Calendar Anomalies in Digital Assets: A Study of Major Cryptocurrencies

In the financial market, seasonality refers to systematic return patterns that recur at specific calendar intervals. It has been studied extensively in the equity space, but little work has been carried out on cryptocurrencies.

Reference [1] addresses this gap. Specifically, it examines seasonality patterns of 10 major cryptocurrencies using data from 2013 to 2024. The paper investigates the (i) Monday effect, (ii) weekend effect, (iii) January effect, and (iv) Halloween effect. The author pointed out,

Our study revisits seasonalities in crypto markets following Kaiser (2019). We do not identify robust return anomalies in the original sample, especially in more mature markets. We thereby show that the few anomalies, that count as “well-established” in prior literature, e.g., the Monday effect in BTC, do not persist in data after 2015 and should therefore be interpreted as a statistical artifact rather than an anomaly. In the cross-section of crypto currencies, the typical Monday effect, if any, appears negative. However, we find that trading activity is significantly and substantially lower at weekends and that this effect is robust across assets and time.

In brief, regarding Bitcoin, the paper concluded,

• It finds no robust or persistent seasonality in Bitcoin returns.
• The historically “well-known” positive Monday effect in Bitcoin disappears after 2015.
• January and Halloween effects are not reliable for Bitcoin—any significance is inconsistent and not stable across time windows.
• Across the full sample and the post-2018 subsample, Bitcoin shows no statistically significant calendar anomalies in returns when tested properly (including bootstrap tests).
• In the cross-section of 500 coins, the typical Monday effect is negative, aligning with equity market patterns, meaning Bitcoin’s earlier positive Monday effect was likely a statistical artifact, not a robust pattern.
• The only stable pattern the paper identifies is lower weekend trading activity.

Seasonality is an important component of trading and risk management. As the crypto market matures, it will be interesting to stay vigilant and observe how these seasonal patterns evolve, if at all. This is also suggested by the author.

Our study, rather descriptive in nature, offers some interesting findings. The entry of institutional investors could lead to increased trading during regular trading hours, thereby increasingly creating inefficiencies around the weekend. Low trading activity on the weekend could also delay the speed of reaction to news. Hence, our insights may be of interest to researchers and traders continuing to challenge the EMH in crypto markets. However, only time will tell whether the negative cross-sectional Monday effect will persist in the long term.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Mueller, L. (2024). Revisiting seasonality in cryptocurrencies. Finance Research Letters, 64, 105429

Article Source Here: Calendar Anomalies in Digital Assets: A Study of Major Cryptocurrencies

source https://harbourfronts.com/calendar-anomalies-digital-assets-study-major-cryptocurrencies/

A Recent Review of Pairs Trading and Statistical Arbitrage

Pairs trading, or statistical arbitrage, is one of the oldest quantitative trading strategies, and it is still employed today. Over the years, it has expanded from classical distance methods to more sophisticated approaches, and practitioners have increasingly questioned its profitability.

Reference [1] provides a thorough review of the pairs trading literature between 2016 and 2023. The findings are as follows.

1. Distance Methods

Distance-based approaches focus on selecting trading pairs using measures such as the sum of squared errors (SSE) or absolute errors (SAE) of normalized price differences. These methods provide simple and intuitive frameworks for identifying co-moving assets and have shown consistent profitability across global markets, including during downturns. Research cited in the document highlights strong market-neutral properties and robustness even after transaction costs. Future work may extend distance methods using richer optimization frameworks, alternative similarity metrics, and broader datasets.

2. Cointegration Methods

Cointegration techniques rely on long-run equilibrium relationships between asset prices, providing a theoretically grounded basis for pairs trading. The document notes extensive evidence supporting their validity across equity and bond markets. Advances involve adaptive modeling, regime-switching structures, and incorporating external variables such as macroeconomic or ESG data. Future work aims to strengthen resilience by integrating alternative datasets and improving modeling flexibility under complex market conditions.

