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Statistical inference for nonergodic weighted fractional Vasicek models [PDF]

Modern Stochastics: Theory and Applications, 2021
A problem of drift parameter estimation is studied for a nonergodic weighted fractional Vasicek model defined as $d{X_{t}}=\theta (\mu +{X_{t}})dt+d{B_{t}^{a,b}}$, $t\ge 0$, with unknown parameters $\theta >0$, $\mu \in \mathbb{R}$ and $\alpha :=\theta ...
Khalifa Es-Sebaiy, Mishari Al-Foraih, Fares Alazemi   +2 more
doaj   +2 more sources

Maximum Likelihood Estimation for the Fractional Vasicek Model [PDF]

Econometrics, 2020
This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case ...
Katsuto Tanaka, Weilin Xiao, Jun Yu
doaj   +4 more sources

A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model. [PDF]

Comput Econ, 2023
Our objective is to solve the time-fractional Vasicek model for European options with a new stabled relaxation method. This new approach is based on the splitting method. Some numerical tests are presented to show the stability and the reliability of our approach with the theory of options.
Kharrat M, Arfaoui H.
europepmc   +3 more sources

Maximum Likelihood Estimation in the Fractional Vasicek Model

Lithuanian Journal of Statistics, 2017
We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1).
Stanislav Lohvinenko, Kostiantyn Ralchenko   +1 more
doaj   +6 more sources

Maximum likelihood estimation in the non-ergodic fractional Vasicek model [PDF]

Modern Stochastics: Theory and Applications, 2019
We investigate the fractional Vasicek model described by the stochastic differential equation $d{X_{t}}=(\alpha -\beta {X_{t}})\hspace{0.1667em}dt+\gamma \hspace{0.1667em}d{B_{t}^{H}}$, ${X_{0}}={x_{0}}$, driven by the fractional Brownian motion ${B^{H}}$
Stanislav Lohvinenko, Kostiantyn Ralchenko   +1 more
doaj   +3 more sources

Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion [PDF]

Algorithms, 2018
In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: d X t = ( μ + θ X t ) d t + d S t H , t ≥ 0 with X 0 = 0 , where S H is a sub-fractional Brownian ...
Shengfeng Li, Yi Dong
doaj   +3 more sources

Least Squares Estimator for Vasicek Model Driven by Fractional Levy Processes [PDF]

JOURNAL OF ADVANCES IN MATHEMATICS, 2018
In this paper, we consider parameter estimation problem for Vasicek model driven by fractional lévy processes defined We construct least squares estimator for drift parameters based on time?continuous observations, the consistency and asymptotic ...
wang, qingbo, Yin, Xiuwei
core   +4 more sources

Asymptotic Properties of Parameter Estimators in~Vasicek Model Driven by Tempered Fractional Brownian Motion

Austrian Journal of Statistics
The paper focuses on the Vasicek model driven by a tempered fractional Brownian motion. We derive the asymptotic distributions of the least-squares estimators (based on continuous-time observations) for the unknown drift parameters. This work continues
Yuliya Mishura, Kostiantyn Ralchenko, Olena Dehtiar   +2 more
doaj   +3 more sources

Simultaneous Calibration of European Option Volatility and Fractional Order under the Time Fractional Vasicek Model

Algorithms
In this paper, we recover the European option volatility function σ(t) of the underlying asset and the fractional order α of the time fractional derivatives under the time fractional Vasicek model.
Yunkang Du, Zuoliang Xu
doaj   +2 more sources

Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models

Fractal and Fractional
Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering.
Yuliya Mishura, Kostiantyn Ralchenko
doaj   +2 more sources