A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method for Bayesian inference of Lévy-driven SDEs with jumps.
Neural networks model financial data with Lévy processes.
Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth …
Deep neural networks approximate option prices in high-dimensional Lévy models efficiently.
NBE method speeds up Lévy process parameter estimation.
Hybrid model outperforms benchmarks in financial forecasting.
These lectures notes aim at introducing Lévy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of Lévy processes. We analyze a `toy' example of a Lévy process, viz. a Lévy jump-diffusion, which yet offers significant insight into the distri…
An unsupervised deep learning method solves PIDEs for option pricing.
Develops information geometry for Lévy processes in finance.
Efficient methods for Lévy models using SINH-regular processes.
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for inst…
Neural networks estimate SDEs with jump noise using a Tamed-Milstein scheme.
We introduce an algorithm for the pricing of finite expiry American options driven by Lévy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm is viable for any Lévy process whose law at an independent, exponentially distrib…
This brief manuscript provides an introduction to Lévy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular Lévy processes are presented in R.
Study of bandit problem with Poisson decision times and Lévy processes.
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a …
Method verifies if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
Universal approximation for rough paths and Lévy processes.
New method estimates volatility for Lévy processes with unbounded jumps efficiently.
Neural Lévy model improves risk and density forecasting for financial returns.
Modeling Bitcoin prices and media attention using jump-type processes.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
Study of deep neural networks with dependent weights leading to new model limits and properties.
Study on pricing American Exchange options using Lévy processes.
This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Our main contribution is a generalization of the result in Loeffen et al.…
Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced w…
This paper presents some new results on Parisian ruin under Levy insurance risk process, where ruin occurs when the process has gone below a fixed level from the last record maximum, also known as the high-water mark or drawdown, for a fixed consecutive periods of time. The law of ruin-time and the position at ruin is …
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…
In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally ne…
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma pr…
Score-fPINN tackles high-dimensional FPL equations using fractional score functions.
We consider an optimal liquidation problem with infinite horizon in the Almgren-Chriss framework, where the unaffected asset price follows a Levy process. The temporary price impact is described by a general function which satisfies some reasonable conditions. We consider an investor with constant absolute risk aversio…
In this note we find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two branches of the same company) divide between them both claims and premia in some specifie…
Researchers calculate the price of a perpetual put option in Lévy models.
We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are fini…
This paper gives examples of explicit arbitrage-free term structure models with Lévy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a Lévy process is a "natural" scale for the process to be the state variable of a market.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the di…
Study analyzes Lévy process structure on manifolds with conjugate points.
New GLPs split Lévy bridges into non-overlapping subprocesses.
The paper evaluates functions of stable Lévy processes and their extrema efficiently.
In this paper, we introduce the concept of \emph{Poissonian occupation times} below level of spectrally negative Lévy processes. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known conti…
Optimizes dividend control in a bankruptcy process using a special Levy process.
The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.