3. Stochastic Control Methods

Stochastic control frameworks treat pairs trading as a continuous-time optimization problem, dynamically adjusting positions based on spread levels, horizon risk, and divergence risk. These methods extend the classical OU process to include jump-diffusions, regime switching, and stochastic volatility, improving realism and adaptability. The document emphasizes strong empirical performance across various markets, while also noting practical challenges such as transaction costs and liquidity constraints. Future research includes integrating AI/ML for improved adaptability and explicitly modeling trading frictions.

4. Time Series Methods

Time series techniques—including GARCH models, OU processes, and fractional OU extensions—focus on short-term dynamics, volatility clustering, and mean reversion. They allow adaptive trading thresholds based on volatility forecasts and have demonstrated improved returns even after accounting for transaction costs. The document highlights opportunities for hybrid models, combining time series techniques with machine learning, copulas, or stochastic control, as well as incorporating slippage, liquidity constraints, and application to emerging markets and high-frequency settings.

5. Other Methods (Copula, Hurst Exponent, Entropic Approaches)

The document identifies several alternative approaches designed to capture features that traditional statistical methods miss. Copula methods model complex joint distributions and tail dependencies; Hurst exponent approaches capture long-memory effects; and entropic methods account for model uncertainty. These techniques enhance robustness by addressing nonlinear dependence structures and heavy-tail behavior in spreads. Future research may refine these methods, integrate them with machine learning, and test them across diverse asset classes and market regimes.

This comprehensive review of statistical arbitrage strategies will assist practitioners in research, particularly in adapting these methods to new asset classes such as crypto.

Regarding the profitability, we believe that while simple methods have historically been profitable, increasing competition and market efficiency mean that more sophisticated approaches are often required to maintain or enhance profitability. However, sophistication alone is not sufficient; effectiveness depends on model design, data quality, and market conditions.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Sun, Y. (2025). A Review of Pairs Trading: Methods, Performance, and Future Directions. WNE Working Papers, 19/2025 (482). Faculty of Economic Sciences, University of Warsaw.

Post Source Here: A Recent Review of Pairs Trading and Statistical Arbitrage

source https://harbourfronts.com/recent-review-pairs-trading-statistical-arbitrage/

Fair Volatility: A Multifractional Model for Realized Volatility

Volatility is an important measure of market uncertainty and risk. For decades, realized volatility has been computed from the squared returns. Recent research, however, has highlighted several deficiencies in traditional volatility measures.

Reference [1] continues this line of inquiry, identifying three key inefficiencies in conventional volatility estimation,

• Volatility is path-independent and blind to temporal dependence and non-stationarity,
• Its relevance collapses in derivative-intensive strategies, where volatility often represents opportunity rather than risk,
• It lacks an absolute benchmark, providing no guidance on what level of volatility is economically fair in efficient markets.

To address these issues, the author introduces the Hurst–Hölder exponent within the Multifractional Process with Random Exponent (MPRE) framework, incorporating it into the stochastic equation describing asset dynamics. This relationship leads to a formal definition of fair volatility—the level of volatility implied under market efficiency, where prices follow semi-martingale dynamics.

The authors pointed out,

This work establishes the Hurst-Hölder exponent as a superior, informationally equivalent substitute for volatility in financial risk measurement, provided price dynamics are locally fractional. Its adoption offers three principal advantages:

• Path-Dependent Risk. It directly quantifies path roughness, capturing deviations from semi-martingale behavior that volatility alone cannot. It moves beyond measuring mere variability to diagnosing the type and intensity of randomness.
• Absolute Benchmarking. Its value is intrinsically meaningful. Unlike volatility, which requires relative comparison, the exponent provides an absolute scale anchored by the martingale benchmark of H(t) =1/2.
• Theoretical Synthesis. It provides a contribution to resolve the apparent dichotomy between market efficiency and behavioral finance. These are not opposing models but alternating market phases, dynamically captured by the exponent’s fluctuation around its efficient equilibrium.

