PRICING DERIVATIVES IN HERMITE MARKETS

Stoyan V. Stoyanov (), Svetlozar T. Rachev (), Stefan Mittnik and Frank J. Fabozzi
Additional contact information
Stoyan V. Stoyanov: College of Business, Stony Brook University, Stony Brook, NY 11794, USA
Svetlozar T. Rachev: Texas Tech University, Lubbock, TX 79409, USA
Frank J. Fabozzi: EDHEC Business School, 93, Promenade des Anglais BP3116, 06202 Nice Cedex 3, France

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 06, 1-27

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.

Keywords: Hermite processes; fractional Brownian motion; Rosenblatt processes; perpetual derivatives; no-arbitrage; arbitrage tax (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Pricing derivatives in Hermite markets (2017)
Working Paper: Pricing Derivatives in Hermite Markets (2016)
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DOI: 10.1142/S0219024919500316

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