Volatility Risk Premium Dynamics Through the Heston Framework

A significant amount of research has been conducted on the volatility risk premium (VRP). Reference [1] contributes to this literature by linking the VRP to the parameters of the Heston model. The Heston model is a widely used stochastic volatility model that captures time-varying volatility and mean-reverting dynamics.

Unlike previous studies, the authors do not rely on a theoretical model to estimate the VRP, but instead use returns from variance-related financial instruments, including variance swaps, VIX futures, and straddles, as proxies, examined over 7- and 30-day horizons. They pointed out,

The economic magnitude is substantial. A one-standard-deviation increase in v0 is associated with approximately 730 basis points lower next-day returns for the 7-day variance swap. This confirms that the current level of market variance is the primary driver of near-term VRP: when variance is elevated, the compensation demanded by investors for bearing variance risk increases, depressing expected returns on long-volatility positions…

This pattern supports Hypothesis 2: greater uncertainty about future variance dynamics leads to larger risk premia and more negative expected returns. The slightly weaker significance for 30-day straddles may reflect the attenuation of uncertainty effects at longer horizons, where the convex payoff structure provides some natural hedging against variance fluctuations…

At the 30-day horizon, the significance of κ diminishes substantially. For variance swaps and straddles, coefficients become statistically indistinguishable from zero. Only for VIX futures does κ retain marginal significance. This differential pattern across maturities—significance at 7 days but not at 30 days—is precisely what Hypothesis 3 predicts and provides validation of the underlying economic mechanism.

In summary, the results show that the initial variance level is a strong negative predictor across all cases, volatility of volatility is also negative and robust, mean reversion is relevant only in the short term, and long-run parameters are largely irrelevant.

These findings suggest that the VRP is primarily driven by current volatility levels and uncertainty rather than long-term factors, providing useful insights for portfolio and risk management.

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

References

[1] Han, C.-H., & Wang, K. (2026), Variance Risk Premia under Volatility Models, Review of Quantitative Finance and Accounting.

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Multifractal Analysis of Herding and Inefficiency in Precious Metals

Gold and silver have been strong recently, with upward trends and increased volatility. Reference [1] studies the price dynamics of leading precious metals, gold, silver, platinum, and palladium, over the period from December 9, 2019, to March 1, 2026, dividing the sample into pre- and post-COVID subperiods. The study employs Multifractal Detrended Fluctuation Analysis (MFDFA) to estimate the generalized Hurst exponent, the magnitude of long memory, and return predictability.

The author pointed out,

The results based on the GHE estimates reveal that the selected precious metals exhibited varying degrees of multifractal properties throughout the sample period. The intensities of multifractal structures differ from coronavirus to its aftermath, but the trend is less pronounced for the latter phases of COVID-19 pandemic, except for gold. Additionally, the same attitude is not relevant for market efficiency where the herd-driven behavior strictly decreased for silver, platinum, and palladium after the outbreak but the market became increasingly inefficient for each asset. Therefore, the degree of herding behavior and market inefficiency differed markedly between the two sub-periods. It is noteworthy that changes in the average values of the multifractal spectrum indicate an increase in multifractality only for gold during the post-pandemic period. This means that the latter phase appears to have intensified herding behavior and market inefficiency in gold transactions. However, the MLM-based inefficiency index indicated that all selected assets became less efficient in the aftermath of COVID-19 pandemic. Within this framework, following the coronavirus disease, the returns of silver, platinum, and palladium - excluding gold – became increasingly predictable, indirectly suggesting reduced volatility.

…In line with the multifractal spectrum results, the evaluation of post-COVID-19 changes in herding behavior through the fractal dimension scale indicates that, during the given period in the precious metals market, herding increased only in gold, while the rest of the metal assets exhibited a decline in herding tendencies…In addition, the rise in the inefficiency index for all precious metals between the two periods indicates that they were exposed to wider market-wide effects related to transaction volumes.

A key contribution of the paper is the separation of herding behavior, measured by the Hurst exponent, from market inefficiency, measured by an inefficiency index, along with the construction of a predictability index.

