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.
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.
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.
Simplifies pricing options in jump-diffusion models using gauge transformations.
problem Pricing European options in affine jump-diffusion models.
method Gauge transformation in the dual space to reduce to diffusion model pricing.
result A general procedure for calculating Φ and applications in pricing and estimation. 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.
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 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.
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…
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.
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.
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 …
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.
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…
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.
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.
Develops stability conditions for estimating affine jump-diffusions.
problem Ergodicity and consistency of parameter estimation for affine jump-diffusions.
method Establishes stochastic stability conditions and ergodicity under specific conditions.
result Proves strong laws of large numbers and functional central limit theorems for additive functionals.
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.
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.
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.
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.
Study cliquet options in a jump-diffusion model with Lévy processes.
problem Pricing cliquet options in a complex financial model with jumps.
method Developed semi-analytic expressions using Lévy process distribution and Fourier transform.
result Inferred semi-analytic expressions for cliquet option prices and derived Greeks.
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 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…
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.
Paper presents fast methods for pricing energy derivatives using mean-reverting jump-diffusion models.
problem Pricing energy derivatives with mean-reverting and occasional spikes.
method Exact and fast simulation of spot price dynamics using Ornstein-Uhlenbeck and jump-diffusion processes.
result Apparent computational advantages of the proposed procedures for pricing Asian options, gas storages, and swings.
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.
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.
Develops a fast and precise method to evaluate likelihood of jump-diffusion models.
problem Evaluating likelihood functions of models with stochastic volatility and jumps.
method Deterministic nonlinear filtering algorithm based on Kitagawa's method.
result Deterministic filtering is faster and more precise than particle filter.
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.
Investors mispricing volatility and jump sensitivity in Delta hedging models still super-replicate the true claim.
problem Investors misestimate volatility and jump sensitivity in Delta hedging models.
method Analyzes the robustness of Delta hedging in jump-diffusion models, proving stochastic flow properties and convexity of value functions.
result An erroneously computed Delta strategy super-replicates the true claim in expectation under a wide class of models.
A new method calibrates jump-diffusion models from option prices.
problem Calibrating jump-diffusion models from market data.
method Forward Dupire-type PIDE, Tikhonov regularization.
result Robust method for identifying local volatility and jump size.
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.
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 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.
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…
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 …
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…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
Proposes a new jump-diffusion model for option pricing.
problem Capturing self-excitation and contagion effects in option pricing models.
method Combines Heston and Queue-Hawkes models with closed-form characteristic function.
result Reduces computational complexity and offers better volatility smile fitting.
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…
Optimal method detects jumps in jump-diffusion processes.
problem Detecting jumps in jump-diffusion processes with improved finite-sample performance.
method Iterative threshold-kernel method to optimally select threshold parameter.
result Approximate optimal threshold depends on spot volatility, jump intensity, and jump density.
News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable est…
Investigates consistency of FX rate dynamics under inversion.
problem Consistency of jump-diffusion dynamics for FX rates under inversion.
method Calibrated Heston and SABR models, analyzed jumps in domestic and foreign measures.
result Determines conditions for consistency in FX rate dynamics under inversion.
In this paper, we propose a modified Levy jump diffusion model with market sentiment memory for stock prices, where the market sentiment comes from data mining implementation using Tweets on Twitter. We take the market sentiment process, which has memory, as the signal of Levy jumps in the stock price. An online learni…
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.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
problem Pricing and delta computation of financial derivatives in jump-diffusion models with stochastic intensity.
method Utilizes Malliavin calculus to price and compute delta, applying the Euler scheme for convergence analysis.
result Established the convergence of approximated solution, financial derivative, and its delta Greeks.
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…