Develops Bilateral Gamma processes for financial market modeling.
problem Modeling financial market fluctuations with Lévy processes.
method Exploration of bilateral Gamma distributions and their Lévy processes.
result Validates Bilateral Gamma processes on real financial data.
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.
New calibration methods improve fitting of weak variance-alpha-gamma process.
problem Improving fitting of a multivariate Lévy process.
method Comparison of three calibration methods: method of moments, maximum likelihood estimation, and digital moment estimation.
result Maximum likelihood estimation produces a better fit when a specific condition holds, while digital moment estimation produces a better fit when the condition is violated.
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based …
Introduces a new Lévy process for modeling illiquid markets.
problem Modeling dynamic of assets in illiquid markets.
method Introduces Variance Gamma++ process, a new Lévy process, and provides efficient path simulation algorithms.
result Efficient pricing formula and parameter estimation for European options.
The article prices exchange options using variance gamma-like models.
problem Pricing exchange options under specific stochastic processes.
method Derives formulas for variance gamma and variance gamma++ processes, constructs multidimensional versions, calibrates parameters with real data.
result Closed formulas and numerical methods for evaluating exchange options.
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
New pricing model uses variance-gamma process for financial assets.
problem Traditional pricing models need improvement for complex financial assets.
method Developed a new class of models based on variance-gamma process.
result The new model can price a variety of financial assets effectively.
New methods model gamma-ray data to better understand Galactic emissions.
problem Uncertain diffuse Galactic gamma-ray emissions bias data interpretation.
method Gaussian processes and variational inference for flexible modeling.
result More robust interpretation of gamma-ray sky, especially dark matter signals.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
problem Calculating transition densities for SDEs driven by gamma processes.
method Taylor-type approximation and conditional expectation of multiple stochastic integrals.
result Efficiency of the proposed method demonstrated through numerical tests.
Efficient GP classification using Polya-Gamma data augmentation.
problem Scalable Gaussian Process Classification.
method Stochastic variational approach with closed-form updates.
result Up to two orders of magnitude faster than state-of-the-art.
Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.
problem Complex pricing of currency options with multi-assets.
method Examined USD-INR currency options, tested several models, compared performance.
result Variance gamma model outperforms Black-Scholes model in various volatility regimes.
Efficient inference for nonparametric Hawkes processes using Pólya-Gamma augmentation.
problem Efficient inference for nonparametric Hawkes processes.
method Pólya-Gamma augmentation, EM algorithm, mean-field variational inference.
result The proposed algorithms can recover well the underlying prompting characteristics efficiently.
Closed pricing formulas for Variance Gamma model payoffs.
problem Pricing path-independent payoffs in the Variance Gamma model.
method Mellin transform theory and multidimensional complex analysis.
result Closed-form pricing formulas with accelerated convergence for short-term options.
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same firsts four cumulants. This approach is particularly convenient for pricing Americ…
The paper uses the variance-gamma model to price options and explain excess kurtosis.
problem Explaining excess kurtosis in stock price data.
method Random-time subordination, Laplace distribution, Esscher transform.
result The variance-gamma model explains excess kurtosis in log-returns data.
Proposes a method for training Bayesian neural networks using synthetic data from Raman and CARS spectra.
problem Limited real observations in Raman and CARS spectroscopy.
method Log-Gaussian Gamma Processes and Bayesian Neural Networks.
result Trained Bayesian neural networks provide accurate estimates of Raman and CARS spectra with uncertainty quantification.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
New EPM models improve model shrinkage in edge partition models.
problem Overfitting and inappropriate model shrinkage in EPMs.
method Proposed two novel EPM models: CEPM and DEPM, incorporating constrained and Dirichlet priors respectively.
result IDEPM model shows state-of-the-art performance in generalization and prediction.
Study of gamma-hedging using rough paths for European and exotic options.
problem Applying rough paths to gamma-hedging strategies for derivatives.
method Rough-path theory applied to discrete-time gamma-hedging strategy.
result Sure replication of European and exotic derivatives under regular pricing signals.
Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…
A Monte Carlo method for pairs trading on mean-reverting spreads with Lévy processes.
problem Trading on mean-reverting spreads with flexible models.
method Monte Carlo simulation with variance gamma and alpha-gamma driving processes.
result Optimal trading strategies are affected by model parameters and correlation.
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) appr…
Deep learning improves gamma-ray energy estimation and event selection.
problem Improving gamma-ray event selection and energy estimation.
method Adapted convolutional neural networks (CNN) for gamma-ray astronomy.
result Significant improvement in gamma-ray energy estimation and event selection.
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We derive also the information geometry of the 3-manifold of McKay bivariate gamma dist…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption t…
The paper analyzes a five-parameter Variance-Gamma model for European option pricing.
problem Developing a stochastic volatility model for accurate European option pricing.
method Introduced a five-parameter Variance-Gamma model and applied it to empirical data.
result The five-parameter VG model produces underpriced OTM and overpriced ITM options compared to the Black-Scholes model.
We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling …
Modeling volatility with Chained Gamma Distributions for financial time series.
problem Volatility clustering in financial time series, especially in estimating temporal autocorrelation of logarithmic variance of returns.
method Dynamic Bayesian Network with conjugate prior relation of normal-gamma and gamma-gamma, using variational methods for quick approximate solutions.
result The model can express heavier tails than Gaussians, achieving positive excess kurtosis, and runs faster than Monte Carlo methods.
Enhanced LSTM model learns complex temporal dependencies.
problem Modeling long-term dependencies in sequential data.
method Gamma-LSTM with hierarchical memory units and gates.
result Gamma-LSTM outperforms regular and stacked LSTMs in sequence prediction.
Efficiently infers Gaussian process density models with Gibbs sampling and variational methods.
problem Density estimation for complex, nonparametric models.
method Augmented likelihood with latent variables, Gibbs sampling, and variational mean field approximations.
result Efficient inference for Gaussian process density models with up to thousands of data points.
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key challenge in either setting is controlling the variance of gradient estimates: rec…
Bayesian method improves few-shot classification accuracy.
problem Few-shot classification with small labeled datasets.
method Gaussian process classifier with Pólya-Gamma augmentation and one-vs-each softmax.
result Improved accuracy and uncertainty quantification.
We unify and extend a number of approaches related to constructing multivariate Variance-Gamma (V.G.) models for option pricing. An overarching model is derived by subordinating multivariate Brownian motion to a subordinator from the Thorin (1977) class of generalised Gamma convolution subordinators. A class of models …
In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible allowing us posterior density estimation and posterior inference for high quantiles. …
New process explains asset volatility patterns.
problem Explains statistical relationship between asset volatility and returns.
method Uses multiplicative Langevin process with adjustable coherence time.
result Exactly equivalent to Inverse Gamma distribution for volatility.
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each 10-minute lag: the Gamma distribution, the inverse Gamma distribution, the Weibull distribution and the log-normal distribution. The volume-price data, whi…
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
Incorporating the side information of text corpus, i.e., authors, time stamps, and emotional tags, into the traditional text mining models has gained significant interests in the area of information retrieval, statistical natural language processing, and machine learning. One branch of these works is the so-called Auth…
Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.
problem Scalability issues and handling of discrete data in Bayesian Tensor Ring factorization.
method Proposes a novel Bayesian Tensor Ring model with a nonparametric Multiplicative Gamma Process prior and Pólya-Gamma augmentation for discrete data. Developed efficient Gibbs sampler and online EM algorithm for scalability.
result Significantly improved scalability and handling of discrete data compared to previous methods.
A new hedging strategy uses deep reinforcement learning to manage gamma and vega risks.
problem Managing gamma and vega risks in derivatives trading with stochastic underlying.
method Deep distributional reinforcement learning (D4PG) combined with quantile regression.
result Optimal hedging strategy depends on objective function, transaction costs, and option maturity.