The results show that gold exhibits stronger herding post-COVID, while other metals show weaker herding, although all markets become more inefficient. In terms of predictability, silver, platinum, and palladium become more predictable post-COVID, whereas gold does not.

This is a noteworthy contribution, showing that the precious metal market does not follow a random walk, that structure has changed after COVID, and that gold behaves differently from other metals, providing useful insights for portfolio and risk management.

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

References

[1] Özdemir, O. (2026). Herding, Market Efficiency, and the Melting Pot Effect: Evidence from the Precious Metals Market. Preprints.org.

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Overnight vs Daytime Returns in Sector ETFs

There is a noteworthy line of research that decomposes asset or strategy returns into daytime and overnight components. This type of decomposition has been discussed previously in the context of the volatility risk premium.

Reference [1] follows a similar approach, examining SPY and nine sector ETFs over the period 1999 to 2025. The study tests 24 simple strategies based on static long/short positions, momentum (“inertia”), and reversal rules, applied separately to daytime and overnight returns. The authors pointed out,

The results provide compelling evidence for the hypothesis that overnight periods generate stronger exploitable momentum than daytime periods. Strategy #1 (Long/Cash), which captures pure overnight returns R_i = RCO_i, consistently outperformed across all ten ETFs with final values ranging from $435 (XLP) to $3165 (XLK). In contrast, Strategy #3 (Cash/Long), capturing pure daytime returns R_i = ROC_i, generated losses in 8 out of 10 ETFs. This stark asymmetry contradicts the efficient market hypothesis and supports behavioral finance theories, which suggest reduced arbitrage activity during non-trading hours…

Conversely, the systematic failure of Strategy #2 (Short/Cash: R_i = −RCO_i) across all ETFs ($2–$18 final values) demonstrates that overnight movements exhibit persistent positive drift rather than random walk behavior. If overnight returns were symmetrically distributed, short and long strategies would show comparable absolute performance, which the data clearly refute…

The enormous outperformance documented for Strategy #18 throughout this paper is therefore attributable to the temporal decomposition of the 24 h period into distinct overnight and daytime sub-periods, rather than to the specific direction of the conditioning signal. The structural asymmetry between overnight returns (persistent positive drift, low volatility, fat tails) and daytime returns (near-zero drift, higher volatility) is the economic substrate that makes sub-period strategies profitable…

In summary, the results show that overnight returns exhibit a persistent positive drift, while daytime returns are significantly weaker, and the best-performing strategies are those that maintain long exposure overnight. A simple overnight-only long strategy also performs well and often outperforms buy-and-hold before transaction costs. Also, autocorrelation analysis suggests that the edge lies in sub-period decomposition rather than long-memory forecasting.

Note, however, that after [glossary_exclude]accounting [/glossary_exclude]for transaction costs, returns decline, making these strategies mainly feasible for managers with low execution costs.

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

References

[1] Salotra, G., Katikireddy, T., Anumolu, Y., & Pinsky, E., A Comparative Analysis of Overnight vs. Daytime Static and Momentum Strategies Across Sector ETFs, Risks, 2026, 14, 84.

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Regime Classification Framework for Mean-Reverting and Trending Markets

Regime classification is important in asset and risk management. Traditional approaches classify regimes based on direction, bullish or bearish, and volatility, high or low. Reference [1] departs from this framework and instead classifies markets as mean-reverting or trending. Specifically, it uses return thresholds of 0.5%, 0.75%, and 1% to define regimes and examines SPY, QQQ, DIA, and IWM over the period 2000 to 2024.

The study incorporates technical indicators such as VIX, RSI, and ATR, along with market data, including returns, range, and volume, and macro events such as CPI releases, employment data, and FOMC meetings and projections. Three models are evaluated: Random Forest, Neural Network (MLP), and XGBoost. Validation is conducted using a rolling window framework with an expanding training set and one-step-ahead testing, including a 252-day evaluation period in 2024.

