arXiv research

Extends nonlinear filtering to predictable jump times.

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…

Study on short-term behavior of ATM-IV for jump-diffusion model.

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…

The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.

Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. Thi…

Enhances RL for jump processes using MSBVE algorithm.

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…

The paper models financial data with multivariate jump processes.

New neural method for inferring Markov jump processes.

Generative model for time series using Schrödinger bridges with jumps.

New framework analyzes pre-stock jump trading behaviors using multivariate time series analysis.

Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets…

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…

A method to identify new classes of price jumps in financial markets.

In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …

We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,Δ_n,2Δ_n,\ldots.$ This process is an Itô semimartingale with stochastic volatility $σ_t^2$. Assuming that $X$ has jumps on $[0,T]$, we derive tests to decide whether the volatility process has jumps occurring simultan…

This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we pr…

Study minimal solutions to a reflected process driven by jump processes.

Solves optimal stopping problem with Poisson constraints using jumps.

Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a competitive inference alternative to the existing tools. This methodology is the…

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.

Quantum computer method for pricing lookback options with jumps.

The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…

Deep learning solves complex stochastic control with jumps.

This paper proposes a new integrated variance estimator based on order statistics within the framework of jump-diffusion models. Its ability to disentangle the integrated variance from the total process quadratic variation is confirmed by both simulated and empirical tests. For practical purposes, we introduce an itera…

In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and aro…

Proposes MLEs for MMJDM with EM-algorithm.

Paper analyzes systematic jump risk around the clock using news narratives.

Generative model handles varying data dimensions using jump diffusion processes.

Robust feature-weighted jump models for time-dependent clustering

Neural Jump ODE improves continuous-time prediction and filtering of irregularly sampled time series.

The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular, we derive an exact formula for the semivariance when the volatility is kept const…

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…

Detects jumps in financial asset prices with U-shape volatility.

Neural Jump ODEs improve online filtering and classification with robust performance.

Study on stochastic volatility models with external shocks triggering jump cascades.

The study reveals unspanned risks in equity option risk premiums, explaining negative premiums for certain options.

Model predicts jump risk premia influencing cryptocurrency futures and option performance.

Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by R. Norberg. In the enlargened fi…

Modeling cryptocurrency volatility and jumps with SVCJ model.

RL for jump-diffusions applies to financial portfolio selection and option hedging.

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary tim…

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization p…

Method detects jumps in high-frequency order prices using local minima.

Generative models using PDMPs with explicit jump rates and kernels.