Spectral estimation of the fractional order of a Lévy process

DOI10.1214/09-AOS715zbMath1181.62151arXiv1001.1820OpenAlexW1964855733MaRDI QIDQ847639

Denis Belomestny

Publication date: 19 February 2010

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1820

zbMATH Keywords

semiparametric estimationBlumenthal-Getoor indexregular Lévy processes

Mathematics Subject Classification ID

Related Items (24)

Optimal \(L^2\)-approximation of occupation and local times for symmetric stable processes ⋮ High-frequency Donsker theorems for Lévy measures ⋮ Estimation of tempered stable Lévy models of infinite variation ⋮ Estimation of the activity of jumps in time-changed Lévy models ⋮ Adaptive nonparametric estimation for Lévy processes observed at low frequency ⋮ Testing whether jumps have finite or infinite activity ⋮ Minimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data ⋮ Third-order short-time expansions for close-to-the-money option prices under the CGMY model ⋮ Realized Laplace transforms for pure-jump semimartingales ⋮ Measuring the roughness of random paths by increment ratios ⋮ Calibration of self-decomposable Lévy models ⋮ Confidence sets in nonparametric calibration of exponential Lévy models ⋮ Statistical inference for time-changed Lévy processes via composite characteristic function estimation ⋮ Testing the characteristics of a Lévy process ⋮ Asymptotically optimal discretization of hedging strategies with jumps ⋮ Quantile estimation for Lévy measures ⋮ Identifying the successive Blumenthal-Getoor indices of a discretely observed process ⋮ HIGH‐ORDER SHORT‐TIME EXPANSIONS FOR ATM OPTION PRICES OF EXPONENTIAL LÉVY MODELS ⋮ Spectral estimation of the Lévy density in partially observed affine models ⋮ Estimation and Calibration of Lévy Models via Fourier Methods ⋮ A NEW LOOK AT SHORT-TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS ⋮ Jump activity estimation for pure-jump semimartingales via self-normalized statistics ⋮ Intermittent process analysis with scattering moments ⋮ Explicit and combined estimators for parameters of stable distributions

Uses Software

• STABLE

Cites Work

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• Nonparametric estimation for Lévy processes from low-frequency observations
• Estimating the degree of activity of jumps in high frequency data
• Spectral calibration of exponential Lévy models
• Volatility estimators for discretely sampled Lévy processes
• Asymptotically efficient estimation of location for a symmetric stable law
• On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution
• Barrier options and touch-and-out options under regular Lévy processes of exponential type
• Hyperbolic distributions in finance
• Weak convergence and empirical processes. With applications to statistics
• Spatial aggregation of local likelihood estimates with applications to classification
• Retrieving Lévy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem
• Sharp Optimality in Density Deconvolution with Dominating Bias. II
• Risk bounds for the non-parametric estimation of Lévy processes
• Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process
• Regression-Type Estimation of the Parameters of Stable Laws
• Stable Distributions in Statistical Inference: 2. Information from Stably Distributed Samples
• Numerical calculation of stable densities and distribution functions
• Financial Modelling with Jump Processes
• Selected Topics in Characteristic Functions
• Estimation in Univariate and Multivariate Stable Distributions
• Stable Distributions in Statistical Inference: 1. Symmetric Stable Distributions Compared to Other Symmetric Long-Tailed Distributions
• Introduction to nonparametric estimation
• Estimation of affine asset pricing models using the empirical characteristic function

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