High-Frequency Data

The Pitfalls of Continuous Heavy-Tailed Distributions in High-Frequency Data Analysis ArXiv ID: 2510.09785 “View on arXiv” Authors: Vladimír Holý Abstract We address the challenges of modeling high-frequency integer price changes in financial markets using continuous distributions, particularly the Student’s t-distribution. We demonstrate that traditional GARCH models, which rely on continuous distributions, are ill-suited for high-frequency data due to the discreteness of price changes. We propose a modification to the maximum likelihood estimation procedure that accounts for the discrete nature of observations while still using continuous distributions. Our approach involves modeling the log-likelihood in terms of intervals corresponding to the rounding of continuous price changes to the nearest integer. The findings highlight the importance of adjusting for discreteness in volatility analysis and provide a framework for incroporating any continuous distribution for modeling high-frequency prices. ...

Community-level Contagion among Diverse Financial Assets ArXiv ID: 2509.15232 “View on arXiv” Authors: An Pham Ngoc Nguyen, Marija Bezbradica, Martin Crane Abstract As global financial markets become increasingly interconnected, financial contagion has developed into a major influencer of asset price dynamics. Motivated by this context, our study explores financial contagion both within and between asset communities. We contribute to the literature by examining the contagion phenomenon at the community level rather than among individual assets. Our experiments rely on high-frequency data comprising cryptocurrencies, stocks and US ETFs over the 4-year period from April 2019 to May 2023. Using the Louvain community detection algorithm, Vector Autoregression contagion detection model and Tracy-Widom random matrix theory for noise removal from financial assets, we present three main findings. Firstly, while the magnitude of contagion remains relatively stable over time, contagion density (the percentage of asset pairs exhibiting contagion within a financial system) increases. This suggests that market uncertainty is better characterized by the transmission of shocks more broadly than by the strength of any single spillover. Secondly, there is no significant difference between intra- and inter-community contagion, indicating that contagion is a system-wide phenomenon rather than being confined to specific asset groups. Lastly, certain communities themselves, especially those dominated by Information Technology assets, tend to act as major contagion transmitters in the financial network over the examined period, spreading shocks with high densities to many other communities. Our findings suggest that traditional risk management strategies such as portfolio diversification through investing in low-correlated assets or different types of investment vehicle might be insufficient due to widespread contagion. ...

Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers ArXiv ID: 2509.02941 “View on arXiv” Authors: Igor Halperin Abstract This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author’s prior arguments that realistic market dynamics are governed by higher-order (cubic and higher) non-linearities in the drift. As the diffusion drift is given by the negative gradient of a potential function, this means that a non-linear drift translates into a non-quadratic potential. These arguments were based both on general theoretical grounds as well as a structured approach to modeling the price dynamics which incorporates money flows and their impact on market prices. Here, we find direct confirmation of this view by analyzing high-frequency crypto currency data at different time scales ranging from minutes to months. We find that markets can be characterized by either a single-well or a double-well potential, depending on the time period and sampling frequency, where a double-well potential may signal market uncertainty or stress. ...

Jump detection in financial asset prices that exhibit U-shape volatility ArXiv ID: 2508.18876 “View on arXiv” Authors: Cecilia Mancini Abstract We describe a Matlab routine that allows us to estimate the jumps in financial asset prices using the Threshold (or Truncation) method of Mancini (2009). The routine is designed for application to five-minute log-returns. The underlying assumption is that asset prices evolve in time following an Ito semimartingale with, possibly stochastic, volatility and jumps. A log-return is likely to contain a jump if its absolute value is larger than a threshold determined by the maximum increment of the Brownian semimartingale part. The latter is particularly sensitive to the magnitude of the volatility coefficient, and from an empirical point of view, volatility levels typically depend on the time of day (TOD), with volatility being highest at the beginning and end of the day, while it is low in the middle. The first routine presented allows for an estimation of the TOD effect, and is an implementation of the method described in Bollerslev and Todorov (2011). Subsequently, the TOD effect for the stock Apple Inc. (AAPL) is visualized. The second routine presented is an implementation of the threshold method for estimating jumps in AAPL prices. The procedure recursively estimates daily volatility and jumps. In each round, the threshold depends on the time of the day and is constructed using the estimate of the daily volatility multiplied by the daytime TOD factor and by the continuity modulus of the Brownian motion paths. Once the jumps are detected, the daily volatility estimate is updated using only the log-returns not containing jumps. Before application to empirical data, the reliability of the procedure was separately tested on simulated asset prices. The results obtained on a record of AAPL stock prices are visualized. ...

Returns and Order Flow Imbalances: Intraday Dynamics and Macroeconomic News Effects ArXiv ID: 2508.06788 “View on arXiv” Authors: Makoto Takahashi Abstract We study the interaction between returns and order flow imbalances in the S&P 500 E-mini futures market using a structural VAR model identified through heteroskedasticity. The model is estimated at one-second frequency for each 15-minute interval, capturing both intraday variation and endogeneity due to time aggregation. We find that macroeconomic news announcements sharply reshape price-flow dynamics: price impact rises, flow impact declines, return volatility spikes, and flow volatility falls. Pooling across days, both price and flow impacts are significant at the one-second horizon, with estimates broadly consistent with stylized limit-order-book predictions. Impulse responses indicate that shocks dissipate almost entirely within a second. Structural parameters and volatilities also exhibit pronounced intraday variation tied to liquidity, trading intensity, and spreads. These results provide new evidence on high-frequency price formation and liquidity, highlighting the role of public information and order submission in shaping market quality. ...

