Volatility Prediction

Hidden Order in Trades Predicts the Size of Price Moves ArXiv ID: 2512.15720 “View on arXiv” Authors: Mainak Singha Abstract Financial markets exhibit an apparent paradox: while directional price movements remain largely unpredictable–consistent with weak-form efficiency–the magnitude of price changes displays systematic structure. Here we demonstrate that real-time order-flow entropy, computed from a 15-state Markov transition matrix at second resolution, predicts the magnitude of intraday returns without providing directional information. Analysis of 38.5 million SPY trades over 36 trading days reveals that conditioning on entropy below the 5th percentile increases subsequent 5-minute absolute returns by a factor of 2.89 (t = 12.41, p < 0.0001), while directional accuracy remains at 45.0%–statistically indistinguishable from chance (p = 0.12). This decoupling arises from a fundamental symmetry: entropy is invariant under sign permutation, detecting the presence of informed trading without revealing its direction. Walk-forward validation across five non-overlapping test periods confirms out-of-sample predictability, and label-permutation placebo tests yield z = 14.4 against the null. These findings suggest that information-theoretic measures may serve as volatility state variables in market microstructure, though the limited sample (36 days, single instrument) requires extended validation. ...

Kronos: A Foundation Model for the Language of Financial Markets ArXiv ID: 2508.02739 “View on arXiv” Authors: Yu Shi, Zongliang Fu, Shuo Chen, Bohan Zhao, Wei Xu, Changshui Zhang, Jian Li Abstract The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis. Our pre-trained model is publicly available at https://github.com/shiyu-coder/Kronos. ...

A Consolidated Volatility Prediction with Back Propagation Neural Network and Genetic Algorithm ArXiv ID: 2412.07223 “View on arXiv” Authors: Unknown Abstract This paper provides a unique approach with AI algorithms to predict emerging stock markets volatility. Traditionally, stock volatility is derived from historical volatility,Monte Carlo simulation and implied volatility as well. In this paper, the writer designs a consolidated model with back-propagation neural network and genetic algorithm to predict future volatility of emerging stock markets and found that the results are quite accurate with low errors. ...

A Deep Learning Approach to Predict the Fall [“of Price”] of Cryptocurrency Long Before its Actual Fall ArXiv ID: 2411.13615 “View on arXiv” Authors: Unknown Abstract In modern times, the cryptocurrency market is one of the world’s most rapidly rising financial markets. The cryptocurrency market is regarded to be more volatile and illiquid than traditional markets such as equities, foreign exchange, and commodities. The risk of this market creates an uncertain condition among the investors. The purpose of this research is to predict the magnitude of the risk factor of the cryptocurrency market. Risk factor is also called volatility. Our approach will assist people who invest in the cryptocurrency market by overcoming the problems and difficulties they experience. Our approach starts with calculating the risk factor of the cryptocurrency market from the existing parameters. In twenty elements of the cryptocurrency market, the risk factor has been predicted using different machine learning algorithms such as CNN, LSTM, BiLSTM, and GRU. All of the models have been applied to the calculated risk factor parameter. A new model has been developed to predict better than the existing models. Our proposed model gives the highest RMSE value of 1.3229 and the lowest RMSE value of 0.0089. Following our model, it will be easier for investors to trade in complicated and challenging financial assets like bitcoin, Ethereum, dogecoin, etc. Where the other existing models, the highest RMSE was 14.5092, and the lower was 0.02769. So, the proposed model performs much better than models with proper generalization. Using our approach, it will be easier for investors to trade in complicated and challenging financial assets like Bitcoin, Ethereum, and Dogecoin. ...

Transformer for Times Series: an Application to the S&P500 ArXiv ID: 2403.02523 “View on arXiv” Authors: Unknown Abstract The transformer models have been extensively used with good results in a wide area of machine learning applications including Large Language Models and image generation. Here, we inquire on the applicability of this approach to financial time series. We first describe the dataset construction for two prototypical situations: a mean reverting synthetic Ornstein-Uhlenbeck process on one hand and real S&P500 data on the other hand. Then, we present in detail the proposed Transformer architecture and finally we discuss some encouraging results. For the synthetic data we predict rather accurately the next move, and for the S&P500 we get some interesting results related to quadratic variation and volatility prediction. ...