The author pointed out,

The results demonstrate consistent improvements over baseline classifiers, though performance varies meaningfully across ETFs and thresholds. For SPY (S&P 500), Neural Networks achieved a 15.4% improvement over the naive classifier at the 0.5% threshold, with AUC values reaching 0.67–0.74 at the 0.75% and 1% thresholds—the strongest and most statistically robust results in the study (bootstrap 95% CIs well above 0.5 at both thresholds). For IWM (Russell 2000), improvements ranged from 5.7% to 13.4% across thresholds, with Neural Network AUC values of 0.59 and 0.55 at the 0.5% and 0.75% thresholds (bootstrap CIs excluding 0.5), indicating genuine predictive power for small-cap market regime classification …

For QQQ (Nasdaq), the Neural Network achieved 4.7–6.1% improvement over the naive classifier, with AUC reaching 0.62 at the 1% threshold (bootstrap CI: [0.55, 0.69]). Performance at lower thresholds was weaker and the 0.5% threshold AUC CI marginally includes 0.5; practitioners should treat QQQ predictions at the 0.5% threshold with caution. These findings underscore that predicting oscillatory behavior in highly volatile, technology-concentrated indices is more challenging than in diversified large-cap indices, and that the choice of oscillation threshold materially affects the reliability of model predictions…

In summary, the results show that the best case achieves a 15.4% improvement in prediction over a naive strategy for SPY using a neural network with a 0.5% threshold; although in many cases the improvement is more modest, in the range of 1 to 5%, and varies significantly across ETFs.

While the study has several limitations, it points to a more relevant research direction: predicting the magnitude-based regime appears slightly easier than predicting direction, and machine learning is effective as a risk or regime filter rather than as a direct alpha-generating signal.

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

References

[1] Azizi, S. (2026). Leveraging Machine Learning for Financial Forecasting: Distinguishing Market Trends from Oscillations in ETFs. Journal of Risk and Financial Management, 19(4), 262.

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Variational Autoencoders in Volatility and Option Pricing

The Black–Scholes–Merton model is a groundbreaking and foundational framework in option pricing; however, it has well-known limitations. Several extensions have been developed to address these issues, including stochastic volatility and Lévy process-based models, which are largely parametric.

Reference [1] proposes a semi-parametric approach to overcome these limitations. Specifically, the model consists of three components:

1. Variational Autoencoder (VAE) to generate return distributions, capturing non-normal features such as skewness and fat tails, using a tail-weighted loss to better represent extreme events and generate realistic synthetic return paths,
2. An implied volatility model based on LightGBM, which predicts volatility using option characteristics and market sentiment, capturing the volatility surface more effectively than constant volatility assumptions, and
3. Pricing framework using Multi-Level Monte Carlo, which simulates paths based on VAE-generated returns and predicted volatility, achieving similar accuracy with lower computational cost than standard Monte Carlo methods.

The authors pointed out,

A VAE model was trained on historical log-returns of the NIFTY50 index to learn a latent representation of returns. This approach allowed us to capture complex, non-Gaussian structures in the return distribution and to generate synthetic return paths that reflect both normal and extreme market behavior. A quantile-based sampling strategy was adopted during data splitting to ensure the preservation of rare tail events in both training and validation sets. This made the model more resilient to imbalanced data and improved its ability to learn representative latent dynamics. Additionally, to estimate implied volatility, we utilized a LightGBM regression model trained on a diverse set of features, including option-specific variables such as strike price, moneyness, time to expiry and market-level sentiment indicators. The synthetic samples generated by the VAE were then used as inputs to a two-level MLMC simulation framework to estimate option prices more efficiently than conventional Monte Carlo methods. The MLMC approach reduced computational time significantly, while maintaining high fidelity in price estimation.

Empirical evaluation of our full pricing framework demonstrated that the proposed pipeline outperformed the classical Black-Scholes model across a wide range of market conditions. This improvement was consistent across both call and put options, as well as for different moneyness criteria. In particular, the model showed a clear edge in scenarios involving longer time to expiry.

In short, VAE was trained to capture non-Gaussian features and generate realistic synthetic return paths. Implied volatility was estimated using a LightGBM model with option features and sentiment inputs, and the resulting outputs were fed into a two-level MLMC framework for efficient option pricing. The approach reduced computational cost while maintaining accuracy and consistently outperformed the BSM model across market conditions, particularly for longer maturities.

