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REVIEW article
Front. Appl. Math. Stat.
Sec. Mathematical Finance
Volume 10 - 2024 |
doi: 10.3389/fams.2024.1456746
APPLICATIONS OF FRACTIONAL STOCHASTIC VOLATILITY MODELS TO MARKET MICROSTRUCTURE THEORY AND OPTIMAL EXECUTION STRATEGIES
Provisionally accepted- Westchester Research, Los Angeles, United States
In this paper, we explore the applications of fractional stochastic volatility (FSV) models within the realm of market microstructure theory and optimal execution strategies. FSV models extend traditional stochastic volatility frameworks by incorporating fractional differentiation, allowing for more flexible and realistic representations of asset price dynamics over time. Our investigation begins with an introduction to FSV models, highlighting their ability to capture long-memory effects and volatility clustering observed in financial markets. These models provide a robust framework for understanding market microstructure dynamics, including order flow behavior, price impact functions, and liquidity provision mechanisms. Furthermore, we discuss recent advancements and empirical findings using FSV models, emphasizing their role in uncovering intraday volatility patterns and their implications for trading strategies under varying market conditions. By incorporating these nuanced volatility dynamics, FSV models contribute to the development of optimal execution algorithms that enhance transaction cost efficiency and market stability. The FSV model, when the Hurst exponent is set to 0.5, effectively reduces to a standard stochastic volatility model. This 𝐻 nested relationship can be formally demonstrated by considering the FSV model's general form and showing that for = 0.5, the fractional Brownian motion H ( ) becomes a standard 𝐻 𝐵 𝑡 Brownian motion , thereby aligning the FSV model with traditional models. Overall, our 𝑊(𝑡) analysis underscores the significance of FSV models in advancing both theoretical insights and practical applications in modern finance, offering new avenues for research in high-frequency trading strategies and market efficiency.
Keywords: Fractional stochastic volatility, Market micro structure, Volatility clustering, Financial econometrics, Hurst exponent
Received: 29 Jun 2024; Accepted: 10 Sep 2024.
Copyright: © 2024 Webb. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Abe Webb, Westchester Research, Los Angeles, United States
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