Volatility Modeling

How to choose my stochastic volatility parameters? A review ArXiv ID: 2512.19821 “View on arXiv” Authors: Fabien Le Floc’h Abstract Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic volatility inside stochastic local volatility models. Keywords: Stochastic Volatility, Local Volatility, Derivatives Pricing, Parameter Estimation, Volatility Modeling, Equity Derivatives ...

Volatility time series modeling by single-qubit quantum circuit learning ArXiv ID: 2512.10584 “View on arXiv” Authors: Tetsuya Takaishi Abstract We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture volatility asymmetry. Our results show that QCL-based volatility predictions preserve the negative return-volatility correlation, a hallmark of asymmetric volatility dynamics. Moreover, analysis of the Hurst exponent and multifractal characteristics indicates that the predicted series, like the original synthetic data, exhibits anti-persistent behavior and retains its multifractal structure. ...

Sentiment and Volatility in Financial Markets: A Review of BERT and GARCH Applications during Geopolitical Crises ArXiv ID: 2510.16503 “View on arXiv” Authors: Domenica Mino, Cillian Williamson Abstract Artificial intelligence techniques have increasingly been applied to understand the complex relationship between public sentiment and financial market behaviour. This study explores the relationship between the sentiment of news related to the Russia-Ukraine war and the volatility of the stock market. A comprehensive dataset of news articles from major US platforms, published between January 1 and July 17, 2024, was analysed using a fine-tuned Bidirectional Encoder Representations from Transformers (BERT) model adapted for financial language. We extracted sentiment scores and applied a Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model, enhanced with a Student-t distribution to capture the heavy-tailed nature of financial returns data. The results reveal a statistically significant negative relationship between negative news sentiment and market stability, suggesting that pessimistic war coverage is associated with increased volatility in the S&P 500 index. This research demonstrates how artificial intelligence and natural language processing can be integrated with econometric modelling to assess real-time market dynamics, offering valuable tools for financial risk analysis during geopolitical crises. ...

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. ...

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator ArXiv ID: 2509.05065 “View on arXiv” Authors: Guillaume Maitrier, Grégoire Loeper, Jean-Philippe Bouchaud Abstract This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [“2”] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible. ...

A Heterogeneous Spatiotemporal GARCH Model: A Predictive Framework for Volatility in Financial Networks ArXiv ID: 2508.20101 “View on arXiv” Authors: Atika Aouri, Philipp Otto Abstract We introduce a heterogeneous spatiotemporal GARCH model for geostatistical data or processes on networks, e.g., for modelling and predicting financial return volatility across firms in a latent spatial framework. The model combines classical GARCH(p, q) dynamics with spatially correlated innovations and spatially varying parameters, estimated using local likelihood methods. Spatial dependence is introduced through a geostatistical covariance structure on the innovation process, capturing contemporaneous cross-sectional correlation. This dependence propagates into the volatility dynamics via the recursive GARCH structure, allowing the model to reflect spatial spillovers and contagion effects in a parsimonious and interpretable way. In addition, this modelling framework allows for spatial volatility predictions at unobserved locations. In an empirical application, we demonstrate how the model can be applied to financial stock networks. Unlike other spatial GARCH models, our framework does not rely on a fixed adjacency matrix; instead, spatial proximity is defined in a proxy space constructed from balance sheet characteristics. Using daily log returns of 50 publicly listed firms over a one-year period, we evaluate the model’s predictive performance in a cross-validation study. ...

Applying Informer for Option Pricing: A Transformer-Based Approach ArXiv ID: 2506.05565 “View on arXiv” Authors: Feliks Bańka, Jarosław A. Chudziak Abstract Accurate option pricing is essential for effective trading and risk management in financial markets, yet it remains challenging due to market volatility and the limitations of traditional models like Black-Scholes. In this paper, we investigate the application of the Informer neural network for option pricing, leveraging its ability to capture long-term dependencies and dynamically adjust to market fluctuations. This research contributes to the field of financial forecasting by introducing Informer’s efficient architecture to enhance prediction accuracy and provide a more adaptable and resilient framework compared to existing methods. Our results demonstrate that Informer outperforms traditional approaches in option pricing, advancing the capabilities of data-driven financial forecasting in this domain. ...

Why is the volatility of single stocks so much rougher than that of the S&P500? ArXiv ID: 2505.02678 “View on arXiv” Authors: Othmane Zarhali, Cecilia Aubrun, Emmanuel Bacry, Jean-Philippe Bouchaud, Jean-François Muzy Abstract The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the (log)-volatilities of factors and residuals are themselves decomposed into factor modes, with a common dominant volatility mode affecting both market and sector factors but also residuals. Here, we consider the case of a single factor where the only dominant log-volatility mode is rough, with a Hurst exponent $H \simeq 0.11$ and the log-volatility residuals are ‘‘super-rough’’ or ‘‘multifractal’’, with $H \simeq 0$. We demonstrate that such a construction naturally accounts for the somewhat surprising stylized fact reported by Wu et al. , where it has been observed that the Hurst exponents of stock indexes are large compared to those of individual stocks. We propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees of its consistency. We demonstrate the effectiveness of our approach through numerical experiments and apply it to daily stock data from the S&P500 index. The estimated roughness exponents for both the factor and idiosyncratic components validate the assumptions underlying our model. ...

Bridging Econometrics and AI: VaR Estimation via Reinforcement Learning and GARCH Models ArXiv ID: 2504.16635 “View on arXiv” Authors: Fredy Pokou, Jules Sadefo Kamdem, François Benhmad Abstract In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the current market dynamics. To overcome these limitations, we propose a hybrid framework for Value-at-Risk (VaR) estimation, combining GARCH volatility models with deep reinforcement learning. Our approach incorporates directional market forecasting using the Double Deep Q-Network (DDQN) model, treating the task as an imbalanced classification problem. This architecture enables the dynamic adjustment of risk-level forecasts according to market conditions. Empirical validation on daily Eurostoxx 50 data covering periods of crisis and high volatility shows a significant improvement in the accuracy of VaR estimates, as well as a reduction in the number of breaches and also in capital requirements, while respecting regulatory risk thresholds. The ability of the model to adjust risk levels in real time reinforces its relevance to modern and proactive risk management. ...

Liquidity-adjusted Return and Volatility, and Autoregressive Models ArXiv ID: 2503.08693 “View on arXiv” Authors: Unknown Abstract We construct liquidity-adjusted return and volatility using purposely designed liquidity metrics (liquidity jump and liquidity diffusion) that incorporate additional liquidity information. Based on these measures, we introduce a liquidity-adjusted ARMA-GARCH framework to address the limitations of traditional ARMA-GARCH models, which are not effectively in modeling illiquid assets with high liquidity variability, such as cryptocurrencies. We demonstrate that the liquidity-adjusted model improves model fit for cryptocurrencies, with greater volatility sensitivity to past shocks and reduced volatility persistence of erratic past volatility. Our model is validated by the empirical evidence that the liquidity-adjusted mean-variance (LAMV) portfolios outperform the traditional mean-variance (TMV) portfolios. ...