We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent …
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48 results for “Self-Exciting Jumps”
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.
Pricing Derivatives under Self-Exciting Dynamics: A Finite-Difference and Transform Approachq-fin.MF
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
The paper models default probabilities and total defaults in credit portfolios using a contagion process with self-exciting jumps.
problem Modeling default probabilities and total defaults in credit portfolios to mitigate credit risk.
method Developed a contagion process with self-exciting jumps to model credit events and derive closed-form expressions for default probabilities and total defaults.
result The proposed framework captures the feedback effect and can be used to price synthetic CDOs.
Optimal reinsurance strategy analyzed for dynamic risk model with self- and externally-excited jumps.
problem Optimal reinsurance in a dynamic contagion model with self-exciting and externally-exciting risks.
method Two methodologies: classical HJB approach and BSDE approach, focusing on Markovian setting.
result Comparison of self-exciting and externally-exciting risks highlights heightened risk from self-exciting component.
We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this fil…
We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…
Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of integrated volatility and price jumps, to the specified model components; with Bay…
The paper models financial data with multivariate jump processes.
problem Capturing the dynamics of financial data with jumps.
method Defined multivariate point processes driven by stochastic jumps, providing stability conditions.
result Nonlinear models fit financial data best, showing jumps cluster during crises.
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general funct…
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process in which point process jumps generate a shot-noise intensity field. Unlike the Ha…
Model captures rough volatility and jump clustering in stock vol dynamics.
problem Capturing the joint evolution of S&P 500 and VIX implied vol smiles.
method Rough Hawkes Heston model with affine Volterra dynamics, power kernel, and exponential jump law.
result Model accurately captures S&P 500 and VIX implied vol smiles with low power kernel.
Researchers prove a new measure for a financial volatility model.
problem Modeling financial volatility with a Hawkes process.
method Prove existence of equivalent martingale measures for a Heston-Hawkes model.
result Existence of a family of equivalent martingale measures for the model.
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
This paper develops a path-first theory using signatures and jump lifts for self-exiting processes.
problem Developing a universal coordinate system for various types of paths and processes.
method Using signatures, jump lifts, and expected signatures, the paper presents a geometricity framework with algebraic properties and obstructions.
result The framework links various mathematical concepts and offers four main contributions to understanding and modeling self-exiting processes.
Paper presents a method for estimating Hawkes process parameters.
problem Estimating parameters of Hawkes processes with self-excitation or inhibition.
method Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition.
result The proposed estimator provides more accurate estimations in the inhibition context.
New model prices options with complex market data structures.
problem Complex market data structures in option pricing.
method Compound CARMA(p,q)-Hawkes model.
result Model can replicate volatility smile in financial markets.
We provide existence, uniqueness and stability results for affine stochastic Volterra equations with -kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is b…
We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price…
Coexisting Hidden and self-excited attractors in an economic system of integer or fractional orderq-fin.GN
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
problem Existence of coexisting hidden and self-excited attractors in economic systems.
method Integer and fractional order analysis of an economic system.
result Integer-order system exhibits multiple combinations of coexisting hidden and self-excited attractors.
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular…
Investigates how 'green' labels affect bond market dynamics.
problem Understanding the impact of 'green' labels on bond market trading activity.
method Used Hawkes processes and a moving average model to analyze high-frequency bond price dynamics.
result Differences in bond market dynamics emerge during periods with interest rate announcements, especially for energy market issuers.
Paper forecasts financial trading durations using a new point process model.
problem Forecasting limit order book durations in high-frequency financial data.
method Self-exciting flexible residual point process incorporating empirical distributional features.
result The model achieves strong predictive performance compared to alternative approaches.
A new model predicts bid-ask spread dynamics in financial markets.
problem Capturing the self-exciting nature of bid-ask spread changes.
method State-dependent Spread Hawkes model (SDSH) incorporating various spread jump sizes and current state impact.
result The SDSH model accurately forecasts spread values at short-term horizons.
Develops a goodness-of-fit test for self-exciting processes.
problem Quantifying how well generative models capture self-exciting point processes.
method Connects to Quasi-maximum-likelihood estimator (QMLE) theory and develops a non-parametric self-normalizing statistic, the Generalized Score (GS) statistics.
result Validates the proposed GS test's good performance through numerical simulation and real-data experiments.
