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…
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48 results for “linear volatility”
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its par…
Empirical study of spot and implied volatility dynamics in equity markets.
problem Understanding the joint dynamics of spot and implied volatility in equity markets.
method Analyzing observable quantities to extract instantaneous variance curves and studying their daily variations with spot returns.
result Non-linearities have significant effects on the pricing and hedging of volatility derivatives.
The abstract discusses solutions to bond market equations with linear volatility and Lévy noise.
problem Existence and non-existence of solutions to Heath-Jarrow-Morton equations with linear volatility and Lévy noise.
method Analyzes conditions for existence and non-existence of solutions in the class of bounded fields, considering Lévy processes without Gaussian and negative jumps.
result Necessary and sufficient conditions for the existence of solutions are formulated in terms of Lévy measure behavior near the origin or Laplace exponent behavior at infinity.
Study compares MoE and RNN models for stock price prediction across volatility profiles.
problem Improving stock price prediction accuracy across different volatility levels.
method Dynamic Mixture of Experts model combining RNN and linear models, adjusting weights through a gating network.
result MoE model outperforms individual models in reducing prediction errors.
Numerical Method for Highly Non-linear Mean-reverting Asset Price Model with CEV-type Processq-fin.RM
New numerical method for non-linear asset price model with CEV volatility.
problem Describing stochastic volatility in asset price dynamics.
method Proposes a mean-reverting theta-rho model with CEV volatility, constructs a truncated EM method.
result Truncated EM solutions can evaluate path-dependent financial products.
Best linear forecast of volatility in financial time seriescond-mat.stat-mech
The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. Such a case admits an explicit analytical solution of the problem of constructing the best linear forecast of a stationary stochastic process. We describe and apply the proposed analytical method …
New method improves volatility forecasts by relaxing linear assumption in leverage effect.
problem Empirical evidence contradicts the leverage effect's ability to improve volatility forecasts.
method Developed a Bayesian stochastic volatility framework with nonlinear leverage effects.
result Nonlinear leverage effect improves predictive performance for 89% of stocks.
Enhanced GARCH model uses autoencoder for volatility forecasting.
problem Selecting optimal realised volatility estimator for forecasting.
method Proposes an autoencoder-enhanced Realised GARCH model combining multiple realised measures.
result The model outperforms traditional linear methods in one-step-ahead rolling volatility forecasting.
Multiple time scales in volatility and leverage correlations: An stochastic volatility modelcond-mat.stat-mech
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been propos…
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
Sharp bounds on weak convergence rate for rough volatility models.
problem Understanding the convergence rate in discretizing rough volatility models.
method Analyzing general and linear models to derive bounds.
result Sharper bound of \(H + 1/2\) for linear models.
Non linear behaviour of stock market volatilitycond-mat.other
We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we find that the process determining market volatility is not stationary while the …
The Bass model is calibrated to vanilla options using a fixed-point equation.
problem Calibration of the Bass local volatility model to vanilla options.
method Solving a fixed-point equation to achieve calibration.
result Existence and uniqueness of the solution to the fixed-point equation, and linear convergence of the fixed-point iteration scheme.
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
The MRS-GARCH model outperforms single-regime GARCH models in crude oil volatility forecasting.
problem Forecasting crude oil market volatility accurately.
method Evaluation of single-regime GARCH models and two-regime MRS-GARCH model at different data frequencies and time horizons.
result The two-regime MRS-GARCH model provides more accurate volatility forecasts for daily data but not for weekly and monthly data.
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth condition…
Filling the gaps smoothlyq-fin.CP
Smooths local volatility model calibration with piecewise linear variance.
problem Calibrating local volatility models to option prices.
method Extends LiptonSepp2011 approach with piecewise linear variance and non-zero interest rates/dividends.
result Analytical tractability with Kummer's hypergeometric functions.
Proposes a new model for estimating financial volatility with jumps.
problem Estimating volatility from financial time series with jumps.
method Gibbs Sampler with exact posterior distributions.
result Model captures speculative movements and propagates jumps in volatility.
Researchers solve optimal investment in Heston model with stochastic volatility.
problem Optimal investment strategy in markets with stochastic volatility.
method Reduction of optimal control problem to a linear parabolic boundary problem, leading to an explicit solution.
result Exact solution for optimal investment in Heston model.
Study classifies Lie symmetries for European options with stochastic volatility.
problem Analyzing Lie symmetries for European options with stochastic volatility.
method Lie symmetry analysis of the Black-Scholes-Merton model for European options with stochastic volatility.
result The model admits different Lie point symmetries depending on the volatility function.
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.
The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
Volatility Dynamics of Wavelet-Filtered Stock Pricesphysics.soc-ph
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of volatility dynamics of denoised series are noticeably different…
A new FV-ADI method calibrates SLV models efficiently.
problem Calibrating SLV models to their underlying local volatility models.
method Finite volume - Alternating Direction Implicit (ADI) approach for solving 1D and 2D forward Kolmogorov equations.
result The proposed method efficiently calibrates SLV models without requiring PDE transformations and conserves numerical mass.