This contribution is valuable and can be extended in several directions, for example, by applying the Variational Autoencoder framework to stress testing. However, the approach has limitations, including the lack of enforcement of no-arbitrage conditions.

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

References

[1] Sapna, S., & Mohan, B. R. (2026). Variational autoencoders for option pricing: A semi-parametric approach to eliminating traditional assumptions. Expert Systems With Applications, 321, 132216.

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The Impact of Retail Options Trading on the Implied Volatility Surface

Retail options trading is rising rapidly, driven by factors such as the growth of retail brokers, the popularity of social media, and more flexible working hours. Alongside this trend, there has been an increased interest in research on retail options trading behavior. We recently discussed retail options trading and its link to gambling behavior.

Reference [1] continues this line of research by examining how retail trading reshapes the implied volatility (IV) surface dynamics. The authors utilize OPRA and Nasdaq data for this study. To isolate the effect of retail options trading, they apply a difference-in-differences approach around retail broker outages, 82 events from 2019 to 2021, comparing implied volatility between high-retail and low-retail stocks, during versus pre-outage periods.

The authors pointed out,

Option market volume has dramatically increased in recent years, driven by an influx of retail investors. Our analysis reveals that retail option trading is particularly concentrated in call, short-dated, and out-of-the-money call options. We examine the effects of retail trading on option market volume and implied volatility, using brokerage outages as exogenous shocks to retail option trading. Our findings indicate that net buying volume by retail investors significantly declines during outages for the types of options they prefer. In contrast, net buying volume rises during outages for long-dated options, consistent with retail investors tending to write rather than purchase longer maturity options.

The paper’s central finding is that retail investor demand pressure significantly impacts option implied volatility. We find that implied volatility significantly decreases during retail brokerage outages, and in particular for call, OTM, and short-dated options. In contrast, implied volatility significantly increases for long-dated options. The effect of retail brokerage outages on implied volatility aligns with the shifts in net retail volume and points towards a significant role for retail investors in shaping the IV surface. Additional robustness analysis indicates that the outage results are unique to the outage period, are not driven by a small number of the most actively traded options, and continue to hold for alternative option trading data.

In short, retail investors systematically buy short-dated, out-of-the-money (especially calls) and sell long-dated options, creating predictable pressure across the surface. When retail trading activity is reduced during brokerage outages, IV falls for short-dated and OTM options but rises for long-dated options.

This paper contributes to a better understanding of retail options trading and shows how retail traders can materially affect the implied volatility surface.

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

References

[1] Eaton, Gregory W., T. Clifton Green, Brian S. Roseman, and Yanbin Wu (2025). Retail Option Traders and the Implied Volatility Surface. SSRN 4104788

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Evaluating Machine Learning Models for S&P 500 Return Prediction

Machine learning (ML) is increasingly applied in finance. In trading in particular, researchers aim to determine whether ML can generate consistent alpha. Reference [1] revisits this question. The authors utilize a long sample dataset from 1970 to 2024 and evaluate a wide range of ML models, including linear, nonlinear, and ensemble methods, to assess whether they can predict one-day-ahead S&P 500 returns and generate trading profits.

In the models, the inputs are price, returns, volume, volatility, market breadth, and simple sentiment proxies. The models include linear methods, such as OLS and elastic net, and nonlinear methods, such as random forest, XGBoost, SVM, and kNN, along with ensemble approaches. They are trained on rolling 10-year windows with recalibration every 2 to 5 years. The trading strategy takes a long position when the forecast is positive and otherwise holds Treasury bills.

The authors pointed out,

This study examined the performance of machine learning architectures applied to financial forecasting within the framework of the adaptive market hypothesis. By comparing 12 models and three ensemble systems over 55 years of daily S&P 500 data, we demonstrated that machine learning with adaptive retraining can be used to obtain stock market profits over an extended period from 1970 to 2024. However, the extent of abnormal returns is limited by transaction costs and the fact that financial markets quickly adapt, reducing the profitability of any machine learning system. Three architectures—elastic nets, logit, and XGboost—consistently outperformed the others, while ensemble designs provided the most resilient returns and stability across changing market regimes. Nevertheless, system profitability declined after 1987, indicating that even sophisticated systems face diminishing arbitrage opportunities as markets learn and adapt. This dynamic is consistent with both adaptive market and adaptive systems perspectives.

