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.
The paper evaluates functions of stable Lévy processes and their extrema efficiently.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
Upper bound on withdrawal success for geometric Levy alpha-stable wealth process.
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…
New method estimates tempered stable Lévy models with high accuracy.
Develops information geometry for Lévy processes in finance.
New financial models use tempered stable subordination for better correlation dynamics.
New method estimates volatility for Lévy processes with unbounded jumps efficiently.
We introduce a simple model for equity index derivatives. The model generalizes well known Lèvy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few …
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…
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…
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…
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of …
Asymptotic expansions for call prices and implied volatilities in exponential Lévy models.
We offer new formulas for European option pricing under tempered stable processes.
New method estimates volatility for processes with jumps of unbounded variation.
Develops a Monte Carlo algorithm for tempered stable process extrema.
Characterizes term structure models driven by Lévy processes.
Research on long-range memory in financial and social systems using various models.
Neural networks model financial data with Lévy processes.
New method for Bayesian inference of Lévy-driven SDEs with jumps.
We apply multilevel Monte Carlo for option pricing problems using exponential Lévy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergen…
We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. Th…
We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…
Study uses AI to price exotic options with a new Levy process model.
In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied …
Modeling risk and performance with Levy-stable distributions.
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …
The paper studies affine models driven by independent Lévy processes and their calibration.
Estimates graph process with high-frequency data, proving asymptotic properties.
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correla…
Method extends option valuation for 2D Lévy models.
Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a Lévy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability distributions are not Lévy stable, a plausible result since commodity markets have …
Optimizes asset allocation for risk measures in a Lévy market.
We study the behavior of the critical price of an American put option near maturity in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the l…
DLPM replaces Gaussian noise with α-stable noise in DDPM, improving data distribution coverage and robustness.
Price fluctuations in financial markets can be characterized by Lévy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long term, they similarly indicated an unique value. On the other hand, when analyzed in …
This work extracts stochastic dynamical systems with -stable Lévy noise.
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
Method extracts stochastic systems with Lévy noise from data.
The recent emergence of cryptocurrencies such as Bitcoin and Ethereum has posed possible alternatives to global payments as well as financial assets around the globe, making investors and financial regulators aware of the importance of modeling them correctly. The Levy's stable distribution is one of the attractive dis…
Extends option pricing framework without risk-free asset using Levy jumps.
The paper studies stochastic gradient descent with infinite variance gradients.
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…
The study examines order flow in financial markets using fractional Lévy stable motion.
We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter ) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in . T…