Improved stable pricing for European options using Fourier-Cosine series.
problem Lack of robustness in the COS method for various cases.
method Stable pricing of call options based on Fourier cosine series expansion.
result Stability demonstrated through error analysis and numerical examples.
New method for European option pricing faster and more robust.
problem Pricing European options efficiently and accurately.
method Fourier cosine series expansions for models with known characteristic functions.
result More robust and faster than the original COS method.
Improved barrier option pricing in Heston model using COS-BEM method.
problem Efficient barrier option pricing in the Heston model.
method Combining Fourier-cosine series (COS) method with Boundary Element Method (BEM).
result Significant computational efficiency improvement and BEM attractiveness for practitioners.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
problem Extending Fourier cosine method to discrete probability distributions.
method Spectral filters and convergence rates analysis.
result Spectral filters achieve one order faster convergence rates than previously recognized.
iCOS method estimates risk-neutral densities and option prices without model assumptions.
problem Estimating risk-neutral densities and option prices without model assumptions.
method Leverages Fourier-cosine technique using option-implied cosine series coefficients, without model assumptions.
result Effective in extracting information from option prices under various market conditions.
The COS method for European options pricing is improved with a new bound for the number of terms.
problem Determining the optimal number of terms in the COS method for accurate European option pricing.
method Using Fourier-cosine expansion, the study finds an explicit bound for the number of terms N in the cosine series approximation.
result The COS method achieves exponential convergence when the log-return density is smooth, but not when it has heavy tails.
Unified method for calculating financial option prices from characteristic functions.
problem Calculating financial option prices from characteristic functions in high dimensions.
method Damped Fourier-cosine expansion (COS) method.
result The method converges exponentially if the characteristic function decays exponentially.
Develops an efficient method for compound option valuation.
problem Valuation of compound options with numerical quadrature.
method Analytic Fourier cosine (COS) method for closed-form expressions.
result Improved computational efficiency with high accuracy.
Novel IMEX scheme solves financial PDEs with mixed derivatives.
problem Numerical approximations for financial PDEs with mixed derivatives.
method Second order finite volume IMEX Runge-Kutta scheme.
result Achieves true second order convergence with non-regular initial conditions.
A new NUFFT method speeds up option pricing for various strikes.
problem Efficiently pricing many options of the same maturity but different strikes.
method Non-uniform fast Fourier transform (NUFFT) applied to the COS method.
result Significantly faster computation of option prices.
Paper introduces a new method for efficient portfolio risk quantification.
problem Efficiently quantify risk in large portfolios with many trades and few dominant risk factors.
method Combines Fourier-cosine series with tensor decomposition techniques for dimension reduction.
result Achieves relative errors below 0.1% with significant runtime improvement.
New COS method formula improves option pricing accuracy.
problem Determining the optimal truncation range for COS method.
method Derive new formula using Markov's inequality to ensure convergence.
result New formula leads to more accurate option pricing.
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU) processes. This models are known to be substantially more flexible than Gaussian …
The paper evaluates integrals for fBm with various Hurst indices.
problem Evaluating integrals for stochastic processes with fractional Brownian motion for different Hurst indices.
method Analytic continuation from complex analysis to extend integral domain.
result Integral formulas for fBm with Hurst indices H ∈ ( 0 , 1 ) H \in (0,1) H ∈ ( 0 , 1 ) are derived. Extends option pricing framework without risk-free asset using Levy jumps.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
A new SINC method for fast and accurate option pricing.
problem Computing option prices efficiently and accurately.
method SINC approach based on Shannon Sampling Theorem.
result SINC provides the most accurate and fast pricing computation.
Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, u i u_i u i , can be detected and quantified by studying the correlations in the magnitude series ∣ u i ∣ |u_i| ∣ u i ∣ , i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact …
This paper presents algebraic structures of Lie-Butcher series.
problem No specific problem is mentioned; it's about the algebraic structures of Lie-Butcher series.
method The paper reviews algebraic operations on Lie-Butcher series and reformulates them as recursive formulae.
result The algebraic theory of Lie-Butcher series has matured.
