Pricing derivatives in hermite markets

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

doi:10.1142/S0219024919500316

Pricing derivatives in hermite markets

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

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English
Article number	1950031
Journal	International Journal of Theoretical and Applied Finance
Volume	22
Issue number	6
DOIs	https://doi.org/10.1142/S0219024919500316
State	Published - Sep 1 2019

Keywords

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

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10.1142/S0219024919500316

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title = "Pricing derivatives in hermite markets",

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, Rosenblatt processes, arbitrage tax, fractional Brownian motion, no-arbitrage, perpetual derivatives",

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T1 - Pricing derivatives in hermite markets

AU - Stoyanov, Stoyan V.

AU - Rachev, Svetlozar T.

AU - Mittnik, Stefan

AU - Fabozzi, Frank J.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Hermite processes

KW - Rosenblatt processes

KW - arbitrage tax

KW - fractional Brownian motion

KW - no-arbitrage

KW - perpetual derivatives

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DO - 10.1142/S0219024919500316

M3 - Article

AN - SCOPUS:85072219008

SN - 0219-0249

VL - 22

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

IS - 6

M1 - 1950031

ER -

Pricing derivatives in hermite markets

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Keywords

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