Leveraging Sample Entropy for Enhanced Volatility Measurement and Prediction in International Oil Price Returns ArXiv ID: 2312.12788 “View on arXiv” Authors: Unknown Abstract This paper explores the application of Sample Entropy (SampEn) as a sophisticated tool for quantifying and predicting volatility in international oil price returns. SampEn, known for its ability to capture underlying patterns and predict periods of heightened volatility, is compared with traditional measures like standard deviation. The study utilizes a comprehensive dataset spanning 27 years (1986-2023) and employs both time series regression and machine learning methods. Results indicate SampEn’s efficacy in predicting traditional volatility measures, with machine learning algorithms outperforming standard regression techniques during financial crises. The findings underscore SampEn’s potential as a valuable tool for risk assessment and decision-making in the realm of oil price investments. ...

Artificial Intelligence-based Analysis of Change in Public Finance between US and International Markets ArXiv ID: 2403.18823 “View on arXiv” Authors: Unknown Abstract Public finances are one of the fundamental mechanisms of economic governance that refer to the financial activities and decisions made by government entities to fund public services, projects, and operations through assets. In today’s globalized landscape, even subtle shifts in one nation’s public debt landscape can have significant impacts on that of international finances, necessitating a nuanced understanding of the correlations between international and national markets to help investors make informed investment decisions. Therefore, by leveraging the capabilities of artificial intelligence, this study utilizes neural networks to depict the correlations between US and International Public Finances and predict the changes in international public finances based on the changes in US public finances. With the neural network model achieving a commendable Mean Squared Error (MSE) value of 2.79, it is able to affirm a discernible correlation and also plot the effect of US market volatility on international markets. To further test the accuracy and significance of the model, an economic analysis was conducted that aimed to correlate the changes seen by the results of the model with historical stock market changes. This model demonstrates significant potential for investors to predict changes in international public finances based on signals from US markets, marking a significant stride in comprehending the intricacies of global public finances and the role of artificial intelligence in decoding its multifaceted patterns for practical forecasting. ...

Forecasting Volatility with Machine Learning and Rough Volatility: Example from the Crypto-Winter ArXiv ID: 2311.04727 “View on arXiv” Authors: Unknown Abstract We extend the application and test the performance of a recently introduced volatility prediction framework encompassing LSTM and rough volatility. Our asset class of interest is cryptocurrencies, at the beginning of the “crypto-winter” in 2022. We first show that to forecast volatility, a universal LSTM approach trained on a pool of assets outperforms traditional models. We then consider a parsimonious parametric model based on rough volatility and Zumbach effect. We obtain similar prediction performances with only five parameters whose values are non-asset-dependent. Our findings provide further evidence on the universality of the mechanisms underlying the volatility formation process. ...

Stock Volatility Prediction Based on Transformer Model Using Mixed-Frequency Data ArXiv ID: 2309.16196 “View on arXiv” Authors: Unknown Abstract With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical and macroeconomic indicators still leaves room for improvement; on the other hand, macroeconomic indicators and peoples’ search record on those search engines affecting their interested topics will intuitively have an impact on the stock volatility. For the convenience of assessment of the influence of these indicators, macroeconomic indicators and stock technical indicators are then grouped into objective factors, while Baidu search indices implying people’s interested topics are defined as subjective factors. To align different frequency data, we introduce GARCH-MIDAS model. After mixing all the above data, we then feed them into Transformer model as part of the training data. Our experiments show that this model outperforms the baselines in terms of mean square error. The adaption of both types of data under Transformer model significantly reduces the mean square error from 1.00 to 0.86. ...

An Empirical Analysis on Financial Markets: Insights from the Application of Statistical Physics ArXiv ID: 2308.14235 “View on arXiv” Authors: Unknown Abstract In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and particles in a physical system, we establish unique measures for the system’s kinetic energy and momentum as a way to comprehend and evaluate the state of limit order book. Our model goes beyond examining merely the top layers of the order book by introducing the concept of ‘active depth’, a computationally-efficient approach for identifying order book levels that have impact on price dynamics. We empirically demonstrate that our model outperforms the benchmarks of traditional approaches and machine learning algorithm. Our model provides a nuanced comprehension of market microstructure and produces more accurate forecasts on volatility and expected returns. By incorporating principles of statistical physics, this research offers valuable insights on understanding the behaviours of market participants and order book dynamics. ...