A new model uses time-changed fractional Brownian motion to price financial options.
problem Non-semimartingale nature of fractional Brownian motion limits option pricing.
method Develops a time-changed fractional Brownian motion and a fractional Variance Gamma model.
result Empirical analysis shows consistent Hurst exponent of approximately 0.45.
The study models mortgage prepayment risk using stochastic housing market activity.
problem Modeling prepayment risk in mortgages under varying housing market conditions.
method Developed a stochastic model for prepayment option value, using swaption pricing formulas and non-standard actuarial hedging.
result Housing market covariance significantly impacts prepayment option prices.
Bayesian variational models improve on ML for Gamma and inverse-Gamma mixture components in MRI analysis.
problem Efficiently segmenting and analyzing medical images with Gamma or inverse-Gamma distributed components.
method Developed a fully analytical Variational Bayes (VB) learning framework for Gamma and inverse-Gamma mixture components.
result Variational Gaussian/inverse-Gamma mixture model is the most robust and cost-effective for MRI analysis.
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.
Study the hedging of cryptocurrency options in a volatile market.
problem Hedging options in a volatile, non-stationary cryptocurrency market.
method Calibrated to SVI-implied volatility surfaces, Monte Carlo price paths generated using SVCJ, GARCH, and historical data. Delta, Delta-Gamma, Delta-Vega, and Minimum Variance strategies applied. Wide range of market models tested.
result Calibration results indicate stochastic volatility, low jump frequency, and infinite activity. Short-dated options less sensitive to volatility or Gamma hedges; longer-dated options benefit from multiple-instrument hedges.
Dynamic model predicts user preferences over time.
problem Static user preferences in collaborative filtering.
method Compound Poisson Factorization with Gamma-Markov chains.
result DCPF achieves higher predictive accuracy than static models.
A new model improves analysis of neural activity from calcium imaging.
problem Statistical modeling of deconvolved calcium signals for neural activity interpretation.
method Proposed a zero-inflated gamma (ZIG) model to characterize calcium responses as a mixture of a gamma distribution and a point mass.
result The ZIG model outperforms simpler models in neural encoding and decoding problems.
New insights into Gamma-Poisson model for count data.
problem Estimating topic/dictionary matrix robustness to rank over-specification.
method Rewriting GaP model free of score/activation matrix, leading to new MME algorithm.
result Automatic pruning of irrelevant dictionary columns observed empirically.
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.
A new model BGAR(1) improves temporal NMF for time series data.
problem Temporal NMF models lack a well-defined stationary distribution.
method Introduced a new Gamma Markov chain model BGAR(1) to overcome the limitation of previous models.
result BGAR(1) model has a well-defined stationary distribution.
For any strictly positive martingale S=exp(X) for which X has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…
Study hedging covered options with linear impact and gamma constraint.
problem Hedging covered options with linear market impact and gamma constraint.
method Stochastic target and partial differential equation smoothing techniques.
result Super-replication price is viscosity solution of a fully non-linear parabolic equation.
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.
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.
Paper studies central bank's strategy to control systemic risk in interbank system.
problem Minimizing average distance between log-monetary reserves and target levels.
method Weak formulation, Ekeland's variational principle, Gamma-convergence, stochastic Fokker-Planck-Kolmogorov equation.
result Proves convergence of optimal strategies as number of banks increases.
Bayesian framework extracts features from high-dimensional spatio-temporal data.
problem Sparse structure and spatio-temporal dependence in high-dimensional data.
method Develops a Bayesian feature-extraction framework using Gaussian and Diffused-gamma priors, employing Bregman divergence likelihood and MCMC for posterior computation.
result Improves recovery of sparse features and enhances interpretability in the presence of spatio-temporal dependence.
We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transitio…
Bayesian method estimates volatility from discrete data.
problem Estimating volatility from discrete time observations.
method Nonparametric Bayesian approach with IGMC prior on piecewise constant volatility.
result Good results in simulation and real-world applications.
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying to capture persistence o…
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt=κt(θt−Vt)dt+λtVtdBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…
This paper extends subordinated models to include stochastic time changes, improving financial modeling.
problem Improving financial models to better capture market features like jump clustering and volatility persistence.
method Subordinated processes with Levy and stochastic arrival mechanisms.
result Strong consistency and asymptotic normality results for VG and VGSA processes under various stochastic arrival models.
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…
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.
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic vol…
Bayesian GED-Gamma model improves SV model for return data.
problem Intractable latent parameters in volatility models.
method Bayesian GED-Gamma SV model with marginal likelihood, non-linear Gaussian evolution.
result Proposed model can be reasonably estimated and provides better fit and prediction.
In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails,…
Time-subordinated Brownian motion models improve financial market stochastic distribution.
problem Improving stochastic distribution modeling in financial markets.
method Fourier theory and methodology for time-subordinated Brownian motion models, extending real domain to complex plane.
result Characterization and direct study of stochastic time-change from full process.
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…
GGP models multivariate time series with latent sub-sequences for diverse behaviors.
problem Modeling multivariate time series with diverse behaviors and patterns.
method Graph Gamma Process (GGP) linear dynamical systems with latent sub-sequences.
result GGP models exhibit good predictive performance and reveal interpretable latent patterns.
New model for time series classification from single example.
problem Classifying time series patterns from limited data.
method Developed a Hidden semi-Markov Model with variable state duration.
result Different representations of state duration have distinct strengths and weaknesses.
Paper presents a multinomial method for option pricing under Variance Gamma.
problem Option pricing under non-standard stochastic processes.
method Discrete time Markov chain approximation of continuous time Variance Gamma process.
result Pricing American and Bermudan options is feasible with this method.
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…
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.
Study on market data relaxation and correlations in mean-reverting models.
problem Analyzing relaxation and correlations in market data using mean-reverting models.
method Derived closed-form expressions for correlation functions and leverage for various models, applied eigenvalue analysis for the Heston model, tested findings on historic financial markets data.
result Agreement between general analysis and Heston model's eigenvalue analysis for correlation function.
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 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.
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.
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.
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.
Proposes a method to identify key components for predicting epidemic dynamics with limited resources.
problem Predicting epidemic dynamics with limited surveillance resources.
method Developed a group sparse Bayesian learning algorithm to identify sentinel components for monitoring.
result The proposed algorithm effectively predicts epidemic dynamics using partial data from sentinel components.
Unified framework for series representations and finite approximations of CRMs.
problem Challenges in exact simulation and scalable inference with infinite-activity CRMs.
method Unified framework based on size-biased sampling of Poisson point process.
result Novel series representations for generalized gamma and stable beta processes.
Develops a deep generative model for radar target recognition using HRRP data.
problem Automatic target recognition in radar systems using high-resolution range profiles.
method Recurrent gamma belief network (rGBN) with hybrid stochastic-gradient MCMC and variational inference.
result Efficient and accurate classification with interpretable latent structure.
Simulation framework assesses ROI of chronic disease adherence and policy timing.
problem Uncertainty in ROI of adherence-enhancing interventions under heterogeneous patient behavior and socioeconomic variation.
method Simulation-based framework integrating disease progression, time-varying adherence, and policy timing.
result Early and adaptive interventions yield highest ROI, exceeding 20% under certain conditions.
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.
We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Pois…
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.
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.
WHAI combines autoencoding and MCMC for scalable topic modeling.
problem Training scalable deep topic models for big corpora.
method Develops a hybrid autoencoding inference network for deep latent Dirichlet allocation.
result WHAI achieves both scalability and speed in topic inference.