Binary Tree Option Pricing Under Market Microstructure Effects: A Random Forest Approach ArXiv ID: 2507.16701 “View on arXiv” Authors: Akash Deep, Chris Monico, W. Brent Lindquist, Svetlozar T. Rachev, Frank J. Fabozzi Abstract We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask spreads, discrete price movements, and serial return correlations. Our framework augments the binomial tree with path-dependent transition probabilities estimated via Random Forest classifiers trained on high-frequency market data. This approach preserves no-arbitrage conditions while embedding real-world trading dynamics into the pricing model. Using 46,655 minute-level observations of SPY from January to June 2025, we achieve an AUC of 88.25% in forecasting one-step price movements. Order flow imbalance is identified as the most influential predictor, contributing 43.2% to feature importance. After resolving time-scaling inconsistencies in tree construction, our model yields option prices that deviate by 13.79% from Black-Scholes benchmarks, highlighting the impact of microstructure on fair value estimation. While computational limitations restrict the model to short-term derivatives, our results offer a robust, data-driven alternative to classical pricing methods grounded in empirical market behavior. ...

An Efficient Multi-scale Leverage Effect Estimator under Dependent Microstructure Noise ArXiv ID: 2505.08654 “View on arXiv” Authors: Ziyang Xiong, Zhao Chen, Christina Dan Wang Abstract Estimating the leverage effect from high-frequency data is vital but challenged by complex, dependent microstructure noise, often exhibiting non-Gaussian higher-order moments. This paper introduces a novel multi-scale framework for efficient and robust leverage effect estimation under such flexible noise structures. We develop two new estimators, the Subsampling-and-Averaging Leverage Effect (SALE) and the Multi-Scale Leverage Effect (MSLE), which adapt subsampling and multi-scale approaches holistically using a unique shifted window technique. This design simplifies the multi-scale estimation procedure and enhances noise robustness without requiring the pre-averaging approach. We establish central limit theorems and stable convergence, with MSLE achieving convergence rates of an optimal $n^{"-1/4"}$ and a near-optimal $n^{"-1/9"}$ for the noise-free and noisy settings, respectively. A cornerstone of our framework’s efficiency is a specifically designed MSLE weighting strategy that leverages covariance structures across scales. This significantly reduces asymptotic variance and, critically, yields substantially smaller finite-sample errors than existing methods under both noise-free and realistic noisy settings. Extensive simulations and empirical analyses confirm the superior efficiency, robustness, and practical advantages of our approach. ...

Microstructure and Manipulation: Quantifying Pump-and-Dump Dynamics in Cryptocurrency Markets ArXiv ID: 2504.15790 “View on arXiv” Authors: Unknown Abstract Building on our prior threshold-based analysis of six months of Poloniex trading data, we have extended both the temporal span and granularity of our study by incorporating minute-level OHLCV records for 1021 tokens around each confirmed pump-and-dump event. First, we algorithmically identify the accumulation phase, marking the initial and final insider volume spikes, and observe that 70% of pre-event volume transacts within one hour of the pump announcement. Second, we compute conservative lower bounds on insider profits under both a single-point liquidation at 70% of peak and a tranche-based strategy (selling 20% at 50%, 30% at 60%, and 50% at 80% of peak), yielding median returns above 100% and upper-quartile returns exceeding 2000%. Third, by unfolding the full pump structure and integrating social-media verification (e.g., Telegram announcements), we confirm numerous additional events that eluded our initial model. We also categorize schemes into “pre-accumulation” versus “on-the-spot” archetypes-insights that sharpen detection algorithms, inform risk assessments, and underpin actionable strategies for real-time market-integrity enforcement. ...

Bayesian Estimation of Corporate Default Spreads ArXiv ID: 2503.02991 “View on arXiv” Authors: Unknown Abstract Risk-averse investors often wish to exclude stocks from their portfolios that bear high credit risk, which is a measure of a firm’s likelihood of bankruptcy. This risk is commonly estimated by constructing signals from quarterly accounting items, such as debt and income volatility. While such information may provide a rich description of a firm’s credit risk, the low-frequency with which the data is released implies that investors may be operating with outdated information. In this paper we circumvent this problem by developing a high-frequency credit risk proxy via corporate default spreads which are estimated from daily bond price data. We accomplish this by adapting classic yield curve estimation methods to a corporate bond setting, leveraging advances in Bayesian estimation to ensure higher model stability when working with small sample data which also allows us to directly model the uncertainty of our predictions. ...

Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades ArXiv ID: 2501.16772 “View on arXiv” Authors: Unknown Abstract We empirically analyze the reversion of financial market trends with time horizons ranging from minutes to decades. The analysis covers equities, interest rates, currencies and commodities and combines 14 years of futures tick data, 30 years of daily futures prices, 330 years of monthly asset prices, and yearly financial data since medieval times. Across asset classes, we find that markets are in a trending regime on time scales that range from a few hours to a few years, while they are in a reversion regime on shorter and longer time scales. In the trending regime, weak trends tend to persist, which can be explained by herding behavior of investors. However, in this regime trends tend to revert before they become strong enough to be statistically significant, which can be interpreted as a return of asset prices to their intrinsic value. In the reversion regime, we find the opposite pattern: weak trends tend to revert, while those trends that become statistically significant tend to persist. Our results provide a set of empirical tests of theoretical models of financial markets. We interpret them in the light of a recently proposed lattice gas model, where the lattice represents the social network of traders, the gas molecules represent the shares of financial assets, and efficient markets correspond to the critical point. If this model is accurate, the lattice gas must be near this critical point on time scales from 1 hour to a few days, with a correlation time of a few years. ...