A new log-volatility factor model reduces dimensionality and identifies cluster contributions to volatility clustering.
problem Understanding the sources of volatility clustering in financial markets.
method Introduced a new factor model using Directed Bubble Hierarchical Tree (DBHT) to identify the number of factors and integrated non-parametric proxy to study volatility clustering.
result Clusters contribute to volatility clustering locally, while the market contributes globally.
A model explains stock returns and volatility using multifractal and rough components.
problem Reconciling multifractal stock returns and rough index volatilities.
method Nested factor model with multifractal and rough volatility components.
result The model explains stock index Hurst exponents larger than individual stock exponents.
The paper designs multi-factor models for rough volatility, making them easier to simulate.
problem Efficient simulation of rough volatility models due to their non-Markovian and non-semimartingale nature.
method Designs tractable multi-factor stochastic volatility models with Markovian structure.
result Derives a numerical method for solving fractional Riccati equations in rough Heston models.
Bitcoin volatility shows multifractal structure, contradicting rough volatility models.
problem Applying rough volatility models to Bitcoin volatility data.
method Normalised p-variation framework, multifractal Detrended Fluctuation Analysis, log-log moment scaling, wavelet leaders.
result Bitcoin volatility exhibits multifractal structure, violating rough volatility model assumptions.
Dynamic model captures spatial, temporal, and spatiotemporal volatility effects.
problem Analyzing volatility in spatial and temporal networks.
method Dynamic spatiotemporal and network ARCH model with common factors, Bayesian estimation.
result Model captures strong spatial/network interactions and spillover effects.
Proves existence and uniqueness of calibrated LSV model.
problem Calibrating a local stochastic volatility model to market data.
method Proves strong existence and uniqueness of solution to a McKean-Vlasov SDE.
result Establishes well-posedness of a calibrated two-factor LSV model.
The aim of our work is to propose a natural framework to account for all the empirically known properties of the multivariate distribution of stock returns. We define and study a "nested factor model", where the linear factors part is standard, but where the log-volatility of the linear factors and of the residuals are…
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
problem Modeling correlated volatility in financial time series with heavy tails and long memory.
method Superstatistical dynamics, Bayesian Inference, Metropolis-Hasting sampling.
result The log-Normal model is reliable for short timescales, while inverse-Gamma is preferred for long timescales.
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors…
In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is …
Model captures rough volatility and jump clustering in stock vol dynamics.
problem Capturing the joint evolution of S&P 500 and VIX implied vol smiles.
method Rough Hawkes Heston model with affine Volterra dynamics, power kernel, and exponential jump law.
result Model accurately captures S&P 500 and VIX implied vol smiles with low power kernel.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
We present a general methodology to incorporate fundamental economic factors to our previous theory of herding to describe bubbles and antibubbles. We start from the strong form of Rational Expectation and derive the general method to incorporate factors in addition to the log-periodic power law (LPPL) signature of her…
New rough stochastic volatility models using log-modulated fractional Brownian motion.
problem Analyzing rough stochastic volatility models over the range 0≤H<1/2. method Introducing log-modulated fractional Brownian motion (log-fBm) to handle H=0 and analyze over the full range. result Obtained skew asymptotics of log(1/T)−pTH−1/2 as To0 for H≥0, no flattening of skew as Ho0. Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.
problem Testing robustness of rough fractional volatility model over various time scales.
method Used large dataset on FX rates, included smoothing and measurement errors, analyzed log-log plots of realized variance increments.
result Found new stylized facts in volatility patterns, including convexity and nonlinear behavior.
Detects jumps in financial asset prices with U-shape volatility.
problem Identifying jumps in financial asset prices with varying volatility.
method Threshold method applied to five-minute log-returns.
result Visualized jumps and volatility patterns for Apple Inc. (AAPL) stock.
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
New model explains low-volatility anomaly using adaptive multi-factor approach.
problem Explaining the low-volatility anomaly in stock markets.
method Used Adaptive Multi-Factor (AMF) model with GIBS algorithm to identify significant risk factors.
result Low-volatility portfolios perform better due to loaded risk factors, not just low volatility.
Study finds GARCH (1,2) best model for forecasting PSEi volatilities.
problem Forecasting the volatilities of Philippine Stock Exchange Composite Index (PSEi).
method Used GARCH models to model log returns of PSEi, selecting GARCH (1,2) based on lowest AIC and highest LL values.
result GARCH (1,2) is the best model for forecasting PSEi volatilities.
Study large deviations in fractional volatility models with non-Gaussian volatility.
problem Large deviations in fractional volatility models with non-Gaussian volatility.
method Established a small-noise large deviation principle for log-price.
result Logarithmic call price asymptotics for large strikes in a special case.
Improved calibration of HJM models using small volatility approximation.
problem Calibration issues in HJM models with deterministic correlations and mean reversals.
method Use of Small Volatility Approximation in calibration of Multi-Factor HJM models.
result Calibration quality is very good and independent of the number of factors.