The convertibility of Hurst-Hölder exponent into realized volatility is established by Proposition 1. This enables the determination of a confidence interval around the volatility level that prevails under conditions of informational market efficiency, that is, when prices exhibit submartingale behavior. This benchmark is the level that we termed fair volatility.

Theoretically, the results are noteworthy, as the paper contributes to the literature addressing inefficiencies in traditional volatility measures and extends the Black–Scholes–Merton framework by [glossary_exclude]accounting [/glossary_exclude]for the behavior (mean-reverting or trending) of the underlying asset.

However, practical applications of this approach remain to be seen. Given that the authors have already defined fair volatility, it would be valuable to see trading strategies developed around this concept and their performance evaluated in real markets.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Sergio Bianchi, Daniele Angelini, Fair Volatility: A Framework for Reconceptualizing Financial Risk, 2025, arXiv:2509.18837

Post Source Here: Fair Volatility: A Multifractional Model for Realized Volatility

source https://harbourfronts.com/fair-volatility-multifractional-model-realized-volatility/

Volatility, Skewness, and Kurtosis in Bitcoin Returns: An Empirical Analysis

As cryptocurrencies become mainstream, researchers have begun examining their statistical properties, particularly volatility, which represents the second moment of the return distribution. However, limited attention has been given to higher-order moments, specifically skewness and kurtosis. Given that cryptocurrencies are highly volatile and exhibit heavy-tail risks, their return distributions are not log-normal, making the study of skewness and kurtosis essential.

Reference [1] effectively analyzes the volatility, skewness, and kurtosis of Bitcoin and their relationships with Bitcoin returns. The authors use 5-minute high-frequency trading data from 2013 to 2024 to study these properties. They pointed out,

This paper employs 5-minute high-frequency data and quantile regression to examine the relationships between returns and higher-order moments in the Bitcoin market. These findings reveal significant asymmetric relationships between returns and higher-order moments in the Bitcoin market. Specifically: First, Bitcoin returns exhibit significant impacts on higher-order moments (namely volatility, skewness, and kurtosis), with contemporaneous returns demonstrating stronger effects than lagged returns. Second, negative returns show significantly negative correlations with changes in volatility and kurtosis, but significantly positive correlations with skewness changes. Third, at the upper quantiles of volatility and kurtosis changes, as well as the lower quantiles of skewness changes, the impact of negative returns on higher-order moments exceeds that of positive returns. Behavioural finance theories help explain these mechanisms.

The paper also provides insights for both investors and regulators

… investors should enhance risk awareness and optimize asset allocation. Investors must fully recognize Bitcoin’s unique risk structure, particularly the tail risks reflected by higher-order moments. When making investment decisions, they should consider not only volatility but also skewness and kurtosis to comprehensively assess risks. Diversification across Bitcoin and traditional assets can mitigate portfolio risks. Investors should also develop science-based strategies aligned with their risk tolerance and investment objectives, avoiding herd behaviour and excessive speculation.

We find this article particularly interesting and important, especially the conclusion that the correlation between Bitcoin returns and volatility is negative. However, we have observed that the options market has not yet priced in this negative correlation. Further research is warranted.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Can Yang and Zhen Fang, The asymmetric relationships between returns and higher-order moments: evidence from the Bitcoin market, Applied Economics, 2025

Article Source Here: Volatility, Skewness, and Kurtosis in Bitcoin Returns: An Empirical Analysis

source https://harbourfronts.com/volatility-skewness-kurtosis-bitcoin-returns-empirical-analysis/

Probabilistic AI in Finance: A Comprehensive Literature Review

Probabilistic AI is a branch of artificial intelligence that models uncertainty explicitly, allowing systems to reason and make predictions even when data is incomplete or noisy. Instead of producing single-point estimates, it generates probability distributions over possible outcomes, capturing both what is known and how confident the model is.