In short, without transaction costs, many models generate positive abnormal returns. However, once realistic trading costs are incorporated, these profits largely disappear, particularly in the post-1987 period. There is also a strong regime effect, with high profitability of around 20% or more during 1970 to 1987, followed by a significant decline to approximately 5% to 9% from 1988 to 2024, often rendering the strategies unprofitable after costs.

This paper finds that while ML strategies can generate abnormal returns and remain adaptive over time, profitability declines in later periods and exhibits significant variability, raising concerns about real-time performance.

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

References

[1] Olson, D., Nusair, S., & Galariotis, E. (2026). Profitability of Machine Learning Models in Forecasting the S&P 500 Index. Information Systems Frontiers.

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Detecting Regimes in the Volatility Surface Using Clustering

Regime identification is important in portfolio and risk management. There are many ways to classify market regimes, for example, based on market direction, such as bullish, bearish, or sideways. Another common classification is based on volatility regimes, such as high or low volatility. Most existing methods for detecting volatility regimes rely on single-point data, such as implied volatility indices or realized volatility measures.

Reference [1] proposes a new regime classification approach based on the entire volatility surface. The method first calculates local gradients, defined as the partial derivatives of implied volatility with respect to moneyness and maturity. These gradient changes are then clustered using an unsupervised algorithm to identify recurring structural transformations of the volatility surface.

The author pointed out,

My goal was to analyze structural changes in the implied volatility surface and study how the surface evolves over time. In this study, I have successfully developed a methodology to represent and quantify daily structural changes in the IV surface using local gradients. I have also used unsupervised clustering algorithm to identify distinct types of surface transformations. I have also included interpretations for some of the clusters in the previous section.

My analysis revealed that there is a number of distinct types of surface transformations that can be identified and interpreted. As expected, the vast majority of daily IV surface changes were classified as noise because structural changes in the volatility surface do not occur often. Therefore, the identified clusters have sizes of up to 18 samples. Notably, several clusters represented specific skew or term structure dynamics for different levels of maturity and moneyness.

In summary, the paper demonstrated that the clusters correspond to specific structural changes in skew and term structure rather than random fluctuations. For example:

• Cluster 1: changes mainly affect short-term maturities (1–2 months) and alter the slope across moneyness, indicating localized movements in the front of the surface.
• Cluster 2: shows term-structure rotation, where longer-maturity implied volatilities fall relative to short maturities for some moneyness levels, making the term structure steeper.
• Cluster 3: reflects a flattening of the skew, where higher-moneyness volatilities decrease relative to lower-moneyness ones, interpreted as increased demand for downside protection (more bearish sentiment).

This paper is exploratory in nature, as it does not prove the economic benefits of using the proposed volatility surface clustering technique. However, it points to an important research direction: volatility regime detection may benefit from analyzing the full volatility surface rather than relying on single volatility indicators, and the paper proposes a practical framework for doing so.

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

References

[1] Dzhafarov, Shakhin (2025). Detecting Structural Evolution of Implied Volatility Surface Using Gradient-Based Features: A Machine Learning Approach to Market Regime Detection. Master’s thesis, Aalto University.

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Retail Options Trading and Gambling Behavior

Options trading volume has risen sharply in recent years, and a significant portion of this increase is attributed to the growing participation of retail traders. We have discussed retail options trading behavior in previous posts. Reference [1] continues this line of research by examining how retail investors trade stock options and how their attention influences options market activity.

The study posits that retail investors often treat stock options similarly to gambling. The authors construct a Search Volume Index (SVI), which measures the intensity of Google searches for specific keywords across U.S. states, and use it as a proxy for retail investors’ attention to stock options, capturing surges in public interest around firm-specific news such as earnings announcements. They pointed out,

This paper examines how regional gambling propensity relates to retail participation in U.S. options markets. Using state-level Google search data, gambling measures, and regulatory and event-based shocks, we analyze whether gambling intensity is associated with option attention and speculative trading behavior.