Research tackles unequal length time series for classification.
problem Unequal length time series in real-world data.
method Identified and evaluated two classes of unequal length mechanisms.
result Practical recommendations for handling unequal length time series.
GRATIS generates diverse time series for benchmarking.
problem Lack of diverse time series data for evaluation.
method Uses mixture autoregressive (MAR) models to generate time series.
result Generates diverse and controllable time series efficiently.
Study series invariants of plumbed 3-manifolds using root lattices.
problem Understanding invariants of plumbed 3-manifolds twisted by root lattices.
method Use formal series to study invariants, decompose Z ^ ( q ) \widehat{Z}(q) Z ( q ) , and compute in specific cases. result Show that Z ^ ( q ) \widehat{Z}(q) Z ( q ) is unique and decomposes into related series invariant under five Neumann moves. Machine learning models outperform traditional time series models in financial series prediction.
problem Precise financial series prediction due to instability and noise.
method Comparison between traditional time series models (ARIMA, GARCH) and machine learning models (deep learning) using real stock index data.
result Machine learning models significantly outperform traditional models in financial series prediction accuracy.
New formula and properties of inverted Habiro series derived from GM series.
problem Understanding and manipulating knot invariants using series expansions.
method Developed a new formula for the inverted Habiro series (IHS) in terms of GM series and theta functions. Proved a multiplication formula for IHS.
result Established a natural ring structure for IHS and studied its residues, applying them to Dehn surgery formulas.
Paper introduces novel distances for clustering ordinal time series.
problem Clustering ordinal time series with discrete response.
method Introduces two novel distances and fuzzy clustering algorithms.
result Fuzzy clustering algorithms accurately group series from similar stochastic processes.
MDF represents time series motifs as images for improved classification.
problem Classifying time series data with high-order patterns.
method Motif Difference Field (MDF) using Fully Convolutional Networks (FCN).
result MDF outperforms other methods on UCR time series datasets.
Catch22 reduces time series feature space to 22 canonical characteristics for efficient analysis.
problem Efficiently capturing and comparing time series properties for diverse applications.
method Inference of minimal sets of time-series features from a comprehensive library.
result Catch22 (22 canonical characteristics) reduces computation time and complexity.
We prove time series data forms a Kolmogorov space with hidden dimensions.
problem Understanding the structure of time series data.
method Defining cyclic coordinates and spinor fields in time series data.
result Time series data has hidden eight dimensions.
MPPN network improves long-term time series forecasting accuracy.
problem Inaccurate long-term time series forecasting due to noise and lack of interpretability.
method MPPN network constructs context-aware multi-resolution semantic units and employs multi-periodic pattern mining and channel adaptive module.
result MPPN significantly outperforms state-of-the-art methods on nine real-world benchmarks.
New infinite series of hyperbolic polytopes with special growth rates found.
problem Finding new infinite series of non-compact hyperbolic polytopes.
method Constructing infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes.
result Growth rates of the constructed polytopes are Perron numbers.
Archive of 20 time series datasets for forecasting evaluation.
problem Lack of comprehensive time series forecasting datasets.
method Compilation and characterisation of 20 datasets from various domains.
result Characterisation and performance evaluation of datasets.
Automatically extracts features from time series data for improved forecasting.
problem Manual feature selection for time series forecasting is inefficient and prone to errors.
method Extracts features from time series using recurrence plots and computer vision algorithms.
result Automatically extracted features lead to highly comparable and sometimes superior forecasting performance.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
Analyzes sequence-to-sequence models for time series forecasting.
problem Choosing between sequence-to-sequence models and classical time series models.
method Theoretical analysis of sequence-to-sequence models for time series forecasting.
result Provides a quantitative guide for practitioners.