Reference [1] reviewed the research literature on probabilistic AI as applied to finance. Specifically, it followed a rigorous article selection process and ultimately analyzed 62 papers published between 2004 and 2024. The authors pointed out,

In this review, we perform a systematic literature review following a SLR approach to review 62 papers on the topic of probabilistic AI in finance. We examine these papers across dimensions such as model type, output, asset class, and uncertainty type. Additionally, we provide insights into the geographical distribution of research, contributor backgrounds, and the historical development of the field. Our findings suggest that most articles on probabilistic AI claim to enhance point predictions, and few articles have an explicit focus on improving uncertainty estimation within finance. Moreover, probabilistic AI offers valuable capabilities for financial modeling, including non- parametric distribution estimation, separation of uncertainty types, and capturing non-linear dynamics. However, the lack of comprehensive benchmarking and robust evaluations, especially in comparison to traditional models, makes it difficult to assess their true performance.

An important implication of our findings is the need for more interdisciplinary collaboration. Analysis of author backgrounds indicates that research in this area is largely dominated by computer scientists, with relatively limited participation from financial experts. As a result, computer scientists often lack the domain-specific knowledge needed to effectively model financial problems, while financial researchers, despite being better positioned to address such challenges, have seldom adopted probabilistic AI techniques, likely due to technical barriers. This review serves as a starting point for bridging these divides, guiding financial researchers in adopting these methods and helping computer scientists better frame their approaches within the financial context.

In short, the review highlights both the promise and the current limitations of probabilistic AI in finance, particularly the lack of robust benchmarking and systematic evaluation against traditional models. Advancing this field will require stronger interdisciplinary collaboration, where domain expertise from finance and innovation from computer science are combined to produce models that are both technically sound and economically meaningful.

We believe that the conclusion regarding domain knowledge and collaboration applies not only to probabilistic AI but also to deterministic, traditional AI and machine learning in finance.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Sivert Eggen, Tord Johan Espe, Kristoffer Grude, Morten Risstad, Rickard Sandberg, Financial Time Series Uncertainty: A Review of Probabilistic AI Applications, Journal of Economic Surveys, 2025; 00:1–39

Post Source Here: Probabilistic AI in Finance: A Comprehensive Literature Review

source https://harbourfronts.com/probabilistic-ai-finance-comprehensive-literature-review/

Expiration Effects and Return Anomalies in Option Markets

A growing body of research has recently investigated anomalies in option returns, such as option return momentum, and these anomalies are often attributed to market inefficiencies. Reference [1], however, proposed and tested a different hypothesis: these anomalies originate from option returns around expiration days.

Specifically, the author isolated the return of delta-hedged call options on the option expiration day—i.e., the third Friday of the month—and the following Monday to examine how these returns contribute to overall monthly option performance. They pointed out,

This paper identifies expiration-driven liquidity effects as a key driver of option return anomalies. We show that predictable option returns are largely concentrated around expiration, when investors rolling over positions create large order imbalances that overwhelm market makers’ risk-bearing capacity. These frictions lead to significant price distortions, explaining much of the observed anomaly predictability.

Our findings reveal that more than half of the monthly anomaly returns occur during the two-day expiration window, while returns outside this period are significantly weaker. This pattern holds across a broad set of stock, fundamental, and option characteristics and is particularly pronounced for S&P 500 stocks, where expiration fully accounts for anomaly returns.

These results challenge the view that option anomalies reflect behavioral biases or inefficiencies. Instead, they highlight the role of intermediary constraints and systematic liquidity demands in shaping option prices. Future research could further explore the impact of expiration dynamics on market participants and whether similar patterns exist in other derivative markets.

In short, the paper demonstrates that expiration effects are a major determinant of option return patterns. Many well-documented anomalies weaken or disappear when the expiration window is excluded, while return predictability is concentrated around expiration.

The authors also provide an explanation for the negative option returns observed near expiration, attributing them to the rollover of covered call positions. Finally, the paper highlights the role of market maker constraints and systematic liquidity demands in shaping option prices.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Pedro A. Garcia-Ares and Dmitriy Muravyev, Option returns: a tale of the expiration rollover day, 2025, fma.org

Article Source Here: Expiration Effects and Return Anomalies in Option Markets

source https://harbourfronts.com/expiration-effects-return-anomalies-option-markets/