arXiv research

Researchers tackle insider trading in incomplete markets using a discrete-time jump process approach.

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…

Study approximates financial market with discrete-time models.

Proposes MLEs for MMJDM with EM-algorithm.

Study bounds for European basket call options in a discrete-time market model with price jumps.

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…

In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the co…

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

This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information. For estimating the hidden drift it is crucial…

Efficient method for pricing European and American options using Markov switching stochastic volatility model.

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using vari…

We consider option hedging in a model where the underlying follows an exponential Lévy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The results are obtained by considering the Lévy model as a perturbation of the Black-Schole…

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…

Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data using a threshold method. The consistency of the volatility estimator has been ob…

Efficiently reconstructs jump-diffusion processes from data using neural networks.

The paper models financial data with multivariate jump processes.

Extended CIR process with jumps at fixed dates for modeling overnight rates.

New neural method for inferring Markov jump processes.

This paper solves the inversion problem for jump processes using Markovian projections.

In this note we investigate the consistency under inversion of jump diffusion processes in the Foreign Exchange (FX) market. In other terms, if the EUR/USD FX rate follows a given type of dynamics, under which conditions will USD/EUR follow the same type of dynamics? In order to give a numerical description of this pro…

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…

New method estimates volatility for Lévy processes with unbounded jumps efficiently.

New model for Knightian uncertainty with jumps.

Projects Markovian processes from Itô semimartingales with jumps.

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

We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up t…

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

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

Improves generative models by adding jump-diffusion noise.

Generative model handles varying data dimensions using jump diffusion processes.

This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whos…

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…

New method estimates volatility for processes with jumps of unbounded variation.

Proposes a new jump-diffusion model for option pricing.

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability a…

Unified analytical tool for non-Markovian jump processes.

A new model for short rates using pure-jump processes.

Study optimizes portfolio liquidation strategies with complex market impacts.

New model estimates corporate defaults using pure jump processes, capturing extreme events.

Develops active learning for Jump Gaussian Process models.

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they are affected by jumps. To this end, we introduce Neural Jump Stochastic Different…

Formula for European option pricing under jump diffusion model.

We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal v…

We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $α$-stable processes with $α\in(1,2]$. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore, we examine the jump clus…

Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of ou…

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

Python package ajdmom simplifies moment formula derivation for jump diffusions.

Study optimizes investment strategies in markets with contagious price jumps.