Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes

DOI10.1016/j.spa.2020.04.010zbMath1456.62038arXiv1904.10660OpenAlexW3020831120MaRDI QIDQ2196535

Arnaud Gloter, Chiara Amorino

Publication date: 3 September 2020

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.10660

zbMATH Keywords

convergence speedhigh frequency dataintegrated variancethreshold estimatorLévy-driven SDE

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Generalizations of martingales (60G48) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Functional limit theorems; invariance principles (60F17) Jump processes on general state spaces (60J76)

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On the nonparametric inference of coefficients of self-exciting jump-diffusion ⋮ Estimation of state-dependent jump activity and drift for Markovian semimartingales ⋮ Inference of binary regime models with jump discontinuities ⋮ Rate-optimal estimation of the Blumenthal-Getoor index of a Lévy process ⋮ Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function ⋮ Rate of estimation for the stationary distribution of jump-processes over anisotropic Hölder classes

Cites Work

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• A Jump-Diffusion Model for Option Pricing
• The Morris-Lecar neuron model embeds a leaky integrate-and-fire model
• The speed of convergence of the threshold estimator of integrated variance
• Discretization of processes.
• Estimation of parameters for diffusion processes with jumps from discrete observations
• On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
• Estimating functions for SDE driven by stable Lévy processes
• Jump filtering and efficient drift estimation for Lévy-driven SDEs
• Markov processes, semigroups and generators.
• Asymptotic properties of realized power variations and related functionals of semimartingales
• Limit theorems for multipower variation in the presence of jumps
• Efficient estimation of integrated volatility in presence of infinite variation jumps
• A remark on the rates of convergence for integrated volatility estimation in the presence of jumps
• Jump activity estimation for pure-jump semimartingales via self-normalized statistics
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Option pricing when underlying stock returns are discontinuous