We document that option attention is higher in gambling-prone states, particularly around salient events such as earnings announcements. We also show that option search intensity is positively associated with brokerage-related search activity, consistent with attention translating into trading-related behavior…

We further find that lottery-like option characteristics—including out-of-the-money contracts, short maturities, and high implied volatility—receive greater attention in high-gambling states. These results suggest that regional gambling propensity helps explain cross-state variation in speculative option demand.

Finally, we relate option attention to household credit outcomes. Elevated option attention in gambling-prone states is associated with higher short-term borrowing and increased delinquency rates. While these associations do not establish household-level causality, they indicate that gambling-motivated financial attention coincides with measures of financial vulnerability at the state level.

Overall, the findings highlight how regional behavioral traits interact with financial market structure to shape retail participation in derivative markets. Future research may examine whether similar dynamics arise in other highly leveraged products or emerging speculative venues.

In short, this paper shows that retail option trading is higher in U.S. states with a stronger gambling culture, especially around earnings announcements when uncertainty is high. It also finds that this gambling-motivated attention increases trading in short-dated out-of-the-money options and is associated with higher implied volatility and higher household debt.

This paper provides additional and interesting insights into retail options behavior. Let us know what you think in the comments below or in the discussion forum.

References

[1] Matthew Flynn, Yifan Liu, Ivilina Popova, Do retail traders gamble on stock options? Journal of Financial Markets, 2026

Originally Published Here: Retail Options Trading and Gambling Behavior

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Entropy-Based Regime Detection of Tail Risks

Identifying market regimes is particularly important in portfolio and risk management. Typically, markets are classified as bullish or bearish, or as being in high- or low-volatility regimes.

Reference [1] proposes an alternative classification by distinguishing between “normal” and heavy-tailed regimes. Specifically, the study develops a nonparametric method to detect financial market regimes using differential entropy rather than volatility alone. The underlying idea is that while volatility measures dispersion, entropy captures the full distributional uncertainty, including tail behavior, which becomes particularly important during crisis periods.

The authors estimate entropy using a kernel density estimator with a heavy-tailed kernel in rolling windows and compare entropy with variance. When markets behave approximately Gaussian, i.e., normally, entropy and variance move together; during turbulent periods, the relationship breaks down, revealing heavy-tailed regimes that volatility alone cannot identify.

They pointed out,

This study demonstrates that differential entropy estimation with a heavy-tailed kernel provides an effective, nonparametric framework for identifying financial market regimes beyond traditional variance-based measures. By integrating entropy and tail-index analysis within a moving-window kernel density approach, the method captures dynamic shifts in distributional behavior without relying on parametric assumptions, offering a flexible tool for regime detection…

Empirically, applying the method to four major stock indices (Ibovespa, S&P 500, Nikkei, and SSE Composite) revealed that heavy-tailed regimes align with well-known episodes of market turbulence, including the Dot-com Bubble, the Global Financial Crisis, the COVID-19 shock, and the recent tariff-related crisis. In contrast, Gaussian regimes correspond to periods of relative stability and market efficiency.

Importantly, we showed that variance and entropy do not need to move in tandem. While volatility quantifies dispersion, entropy captures broader uncertainty and tail risk, remaining well-defined even when higher-order moments fail to exist. This divergence underscores the limitations of moment-based measures and highlights the potential of entropy as a complementary indicator of systemic instability.

In short, the paper developed a regime detection method based on entropy, which provides an alternative regime indicator that captures tail risk and structural shifts that standard volatility measures may miss.

Applying the method to Ibovespa, S&P 500, Nikkei, and SSE shows that detected heavy-tailed regimes coincide with major crises such as the Dot-com crash, the Global Financial Crisis, COVID-19, and other stress events, while Gaussian regimes correspond to calmer market periods.

This represents an important contribution to the literature, particularly in the context of managing tail risks and risk management more broadly.

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

References

[1]  Raul Matsushit, Iuri Nobre, Sergio Da Silva, Beyond volatility: Using differential entropy to detect financial market regimes, Chaos, Solitons and Fractals 202 (2026) 117553

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