We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on ma…
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.
The paper optimizes trading times in a market with price dynamics and transaction costs.
problem Optimizing trading times in a market with price dynamics and transaction costs.
method Solving an optimal double stopping problem and related optimal switching problem for an exponential Ornstein-Uhlenbeck process.
result Investors generally enter when prices are low but may wait if prices are close to zero.
The paper defines the OU matrix for braid diagrams and finds determinant relationships.
problem Understanding the layeredness of braid diagrams.
method Defining the OU matrix and analyzing its determinant for layered braid diagrams.
result The determinant of the OU matrix for layered braid diagrams is the product of the determinants of the layers.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
Calculates lower bounds for type III Reidemeister moves in link diagrams.
problem Determining the minimum number of Reidemeister III moves between link diagrams.
method Introducing non-self OU sequence and OU number for link diagrams.
result Provides a lower bound for the number of Reidemeister III moves.
Characterizes sequences from two-component link diagrams.
problem Understanding information from non-self crossing sequences of link diagrams.
method Investigated and characterized pairs of non-self OU sequences of two-component link diagrams.
result Completely characterized pairs of non-self OU sequences of diagrams of two-component links.
Deep learning outperforms traditional methods in estimating OU process parameters.
problem Parameter estimation of the Ornstein-Uhlenbeck process is challenging.
method Used a multi-layer perceptron to estimate OU process parameters compared to traditional methods like Kalman filter and maximum likelihood estimation.
result Deep learning method outperforms traditional methods in parameter estimation of the OU process.
The Kalman filter and Heston model are used to estimate asset prices and trading performance.
problem Estimating asset prices using stochastic models.
method Kalman filter applied to mean-reverting processes and Heston model with method of moments.
result The Kalman filter and Heston model provide effective methods for estimating asset prices and trading performance.
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its anal…
This study shows how DDPM can be represented by the OU process.
problem Designing optimal noise schedules for DDPM.
method Formal equivalence between DDPM and OU process, heuristic designs based on Fisher Information.
result Fisher-Information-motivated schedule corresponds to cosine noise schedule.
This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigro…
Novel AMM model for pegged cryptoassets using nested OU processes.
problem Liquidity and risk management in markets for pegged cryptoassets.
method Multi-level nested Ornstein-Uhlenbeck (OU) processes for exchange rate dynamics, calibrated and filtered AMM model.
result Consistent efficient quotes and improved liquidity provision for pegged cryptoassets.
Pairs trading strategy improved using Ornstein-Uhlenbeck process.
problem Improving pairs trading strategy effectiveness.
method Used Ornstein-Uhlenbeck process to model stock price spreads.
result OU model captures signals and trends effectively but underperforms compared to naive model.
Optimizes portfolios with constraints and stochastic factors, deriving explicit solutions.
problem Optimizing expected utility in an incomplete market with stochastic factors and convex constraints.
method Fundamental duality results and HJB PDE, derived condition for exponential affine solutions.
result Explicit expressions for optimal allocations and Riccati ODE solutions in specific markets.
Develops semi-closed form solutions for barrier and American options on time-dependent OU process.
problem Valuation of barrier and American options on a time-dependent Ornstein-Uhlenbeck process.
method Semi-closed form solutions involving numerical solution of Fredholm equations and integration of Jacobi theta functions.
result Method is more efficient than backward finite difference method and can be as efficient as forward finite difference solver with better accuracy and stability.
Ridge regression linked to Poisson resetting in statistical physics.
problem Understanding and extending ridge regularization in machine learning.
method Connecting stochastic resetting from statistical physics with ridge regularization in machine learning, using renewal processes.
result Exact filter identities for ridge regularization in various reset laws, including exponential and non-exponential.
Study on gamma-related OU processes with simulation methods.
problem Distributional properties and simulation of gamma-related OU processes.
method Investigation of gamma and bilateral gamma laws, derivation of closed-form densities and characteristic functions, and development of efficient simulation algorithms.
result Efficient algorithms for generating gamma-related OU processes with significantly faster performance than existing methods.
Modeling bank portfolio risk under climate transition impacts.
problem Evaluating risk measures for a bank's collateralized loans in a climate transition economy.
method Developed an end-to-end modeling framework using stochastic processes and dynamic macroeconomic variables.
result Derived expressions for risk measures as functions of climate transition parameters.
Nous considérons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-variété de dimension k. Les quasi-variétés généralisent les variétés et les V-variétés et représentent le cadre naturel pour la réduction symplectique par rapport à l'action i…
New simulation technique speeds up Lévy-driven OU process pricing.
problem Inefficient Monte Carlo simulations of Lévy-driven OU processes.
method Numerical inversion of characteristic function combined with FFT for fast and accurate simulations.
result The proposed technique is at least one order of magnitude faster than existing methods.
Paper discusses gliding algorithm to transform tangle diagrams into a specific form.
problem Transforming tangle diagrams into a specific form.
method Gliding algorithm to bring tangle diagrams to Over-then-Under (OU) form.
result Obtained a braid classification result and extended it to virtual braids.
Derives semi-closed form prices for barrier options in the Hull-White model.
problem Calculating prices of barrier options in the Hull-White model with time-dependent parameters.
method Applies generalized integral transform and heat potentials to solve linear Volterra equations of the first kind.
result The method provides more efficient and accurate solutions compared to finite difference methods.
