Pricing derivatives in hermite markets

Stoyan V. Stoyanov, Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number1950031
JournalInternational Journal of Theoretical and Applied Finance
Volume22
Issue number6
DOIs
StatePublished - Sep 1 2019

Keywords

  • Hermite processes
  • Rosenblatt processes
  • arbitrage tax
  • fractional Brownian motion
  • no-arbitrage
  • perpetual derivatives

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