Paper proposes a robust time series classification method using ResNet and Recurrence Plots.
problem Classifying time series data is challenging and underexplored.
method Transfer learning in Deep Neural Networks, 2D Recurrence Plots, ResNet architecture, simplified preprocessing.
result First time multi-time series classification using a single network.
Two new data synthesizers generate multidimensional time series for analysis.
problem Evaluate distance functions on high-dimensional time series.
method Proposed two new data synthesizers: CBF and RAM.
result Evaluation of 1-nearest neighbor classifier using DTW on generated datasets.
Improved prediction of hierarchical time series using structured regularization.
problem Making coherent forecasts for hierarchical time series.
method Structured regularization method for bottom-level time series predictions.
result Superior prediction accuracy and computational efficiency compared to previous methods.
New kernel handles irregularly-spaced multivariate time series.
problem No kernel exists for irregularly-spaced multivariate time series.
method Built a series kernel from vector kernels, ensuring it's PSD.
result Validated the series kernel on multiple datasets and time series classification.
New method uses Transformers for flu forecasting.
problem Forecasting influenza-like illness trends.
method Transformer-based machine learning models with self-attention.
result Forecasting results are competitive with state-of-the-art methods.
Modeling regime shifts in co-evolving time series with interactions and time-dependency.
problem Discovering and modeling regime shifts in multiple time series with relationships and time-dependent behaviors.
method Modeling interactions and time-dependency in co-evolving time series using a mapping grid and dynamic network representation for regime identification and time-dependent Cox regression for regime transition probabilities.
result A principled approach for modeling interactions and time-dependency in co-evolving time series.
Introduces a new benchmark for time series extrinsic regression.
problem Predicting a single continuous value from univariate or multivariate time series, not necessarily related to the predictor.
method Developed a new benchmarking archive for time series extrinsic regression.
result Initial benchmarking of existing models on the new TSER datasets.
Proximity Forest classifies time series in milliseconds from large datasets.
problem Classifying time series from large datasets with high accuracy and speed.
method Ensemble of randomized Proximity Trees, leveraging proximity measures instead of attribute values.
result Proximity Forest achieves high accuracy on large datasets and is significantly faster than state-of-the-art models.
Few-shot learning improves time-series forecasting with limited data.
problem Limited data in target tasks degrade forecasting performance.
method A few-shot learning method using recurrent neural networks with attention.
result The model forecasts future values effectively with minimal data.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Transformers improve time series modeling by capturing long-range dependencies.
problem Capturing long-range dependencies in time series data.
method Summarized and reviewed adaptations of Transformers for time series analysis.
result Transformers enhance time series forecasting, anomaly detection, and classification.
Global models outperform univariate benchmarks in complex time series forecasting.
problem Comparing global forecasting models to univariate benchmarks in various challenging scenarios.
method Simulated datasets with controlled characteristics, including homogeneity, complexity, and series lengths. Global forecasting models (RNN, LGBM) compared to univariate techniques.
result Global models like RNN and LGBM are competitive in complex scenarios with short series lengths and heterogeneous data.
Adversarial regularization helps learn interpretable shapelets for time series classification.
problem Difficult to interpret learned shapelets in time series classification.
method Use of adversarial regularization to constrain model to learn more interpretable shapelets.
result Adversarially regularized method learns interpretable shapelets.
Proposes copulas for heteroskedastic time series with improved volatility measures.
problem Capturing serial dependence in stationary time series with varying volatility.
method Developed parametric copulas for Markov and multivariate series, derived volatility proxy copulas, and proposed new volatility dependence measures.
result Proposed copulas outperform GARCH models in capturing volatility and producing accurate risk forecasts.
A novel time series clustering method that considers segment typologies.
problem Lack of consideration for the similarity of different subsequences in time series clustering.
method Two-stage clustering: polynomial segmentation followed by hierarchical clustering of segments, then final clustering of time series.
result The method outperforms state-of-the-art techniques on UCR Time Series Classification Archive datasets.