Financial modelling with ornsteinuhlenbeck processes. Abstract in this article we propose a maximum likelihood methodology to estimate the parameters of a onedimensional stationary process of ornstein uhlenbeck type that is constructed via a selfdecomposable distribution d. The most popular model is the ornstein and uhlenbeck 1930 ou process, also. Pdf parameter estimation for the discretely observed fractional.
A general lower bound of parameter estimation for reflected ornstein uhlenbeck processes volume 53 issue 1 qingpei zang, lixin zhang. Abstract in this article we propose a maximum likelihood methodology to estimate the parameters of a onedimensional stationary process of. Parameter estimation of complex fractional ornsteinuhlenbeck processes with fractional noise yong chen, yaozhong hu and zhi wang school of mathematics, hunan university of science and technology xiangtan, 411201, hunan, china. Robust parameter estimation for the ornsteinuhlenbeck. Statistics and probability letters 79 2009 2076 2085. This paper considers parameter estimation in the ornsteinuhlenbeck process observed in the presence of gaussian white noise. On parameter estimation of hidden ergodic ornstein. This paper deals with the problem of estimating the parameters for fractional ornsteinuhlenbeck processes from discrete observations when the hurst parameter h is known. We study the problem of parameter estimation for generalized ornstein uhlenbeck. Pdf parameter estimation from observations of first.
In section 3, we give subdiffusion concept then we describe the subordinated ornstein uhlenbeck processes with inverse tempered stable subordinator. Nonergodic case parameter estimation for fractional ornsteinuhlenbeck processes. In this paper, we consider the problem of parameter. Both the drift and the diffusion coefficient estimators of discrete form are obtained based on approximating integrals via riemann sums with hurst parameter h. The trending ornsteinuhlenbeck process and its applications in mathematical finance dr christian thierfelder hertford college university of oxford a thesis submitted for the degree of mathematical finance april 12, 2015. Ornstein uhlenbeck diffusion of hermitian and nonhermitian matrices unexpected links. This paper studies the least squares estimator lse for the drift parameter of an ornsteinuhlenbeck process driven by fractional brownian motion, whose observations can be made either continuously or at discrete time instants. Its original application in physics was as a model for the velocity of a massive brownian particle under the influence of friction. Parameter estimation for an ornstein uhlenbeck process. Subsequently, we discuss linear models for which negativity is ruled out.
On parameter estimation of the hidden ornsteinuhlenbeck process. In this paper, we study the estimation problem of an unknown drift parameter matrix for fractional ornstein uhlenbeck process in multidimensional setting. Pdf l\evy area of fractional ornsteinuhlenbeck process. Parameter estimation, nonergodic gaussian ornstein uhlenbeck process. Estimation for partially observed ornstein uhlenbeck process benjamin favetto and adeline samson map5, university paris descartes, france 1 hal003243, version 2. Maximum likelihood estimation in processes of ornstein. In the present paper we consider the drift parameter estimation problem for the nonergodic. Maximumlikelihood estimation of ou parameters pnas. Maximum likelihood estimation of mean reverting processes. Then we estimate the unknown identi able parameters in our model. They are widely used to model interest rates, and are of particular use to those modelling commodities. L evy area of fractional ornsteinuhlenbeck process and.
Bias in the estimate of a mean reversion parameter for a. Statistics and probability letters least squares estimator. Uhlenbeck model is that the probability density function pdf of these times is not. In this paper, we study the problem of parameter estimation for the ornstein uhlenbeck processes dxt. Maximum likelihood estimation in processes of ornsteinuhlenbeck. Thus in the case ornsteinuhlenbeck, it is hard to estimate parameters from. Parameter estimation from observations of firstpassage times of the ornstein uhlenbeck process and the feller process. Parameter estimation for ornsteinuhlenbeck processes driven by stable levy motions yaozhong hu and hongwei long abstract. Parameter estimation of complex fractional ornstein. Ouknine3 1 polydisciplinary faculty of taroudant, university ibn zohr, taroudant, morocco. Parameter estimation, nonergodic gaussian ornsteinuhlenbeck process. Parameter estimation for an ornstein uhlenbeck process with a periodic in time drift dominique dehay universit. How can i estimate the ornsteinuhlenbeck paramters of.
Stable motions1 yaozhong hu2 department of mathematics, university of kansas, 601 snow hall, lawrence, kansas 660452142, usa hongwei long3 department of mathematical sciences, florida atlantic university, boca raton, florida 334310991, usa abstract. How can i estimate the ornsteinuhlenbeck paramters of some mean reverting data that i have on r. Parameter estimation for a partially observed ornstein uhlenbeck process with longmemory noise. An application of ornsteinuhlenbeck process to commodity pricing.