We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.
problem Analyzing the log-normal SABR model's time-discretized behavior and implied volatility surface.
method We use the Euler-Maruyama scheme for time discretization and derive asymptotic properties in the limit of large number of time steps.
result We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in the asymptotic regime.
Study finds Bitcoin volatility exhibits roughness, not constant over time.
problem Investigating roughness in Bitcoin volatility.
method Multifractal detrended fluctuation analysis and shuffled time series analysis.
result Bitcoin volatility exhibits roughness (generalized Hurst exponent < 1/2).
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
The study examines how global economic policy uncertainty affects crude oil futures volatility.
problem Predicting crude oil futures volatility using global economic policy uncertainty.
method Established single-factor and two-factor models under the GARCH-MIDAS framework, tested with rolling-window and fixed-span specifications.
result GEPU changes have stronger predictive power than the GEPU index for crude oil futures volatility.
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbec…
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
Study on stock market volatility and return dispersion during COVID-19.
problem Impact of COVID-19 on stock market volatility and return dispersion.
method Used Google index to proxy epidemic impact, modeled volatility, and analyzed influencing factors of log-return.
result Volatility significantly affected by epidemic and cross-sectional return dispersion, with positive coefficients.
The paper analyzes Euler approximations for complex volatility models with strong convergence rates.
problem Analyzing strong convergence rates for Euler approximations in stochastic path-dependent volatility models.
method Proposes a Monte Carlo simulation scheme combining log-Euler and truncation/Euler-Maruyama schemes.
result Establishes strong convergence rate of 1/2 for the approximation process up to a critical time.
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
This paper examines Bachelier implied volatility at extreme strikes.
problem Investigates appropriate implied volatility extrapolation at extreme strikes.
method Compares Bachelier and Black-Scholes models, focusing on normal distribution and vanilla options.
result Bachelier implied variance grows at most linearly in log-moneyness, similar to Black-Scholes.
Study on implied volatility for multi-factor rough volatility models.
problem Understanding implied volatility in multi-factor rough volatility models.
method Large deviations principle and numerical methods to compute rate function.
result Identification of models generating non-linear smiles.
New model approximates slow volatility factor using parabolic arcs.
problem Modeling slow factor of volatility in stochastic volatility models.
method Perturbation technique to derive approximate European option prices.
result Simplified expression for European option prices around modified Black-Scholes price.
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
problem Implied volatility constraints under finite log-moments.
method Analyzes stock price martingale with finite log-moments, derives new bounds and proof.
result New bounds on implied volatility growth, relaxes moment assumptions.
We find multi-factor CIR models can exhibit unspanned stochastic volatility.
problem Unspanned stochastic volatility in fixed income markets.
method Formal review and necessary/sufficient conditions for multi-factor CIR models.
result We construct three-factor CIR models that exhibit unspanned stochastic volatility.
Study improves S&P 500 volatility forecasting using hybrid models.
problem Improving accuracy of S&P 500 volatility predictions.
method Hybrid LSTM-GARCH models, including VIX index.
result Hybrid models outperform traditional GARCH model.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
PCA reveals a market factor in S&P500 implied volatilities.
problem Constructing factor models from implied volatility data.
method PCA on implied volatility tensor structure.
result An OI and Vega-weighted index is a significant factor.
Study on implied volatility of an affine jump-diffusion model.
problem Characterize implied volatility of an affine jump-diffusion model.
method Explicit moment generating function derived from solving ODEs; large deviation principle applied.
result Asymptotic behaviors of implied volatility in large-maturity and large-strike regimes characterized.
In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in …
A new framework improves volatility forecasting for financial markets.
problem Static factor models fail to capture evolving volatility co-movements.
method Time-varying factor model integrating dynamic cross-sectional factors.
result Framework demonstrates strong performance in AI-driven models and pairs trading.
Proposes models for dynamic tail inference in heavy-tailed time series.
problem Predicting time-varying extreme event probabilities in heavy-tailed and nonlinear time series.
method White noise process with conditionally log-Laplace stochastic volatility, conditional Pareto-tailed, with tail exponent from log-volatility's mean absolute innovation.
result Effective estimation of dynamically changing extreme event probabilities with a simple modeling method.
The MAXFLAT low-pass filter improves factor adjustment for better portfolio performance in China's stock market.
problem Improving factor adjustment for better portfolio performance in China's stock market.
method Using MAXFLAT low-pass volatility model to adjust factors and construct portfolios.
result Adjusted factors by MAXFLAT volatility model show better performance in both large and small cap universes.
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumptio…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic d…
Study provides LDP for non self-similar stochastic volatility models.
problem Analyzing non self-similar stochastic volatility models.
method Short-time large deviation principle (LDP) for models with Volterra process.
result Derives consequences for option prices, implied volatility surfaces, and skew.