Proposes NDIG model to capture bitcoin volatility and option pricing.
problem Capturing the volatility and option pricing of cryptocurrency Bitcoin.
method Doubly subordinated Levy process (NDIG) to model Bitcoin time series properties.
result NDIG model perfectly captures observed in-sample volatility.
Enhances stock volatility analysis using machine learning.
problem Stock volatility analysis and arbitrage strategies.
method Smooth Transition Regression models and Artificial Neural Networks.
result Improved empirical evidence on stock arbitrage strategies.
We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic sh…
Simple Black-Scholes formula with linear interpolation outperforms other methods.
problem Estimating pricing functionals for European options.
method Non-parametric estimators of pricing functionals using historical data.
result Simple approach based on Black-Scholes formula and linear interpolation outperforms other methods.
Study improves caplet calibration for 1Y maturity using different models.
problem Calibrate 1Y caplet smile better across strike range.
method Alternative local volatility terms and stochastic volatility models.
result Some models calibrate well to 1Y caplet smile across strike range.
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we …
The paper models VIX with jumps and stochastic volatility using VVIX as a proxy.
problem Capturing the dynamics of VIX with jumps and stochastic volatility.
method Double-jump stochastic volatility model with MCMC estimation.
result The jump in VIX and volatility factor are statistically significant.
Hydropower reduces system electricity price and volatility, especially at extreme levels.
problem Impact of hydropower on system electricity price and volatility.
method Robust statistical analysis using multiple linear regression and quantile regression.
result Hydropower reduces system electricity price and volatility, especially at extreme levels.
Realized Volatility Forecasting for New Issues and Spin-Offs using Multi-Source Transfer Learningcs.LG
Paper improves volatility forecasting for new issues and spin-offs.
problem Forecasting volatility with limited historical data.
method Multi-source transfer learning approach.
result Transfer learning approach outperforms alternative models.
This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distribu…
Given that the terminal condition is of at most linear growth, it is well known that a Cauchy problem admits a unique classical solution when the coefficient multiplying the second derivative (i.e., the volatility) is also a function of at most linear growth. In this note, we give a condition on the volatility that is …
This study develops a multi-factor framework where not only market risk is considered but also potential changes in the investment opportunity set. Although previous studies find no clear evidence about a positive and significant relation between return and risk, favourable evidence can be obtained if a non-linear rela…
Efficiently simulates the Heston model with large time steps using a novel method.
problem Challenges in simulating the Heston model with large time steps.
method Implicit integrated variance scheme exploiting the near-linear nature between stochastic driver and conditional integrated variance process.
result Achieves near-exact accuracy with coarse discretizations, efficient for large time steps.
Study uses topological signatures to quantify financial market complexity.
problem Capturing temporal organization beyond volatility measures.
method Null validated topological approach using norm of persistence landscapes.
result Persistence landscape norms reveal dynamical structure during market stress.
The paper calibrates SLV models to LV models using an adjoint method.
problem Calibrating stochastic local volatility models to their underlying local volatility models.
method An adjoint semidiscretization of the forward Kolmogorov equation to solve for the leverage function.
result The method ensures that the fair values of European-style options in SLV and LV models match.
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.
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…
This paper compares two extensions of the Heston model for option pricing.
problem Improving the accuracy of option pricing models.
method Empirical analysis and non-linear least square optimization of parameters.
result The multiscale stochastic volatility model outperforms the Heston model.
Method predicts LFSM increments from past observations using codifference.
problem Forecasting LFSM increments from discrete-time observations.
method Uses codifference for serial dependence, with conditional expectation or projection for or .
result Method shows promising performance in forecasting volatilities, capturing kurtosis and serial dependence.
Deep learning model predicts stock volatility using Google trends.
problem Predicting stock volatility using neural networks.
method Long Short-Term Memory neural network with Google domestic trends as input.
result Model outperforms benchmarks with MAPE of 24.2%.
Guyon-Lekeufack model accurately predicts market volatility.
problem Modeling and predicting market volatility accurately.
method Path-dependent volatility model with weighted past price returns and squared volatility.
result Wellposedness of the coupled system of stochastic differential equations for all parameter values.
We study historical correlations and lead-lag relationships between individual stock risk (volatility of daily stock returns) and market risk (volatility of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over all stocks, using 71 stock pr…
Implied and Realized Volatility: A Study of Distributions and the Distribution of Differenceq-fin.ST
Study on distributions of realized and implied volatility, using Generalized Beta distribution.
problem Understanding the differences and relationships between realized and implied volatility distributions.
method Used Generalized Beta distribution to fit distributions of realized variance and implied volatility (VIX, VXO). Analyzed differences and correlations.
result Generalized Beta distribution provides the best fit for realized variance but not for implied volatility indices (VIX, VXO).