Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
New method generates novel samples from closed-form diffusion models.
problem Closed-form SGMs memorize training data and cannot generate novel samples.
method Explicitly smooth closed-form score, use nearest-neighbor estimator.
result Efficient method generates novel samples without training.
Improved image generation quality using closed-form discriminator guidance in diffusion models.
problem Enhancing the quality of images generated by diffusion models.
method Theoretical framework to analyze GAN discriminator's effect on Langevin sampling, proposing IPM-GAN optimization as smoothed score-matching.
result Closed-form kernel-based discriminator guidance improves metrics like CLIP-FID and KID.
We solve a Schrödinger bridge with a quadratic state cost, finding a closed-form solution.
problem Optimizing diffusion processes between given distributions.
method Regularized Schrödinger bridge with a quadratic state cost.
result Closed-form solution for the Markov kernel of the regularized Schrödinger bridge.
Proposes a new method for data assimilation using closed-form conditional diffusion models.
problem Data assimilation for systems with complex, non-Gaussian probability distributions.
method Uses kernel density estimation to model joint distributions and leverages the score function for efficient evaluation.
result Outperforms ensemble Kalman and particle filters in nonlinear data assimilation problems.
Unified framework for pricing various debt securities.
problem Pricing of different types of debt securities under general short-rate processes.
method Unifying framework using continuous-time Markov chain approximations and bi-dimensional diffusion processes.
result Closed-form matrix expressions and efficient algorithms for pricing various debt securities.
We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicabl…
We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elastic…
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
We study the effect of parameters uncertainties on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, thanks to Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to hedging procedures in order to compute the sensitivities of SDE trajectories with respect…
We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter …
Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.
Iterative tilting fine-tunes diffusion models for reward-tilted distributions.
problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.
We develop a new model for VIX derivatives with closed-form solutions.
problem VIX derivatives pricing and risk management.
method Data-driven Legendre polynomial model for VIX volatility, deriving analytical series solutions.
result Equal or superior accuracy compared to existing models, offering an efficient alternative.
We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…
AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.
problem Optimizing the intermediate-time dynamics in diffusion-based samplers.
method Develops a time-varying stiffness schedule using Piece-Wise-Constant (PWC) parametrizations and a hierarchical refinement approach.
result QoS-driven PWC schedules consistently improve sampling fidelity and accuracy.
Study on hedging risky assets with jumps and costs.
problem Hedging in jump-diffusion models with transaction costs.
method Conditional least square hedging strategy, explicit form for European call options.
result Explicit form of hedging strategy for European call options under transaction costs.
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot va…
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
Proposes a new method for sampling from unknown distributions.
problem Challenges in sampling from distributions without direct sampling.
method Uses a dilation path to estimate score vectors in closed-form, guiding Langevin dynamics.
result Demonstrates improved sampling performance compared to classical methods.
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…
Develops a smooth operator framework for analyzing neural network representations.
problem Analyzing the geometry of feedforward neural network representations.
method Introduces a smooth operator-theoretic approach based on diffusion Markov operators derived from feature clouds.
result Establishes a stable operator-geometric framework for tracking training, width, and perturbation stability.
Python package ajdmom simplifies moment formula derivation for jump diffusions.
problem Deriving moment formulae for complex jump diffusion processes.
method Automatically generates closed-form expressions and derivatives for any order of moments.
result Enhances usability and usability of affine jump diffusion models.
Improved diffusion models for manifold learning.
problem Learning distributions on general manifolds with geometric complexity.
method Revised approximations for score matching on symmetric spaces.
result Improved performance and scalability to high dimensions.
This paper tackles infinite-dimensional diffusion bridge simulation using operator learning.
problem Challenges in simulating diffusion bridges for modeling natural data due to intractable drift terms and continuous data representations.
method Merges score matching techniques with operator learning to directly learn infinite-dimensional bridges.
result Demonstrates high efficacy in simulating diffusion bridges for various applications, including real-world biological data.
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback. But the Tsallis model is only one of a very large class of linear diffusion with…
Method differentiates diffusion model training to predict sample sensitivity.
problem Predict how diffusion model samples change with small perturbations.
method Closed-form procedure for computing directional derivatives of the map.
result Estimates sensitivity of diffusion model samples to additive perturbations.
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there i…
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…
This work improves diffusion models by estimating the optimal loss value for better training diagnostics.
problem The optimal loss value of diffusion models is unknown and not indicative of absolute data-fitting quality.
method Derive the optimal loss in closed form and develop effective estimators, including a stochastic variant.
result Unlocking the optimal loss as a metric for diagnosing training quality of diffusion models.
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
problem Heat kernel computations for manifold diffusion models are computationally expensive and infeasible.
method Spatially-varying covariance diffusion model, efficient objective derived via Ito's Lemma.
result Our model reduces training time and arithmetic operations by orders of magnitude.
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X,D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it wi…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…
Improves generative models by adding jump-diffusion noise.
problem Limited performance of diffusion models in generating samples from unknown distributions.
method Generalizes diffusion processes to include jump-diffusion noise, deriving closed-form generalized score functions.
result Jump-diffusion models outperform Gaussian models in specific parameter regimes.
Closed-form flow matching yields similar performance to stochastic version, improving model performance.
problem Understanding why flow matching models generalize well.
method Empirical analysis and comparison of stochastic and closed-form flow matching losses.
result Closed-form flow matching can improve model performance.
Study N-player and mean-field games in Itô-diffusion markets with competitive or homophilous interactions.
problem Optimal portfolio choice in a common market with N interacting players. method Analyzes N-player and mean-field games in incomplete and complete markets with CARA utilities and random risk tolerances. result Derives explicit or closed-form solutions for equilibrium processes and game values.
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
CDS combines PT and diffusion for efficient sampling from multimodal distributions.
problem Sampling from unnormalized multimodal distributions efficiently.
method Conditional Diffusion Sampling (CDS) using Conditional Interpolants and Parallel Tempering.
result CDS achieves a superior trade-off between sample quality and density evaluation cost.
Paper introduces a fast, robust, scalable method for detecting changes in data streams.
problem Detecting changes in data streams efficiently and reliably.
method Bayesian online changepoint detection with provable robustness and scalability.
result The proposed method is more than 10 times faster than previous approaches and provides provable robustness.
Optimizes diffusion processes for target distributions.
problem Efficiently generating target distributions from point masses.
method Stochastic interpolant framework with conditional expectation drift.
result Optimal diffusion coefficient minimizes path-space KL divergence.
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric structures in the data. Recently, it was suggested to replace the standard kernel …
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
problem Inaccurate option pricing due to Black-Scholes assumptions.
method Monte Carlo simulation, GARCH model, Heston model, Merton jump-diffusion model.
result Heston model produces estimates closer to market prices, Merton model performs well for volatile assets, GARCH model improves volatility forecasts.
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are switching. We argue that such a model captures well the stock price dynamics under per…
Paper improves American option valuation in complex models.
problem Valuation of American options in time-dependent jump-diffusion models.
method Integral equations and characteristic functions for explicit exercise boundary determination.
result Efficient and accurate pricing method for American options in various models.
Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.
problem Understanding the geometric structure of diffusion-based generative models.
method Characterization of deterministic sampling trajectories using low-dimensional subspace and kernel-estimated data modeling.
result Sampling trajectories in diffusion models are confined to a low-dimensional subspace and exhibit a boomerang shape.