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Arbitrage Taxes for Pricing Derivatives in Hermite Markets

Article arXiv papers · Author: Stoyan V. Stoyanov et al.
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Summary

The document outlines a framework for pricing derivatives in financial markets driven by Hermite processes, a family that includes fractional Brownian and fractional Rosenblatt markets. It considers both pure and mixed Hermite market settings, extending beyond either model on its own.

The proposed mechanism is a strategy-specific arbitrage tax tied to how quickly transaction volume in a hedging portfolio accelerates as risky asset prices move. The authors say this adjustment can convert markets that permit arbitrage into markets without arbitrage, within the class of Markov trading strategies. The abstract gives no derivation, assumptions in detail, worked examples, or empirical evaluation, so it does not establish how the tax would be calibrated or how broadly the result applies beyond that strategy class.

Key ideas

  • The framework covers pure and mixed markets driven by Hermite processes.
  • Hermite markets generalize fractional Brownian and fractional Rosenblatt market models.
  • The proposed tax depends on acceleration in hedging portfolio transaction volume as risky prices change.
  • The authors claim the adjustment removes arbitrage opportunities for Markov trading strategies.
  • The abstract provides no empirical evidence or detailed calibration procedure.

Tags

Derivatives pricingArbitrageStatistics
Full text
# Pricing derivatives in Hermite markets


# Pricing derivatives in Hermite markets









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.