We derive PDEs for the price of such strategies in the presence of an arbitrage tax in pure Hermite, mixed Hermite, and Black–Scholes–Merton diffusion markets.