A new MCMC method on Lie groups using irreversible dynamics.
problem Sampling from distributions on Lie groups efficiently.
method Constructing an irreversible HMC-like algorithm on Lie groups using dissipation fields and symplectic integrators.
result The method can recover HMC as a special case and is faster than reversible MCMC.
New framework uses dynamics to justify Gaussian process for turbulent flows.
problem Lack of rigorous justification for Gaussian process priors in turbulent flows.
method Introduces a dynamics-informed Gaussian process framework based on quasi-Gaussianity.
result Provides a principled, long-time dynamical justified GP prior for turbulent flows.
The paper analyzes futures trading under mean-reverting spot prices, incorporating timing and chooser options.
problem Trading futures with transaction costs under mean-reverting spot prices.
method Modeling spot dynamics with OU, CIR, or XOU models; deriving futures term structure; solving optimal double stopping problems.
result The option to choose between long or short positions delays market entry compared to pre-committing.
This paper optimizes perpetual contract liquidity by accounting for funding rates.
problem Optimal liquidity provision for perpetual contracts with stochastic funding rates.
method Formulated a control problem, solved with a HJB scheme, and calibrated on real data.
result Funding-aware market making improves performance and reduces inventory risk.
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump Lévy process and models the characteri…
Improves SGM convergence bounds in W2-distance without strict assumptions.
problem Convergence bounds for SGMs in W2-distance require stringent assumptions.
method Novel framework using the OU process and PDE analysis.
result Log-concavity evolves from weak to strong over time.
Two new models improve option valuation for negative or mean reverting futures markets.
problem Valuation of futures contracts with negative underlying prices.
method Proposed two models: Ornstein-Uhlenbeck and continuous time GARCH.
result Improved option values compared to Black 76, especially for negative or mean reverting markets.
TT-DAC-PS: A deterministic actor-critic approach for optimal trade execution
problem Optimal execution of large stock sell programs
method Twin-Target Deterministic Actor-Critic with Policy Smoothing
result Reduces mean implementation shortfall percentage
Researchers infer the drift of a high-dimensional OU process with row-sparsity.
problem Inferring the drift parameter of a high-dimensional Ornstein-Uhlenbeck process under row-sparsity.
method Negative log-likelihood penalized by an ℓ1-penalization (Lasso and Adaptive Lasso). result Sharp oracle inequality and asymptotic consistency for variable selection.
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time T for multi-modal data distributions. Study uses a bivariate model to price crude oil futures.
problem Pricing crude oil futures using latent factors and state-space models.
method Modelled short and long term factors as OU processes, estimated using Kalman Filter and maximised Gaussian likelihood.
result Successfully estimated model parameters and factors from WTI Crude Oil NYMEX futures data.
New process from fractional BM and OU process yields simpler variance.
problem Simpler model for autocovariance structure.
method Construct new process using fractional BM and OU process, analyze increments.
result Variance of new process easier to compute than FARIMA.
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
problem Capturing volatility dynamics in financial markets.
method Two-factor Quintic Ornstein-Uhlenbeck (OU) model with polynomial volatility.
result Model accurately represents SPX and VIX volatility surfaces and SSR.
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in R2. result New inequalities and proofs for star bodies.
New error bound for diffusion models without dimensionality constraints.
problem Error estimation in diffusion generative models without dimensionality constraints.
method Derive dimension-free error bound using a smooth test functional.
result Explicit, dimension-free bound on generated vs true data distributions.
Paper answers part of a conjecture about submersions from 3D spaces.
problem Generalized Chen's conjecture for triharmonic Riemannian submersions.
method Analyzes submersions from 3D space forms into surfaces.
result Triharmonic submersions are harmonic.
The market events of 2007-2009 have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a Poisson trade arrival model with variable…
RegPred Net forecasts foreign exchange rates with improved accuracy and interpretability.
problem Multi-step forecasting of Foreign Exchange (FX) rates.
method Bayesian optimization for hyperparameter tuning of a multi-layered regression network.
result RegPred Net significantly outperforms other models in terms of RMSE and correlation metrics.
For a rational homology 3-sphere Y with a $\spinc$ structure $\s$, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology lead to a collection of variants which are topological invariants. We establish exact sequences relating them, we show that they satisfy a dua…
In the biharmonic submanifolds theory there is a generalized Chen's conjecture which states that biharmonic submanifolds in a Riemannian manifold with non-positive sectional curvature must be minimal. This conjecture turned out false by a counter example of Y. L. Ou and L. Tang in \cite{Ou-Ta}. However it remains inter…
The Open University studies student online behavior in virtual learning environments.
problem Improving retention rates in online modules.
method GUHA and Markov chain-based analysis of student activity.
result Both methods are valid for modeling student activities.
Study optimal investment and consumption in financial markets using Ornstein-Uhlenbeck process.
problem Optimal consumption/investment problem in financial markets with logarithmic utility.
method Stochastic dynamical programming method and Hamilton-Jacobi-Bellman (HJB) equation.
result Explicit solution to the HJB equation and optimal financial strategies constructed.
The CN matrix of a pure braid projection is characterized and applied.
problem Understanding the structure of CN matrices for braid projections.
method Discussion and characterization of patterns and specific matrices.
result Characterization of CN matrix of a pure 6-braid projection and related matrices.
AMIDST is a Java toolkit for scalable probabilistic machine learning.
problem Scalable probabilistic machine learning for massive streaming data.
method Flexible modeling language, parallel/distributed Bayesian learning algorithms, variational message passing.
result Supports a wide range of probability distributions and interfaces with various software tools.