A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategiesq-fin.MF
Study optimizes portfolio liquidation strategies with complex market impacts.
problem Optimizing portfolio liquidation with transient market impacts and self-exciting order flow.
method Mean-field control problem with semimartingale strategies, passing to continuous-time limit, and solving Riccati equations.
result Existence of optimal strategy with jumps only at start and end of trading period.
FinStressTS creates synthetic benchmarks for financial forecasting, revealing model weaknesses.
problem Limited failure attribution in real-world financial benchmarks.
method Synthetic benchmark with 30 diagnostic environments linked to six mechanism families.
result Model performance varies by mechanism type, with autoregressive models often outperforming Transformers.
Study optimal dividend and capital injection in insurance portfolios with self-exciting claim arrivals.
problem Optimal dividend and capital injection in insurance portfolios with Hawkes process claim arrivals.
method Analytical properties, explicit threshold, HJB variational inequality, finite-difference scheme, policy-gradient, actor-critic methods.
result Learned strategies closely match the PDE benchmark and remain stable across initial conditions.
Paper introduces MSPD for multivariate risk processes with dependencies.
problem Computing risk valuations with dynamic dependencies between frequency and severity.
method Combines Poisson imbedding, pseudo-chaotic expansion, and Malliavin calculus.
result Explicit general correlation formula for MSPDs.
This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is provided. In particular, the efficiency of an adaptive parameter estimation algorithm…
The Identification of Thresholds and Time Delay in Self-Exciting Threshold AR Model by Waveletmath-ph
In this paper we studied about the wavelet identification of the thresholds and time delay for more general case without the constraint that the time delay is smaller than the order of the model. Here we composed an empirical wavelet from the SETAR (Self-Exciting Threshold Autoregressive) model and identified the thres…
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-excitin…
Ubiquitous power law scaling in nonlinear self-excited Hawkes processescond-mat.stat-mech
New mechanism found for power laws including Zipf's law.
problem Understanding the ubiquity of power law distributions.
method Introduced nonlinear self-excited Hawkes processes with fast-accelerating intensities.
result Wide class of nonlinear Hawkes processes have power law intensity PDFs.
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.
Paper introduces a new model for cyber insurance pricing.
problem Inaccurate pricing of cyber insurance due to multiple, contagious losses.
method Developed a bivariate compound dynamic contagion process.
result Analytical expressions for the compound process and its moments.
We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the…
Hawkes processes for credit indices time series analysis: How random are trades arrival times?stat.AP
Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual interactions phenomena. The authors propose here a simple yet conclusive method for f…
New model shows negative resilience can improve trading efficiency.
problem Optimal trade execution in limit order books with negative resilience.
method Stochastic order book model with negative resilience.
result Negative resilience can lead to more efficient trading.
In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis …
We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simpli…
Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a scenario where certain interaction events lack information about participants. Ins…
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter , where is the time-varying parameter, and we consider the high-frequency…
Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.
problem Analyzing interactions and shock propagation in default portfolios with multiple sectors.
method Applied multidimensional self-exciting negative binomial distribution (SE-NBD) process to 13 sectors.
result Identified upstream and downstream sectors, showing shock amplification in default portfolios.
Develops a new model for multi-currency volatility using CBI-time-changed Lévy processes.
problem Capturing the risk characteristics of FX markets and their self-exciting dynamics.
method CBI-time-changed Lévy processes, affine processes, Fourier methods, deep-learning techniques.
result An analytically tractable model with a semi-closed pricing formula for currency options.
We introduce a new measure of activity of financial markets that provides a direct access to their level of endogeneity. This measure quantifies how much of price changes are due to endogenous feedback processes, as opposed to exogenous news. For this, we calibrate the self-excited conditional Poisson Hawkes model, whi…
Study models market volatility with persistent and temporary impacts.
problem Microstructure of rough volatility models driven by Poisson measures.
method Existence and uniqueness of solutions for stochastic path-dependent Volterra equations.
result Volatility process converges to fractional Heston model with spikes.