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Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Machine Learning · Statistics 2025-11-26 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…

Statistical Finance · Quantitative Finance 2015-05-08 Gordon J. Ross

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…

Statistical Finance · Quantitative Finance 2020-01-03 D. S. Grebenkov , J. Serror

Volatility clustering is a crucial property that has a substantial impact on stock market patterns. Nonetheless, developing robust models for accurately predicting future stock price volatility is a difficult research topic. For predicting…

Computational Finance · Quantitative Finance 2025-05-20 Ananda Chatterjee , Hrisav Bhowmick , Jaydip Sen

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…

Statistical Mechanics · Physics 2009-11-10 James P. Gleeson

Volatility-based trading strategies have attracted a lot of attention in financial markets due to their ability to capture opportunities for profit from market dynamics. In this article, we propose a new volatility-based trading strategy…

Trading and Market Microstructure · Quantitative Finance 2023-08-21 Ivan Letteri

Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…

Econometrics · Economics 2020-10-09 Yuta Yamauchi , Yasuhiro Omori

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…

Computational Finance · Quantitative Finance 2025-08-27 Zong Ke , Jingyu Xu , Zizhou Zhang , Yu Cheng , Wenjun Wu

Stock market volatility forecasting is a task relevant to assessing market risk. We investigate the interaction between news and prices for the one-day-ahead volatility prediction using state-of-the-art deep learning approaches. The…

Statistical Finance · Quantitative Finance 2018-12-31 Marcelo Sardelich , Suresh Manandhar

This paper introduces a global stock market volatility forecasting model that enhances forecasting accuracy and practical utility in real-world financial decision-making by integrating dynamic graph structures and encompassing all active…

General Finance · Quantitative Finance 2025-09-17 Zhengyang Chi , Junbin Gao , Chao Wang

This paper models stochastic process of price time series of CSI 300 index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model,…

Statistical Finance · Quantitative Finance 2023-01-19 Xianfei Hui , Baiqing Sun , Indranil SenGupta , Yan Zhou , Hui Jiang

Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define…

Trading and Market Microstructure · Quantitative Finance 2013-07-16 Fulvio Baldovin , Francesco Camana , Massimiliano Caporin , Michele Caraglio , Attilio L. Stella

One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known…

Statistical Finance · Quantitative Finance 2008-12-02 Sonia R. Bentes , Rui Menezes , Diana A. Mendes

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…

Applications · Statistics 2016-02-02 Georgi Dinolov , Abel Rodriguez , Hongyun Wang

While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring the temporal behavior of stocks, and show that stock prices…

Statistical Finance · Quantitative Finance 2010-07-30 Achilles D. Speliotopoulos

This paper captures irregularities in financial time series data, particularly stock prices, in the presence of COVID-19 shock. We conjectured that jumps and irregularities are embedded in stock data due to the pandemic shock, which brings…

Computational Engineering, Finance, and Science · Computer Science 2023-11-23 Leonard Mushunje , David Allen , Shelton Peiris

High frequency financial data is burdened by a level of randomness that is unavoidable and obfuscates the task of modelling. This idea is reflected in the intraday evolution of limit orders book data for many financial assets and suggests…

Trading and Market Microstructure · Quantitative Finance 2021-10-15 Myles Sjogren , Timothy DeLise

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

Computational Engineering, Finance, and Science · Computer Science 2009-11-07 Joseph L. McCauley , Gemunu H. Gunaratne

This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling…

There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic…

Statistical Finance · Quantitative Finance 2024-07-01 Andrei Renatovich Batyrov