SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matri…
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.
problem Analyzing financial markets with sticky asset prices and proving no arbitrage conditions.
method Introduced a financial market model with a risky asset following a sticky geometric Brownian motion and a riskless asset with a constant interest rate. Proved no arbitrage conditions and derived pricing equations.
result No arbitrage conditions are met only when the interest rate is zero, and all replicable payoffs are derived under this condition.
Upper bounds on constants for Brownian motion with sticky boundary.
problem Bounding constants for Brownian motion with sticky boundary.
method Interpolation approach based on energy interactions and Reilly formula.
result Upper bounds on Poincaré and Logarithmic Sobolev constants.
Study bounds for Brownian motion on manifolds with sticky boundary conditions.
problem Proving geometric bounds for Brownian motion on manifolds with sticky boundary conditions.
method Interpolation involving energy interactions between boundary and interior of the manifold.
result Explicit geometric bounds on Steklov eigenvalues, boundary trace operators, and boundary trace logarithmic Sobolev constants.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Efficiently reconstructs jump-diffusion processes from data using neural networks.
problem Reconstructing jump-diffusion processes from data.
method Temporally decoupled squared Wasserstein distance method using parameterized neural networks.
result Enhanced reconstruction of jump-diffusion processes from data.
RL for jump-diffusions applies to financial portfolio selection and option hedging.
problem Optimizing control in systems with jump-diffusion dynamics.
method Entropy-regularized exploratory control with stochastic policies, using existing diffusion algorithms with modifications.
result RL algorithms and parameterizations are invariant to jumps in jump-diffusion systems.
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
problem Improving the performance of discrete diffusion models.
method Conditioning on the jump schedule of discrete Markov processes.
result Schedule-conditioned discrete diffusion (SCUD) models outperform classical and masking diffusion models.
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for…
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.
Optimal wealth strategy derived for jump-diffusion models with liabilities.
problem Maximizing utility in jump-diffusion models with random liabilities.
method Forward Backward SDEs system for optimal strategy.
result Explicit results for pure jump model and exponential utilities.
Study shows how crypto asset liquidity is affected by wash trading and proposes treatment to reduce liquidity diffusion.
problem Understanding and reducing crypto asset wash trading to improve liquidity.
method Proposed a two-component model for liquidity (jump and diffusion) and demonstrated the effectiveness of autoregressive models.
result Treatment on wash trading significantly reduces liquidity diffusion but not liquidity jump.
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
Study short maturity Asian options in jump-diffusion models with local volatility.
problem Analyzing Asian options pricing in models with jumps and local volatility.
method Asymptotic analysis for short maturity, considering fixed and floating strike options.
result Explicit results for Asian option prices in several models, including Merton, double-exponential, and Variance Gamma models.
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…
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.
The paper simplifies complex jump-diffusion markets to complete models.
problem Pricing and hedging derivatives in incomplete jump-diffusion markets.
method Filtration reduction to a complete market, then consistency to original market.
result A unique equivalent martingale measure is obtained for pricing.
Proposes MLEs for MMJDM with EM-algorithm.
problem Estimating stock prices with varying drift and volatility.
method EM-algorithm for MLEs of MMJDM.
result Validated with simulated data and fitted to Amazon and Netflix stock prices.
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is …
In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingal…
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This …
Paper develops models for better HFT and algorithmic trading.
problem Inaccurate LOB dynamics in financial markets.
method Semi-Markov and Hawkes jump-diffusion models for LOB dynamics.
result Improved trading strategies through precise model application.
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of recent work developing a mathematical framework for simulating finite dimensional …
Formula for European option pricing under jump diffusion model.
problem Option pricing under complex stochastic processes.
method Infinite series of Black-Scholes terms for Levy-driven processes.
result Series solution converges with a radius of convergence.
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.
Develops a more flexible HDP-HMM for temporal data segmentation.
problem Limited expressiveness of sticky HDP-HMM due to stationary self-persistence probability.
method Introduces recurrent sticky HDP-HMM with a novel Gibbs sampling strategy.
result RS-HDP-HMM outperforms other models in segmentation tasks.
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the…
Generative model handles varying data dimensions using jump diffusion processes.
problem Handling data of varying dimensionality in generative models.
method Formulated as a jump diffusion process, learning to approximate the process with a novel evidence lower bound.
result Effective sampling of data of varying dimensionality, better compatibility with test-time diffusion guidance imputation tasks.
In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity and its rate of occurrence. Demonstration on how to use these parameters to estima…
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.
Robustly detects jumps in high-frequency CIR and CKLS models.
problem Jump detection in high-frequency jump-diffusion processes.
method MDPDE-based robust estimators for drift and diffusion coefficients.
result Maximum of normalized residuals converges to Gumbel distribution.
The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
problem Stochastic invariance of cones in SPDEs with jumps.
method Sufficient conditions for stochastic invariance of closed convex cones in abstract L2-spaces. result Conditions for stochastic invariance of cones are provided and analyzed.
Study on implied volatility of an affine jump-diffusion model.
problem Characterize implied volatility of an affine jump-diffusion model.
method Explicit moment generating function derived from solving ODEs; large deviation principle applied.
result Asymptotic behaviors of implied volatility in large-maturity and large-strike regimes characterized.
We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form $e^{iΦ(-i\dd_x)}$ (gauge transformation in the dual s…
We consider a Markov process X, which is the solution of a stochastic differential equation driven by a Lévy process Z and an independent Wiener process W. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of $Z…
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.
Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.
problem Pricing American options in models with time-dependent and exponential jumps.
method Generalizes existing methods for barrier and American options to handle arbitrary time dependencies and solves the problem through algebraic and Fredholm-Volterra equations.
result Presents a semi-analytic solution for American options in time-dependent jump-diffusion models with exponential jumps.
In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-diffe…
Generative model for time series using Schrödinger bridges with jumps.
problem Creating realistic synthetic time series from observed data.
method Entropic optimal transport, Schrödinger bridge framework, jump-diffusion process.
result Jump-diffusion Schrödinger bridge model generates more realistic time series.
Paper models transition risk using jump-diffusion model to price credit swaps.
problem Capturing transition risk in financial markets.
method Calibrated jump-diffusion model to CDS term structure, using quantile regression.
result Jump-diffusion model captures transition risk, jumps represent green policies.
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the …
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of this op…
New deep learning method for option pricing in jump-diffusion models.
problem Option pricing in jump-diffusion models with high-dimensional assets.
method Implicit-explicit minimizing movement time-stepping approach using deep ANNs.
result Consistent and asymptotically correct solutions for large underlyings.
A subset of Rd is called "sticky" if it cannot be isotoped off of itself by a small ambient isotopy. Sticky wild Cantor sets are constructed in Rd for each d≥4.