Estimation of parameters and local times in a discretely observed threshold diffusion model
Preprint
Abstract
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the process, with a generalized moment estimator and a maximum likelihood estimator. We develop the asymptotic theory of the estimators when the time horizon of the observations goes to infinity, considering both cases of a fixed time lag (low frequency) and a vanishing time lag (high frequency) between consecutive observations. In the setting of low frequency observations and infinite time horizon we also study the convergence of three local time estimators, that are already known to converge to the local time in the setting of high frequency observations and fixed time horizon. We find that these estimators can behave differently, depending on the assumptions on the time lag between observations.Keywords
All Related Versions
This publication has 34 references indexed in Scilit:
- Arbitrage problems with reflected geometric Brownian motionFinance and Stochastics, 2023
- A reinforcement learning algorithm for trading commoditiesApplied Stochastic Models in Business and Industry, 2023
- Parameter estimation for threshold Ornstein–Uhlenbeck processes from discrete observationsJournal of Computational and Applied Mathematics, 2022
- Approximate maximum likelihood estimation of a threshold diffusion processComputational Statistics & Data Analysis, 2020
- Extreme at-the-money skew in a local volatility modelFinance and Stochastics, 2019
- Variance swaps under the threshold Ornstein–Uhlenbeck modelApplied Stochastic Models in Business and Industry, 2017
- Quasi-likelihood estimation of a threshold diffusion processJournal of Econometrics, 2015
- On identification of the threshold diffusion processesAnnals of the Institute of Statistical Mathematics, 2010
- Bounds for the transition density of time-homogeneous diffusion processesStatistics & Probability Letters, 2009
- Convergence results for multivariate martingalesStochastic Processes and their Applications, 2005