First, refer to maximumlikelihood estimation of ou parameters section of methods. Viens, parameter estimation for a partially observed ornstein uhlenbeck process with longmemory noise, stochastics 89 2017 431468. This paper proposes a twostage method for estimating parameters in the fractional ornstein uhlenbeck model based on discretesampled observations. Finally, a class of nonlinear models will be considered. This note develops a maximumlikelihood ml methodology for parameter estimation of 1dimensional ornstein uhlenbeck or mean reverting processes. To estimate the parameters of an observed ornsteinuhlenbeck process, we. Estimation of ornsteinuhlenbeck process using ultrahigh. Parameter estimation for close prices of gm parameter estimated value 47. Here we use the ornsteinuhlenbeck process to model gene expression divergence. Parameter estimation for nonstationary reflected ornstein. We assume that the unobserved ornstein uhlenbeck process depends on some unknown parameter and. Least squares estimator for ornsteinuhlenbeck processes.
This paper is concerned with the parameter estimation problem for nonstationary reflected ornstein uhlenbeck processes driven by stable noises by using the trajectory fitting method combined with the weighted least squares technique. L evy area of fractional ornstein uhlenbeck process and parameter estimation zhongmin qian and xingcheng xuy april 4, 2018 abstract in this paper, we study the estimation problem of an unknown drift parameter matrix for fractional ornstein uhlenbeck process in multidimensional setting. The next section starts with the general ornstein uhlenbeck process which has the drawback of allowing for negative values. On the simulation and estimation of the meanreverting. On parameter estimation of hidden ergodic ornstein uhlenbeck process yury a. Parameter estimation for a discrete sampling of an integrated. I discuss the estimation of the parameters, in particular the difficult of estimating the speedofmeanreversion parameter. Shen and yu obtained consistency and the asymptotic distribution of the estimator for ornstein uhlenbeck processes with. Parameter estimation for the discretely observed fractional ornstein. Parameter estimation for fractional ornsteinuhlenbeck. Although the ornstein uhlenbeck process is defined for all h. In this paper we study the parameter estimation problem for the ornstein uhlenbeck process driven by fractional brownian motion with hurst parameter h 1. For the estimation of the drift, the results are obtained only in the case when 1 2 ornstein and uhlenbeck 1930 zou process, also known as the vasicek 1977 process.
We study a least squares estimator for the ornstein uhlenbeck process, driven by fractional brownian motion bh with hurst parameter. Bias in the estimate of a mean reversion parameter for a fractional ornsteinuhlenbeck process by wai man ng a thesis presented to the university of waterloo in ful llment of the thesis requirement for the degree of master of quantitative finance waterloo, ontario, canada, 2017 c wai man ng 2017. Drift parameter estimation for fractional ornsteinuhlenbeck process of the second kind. Parameter estimation for the nonergodic ornsteinuhlenbeck. For the estimation of the drift, the results are obtained only in the case when 1 2 pdf we study the asymptotic behaviors for estimators of the parameters in the nonstationary ornstein uhlenbeck process with linear drift. It is named after leonard ornstein and george eugene uhlenbeck. Mean reverting processes are widely seen in finance.
Subdiffusive ornsteinuhlenbeck processes and applications. Parameter estimation for a bidimensional partially observed ornstein uhlenbeck process with biological application running headline. Parameter estimation for gaussian meanreverting ornstein. Simula tion and estimation of the process are already wellstudied, see iacus simulation and inference for. Recently, ricciardi and sato, 15, did a detailed study of this. The development of stochastic calculus with respect to the fgp allowed. The most popular model is the ornstein and uhlenbeck 1930 zou process, also known as the vasicek 1977 process. Parameter estimation for the discretely observed fractional ornsteinuhlenbeck process and the yuima r package. In mathematics, the ornstein uhlenbeck process is a continuoustime stochastic process defined as the solution of a special kind of stochastic differential equation, called the langevin equation. Section 3 presents consistent and asymptotically gaussian estimators. Estimation and inference in fractional ornsteinuhlenbeck. Parameter estimation for fractional ornstein uhlenbeck processes yaozhong hu.
The statistical analysis for equations driven by fractional gaussian process fgp is obviously more recent. I discuss the model briefly, including matlab code to simulate the process. In this paper, we study the case where xt is a strictly stationary ornstein uhlenbeck process. Thus in the case ornstein uhlenbeck, it is hard to estimate parameters from available data, to judge the goodness of. Javakhishvili tbilisi state university abstract an estimation procedure for ornstein uhlenbeck process drift and volatility coefficients is given.
Estimation of all parameters in the fractional ornstein. Least squares estimator for ornsteinuhlenbeck processes driven by. Maximum likelihood estimation in processes of ornstein uhlenbeck type. Javakhishvili tbilisi state university abstract an estimation procedure for ornstein uhlenbeck process. Parameter estimation for ornsteinuhlenbeck processes. Pdf we study the asymptotic behaviors for estimators of the parameters in the nonstationary ornsteinuhlenbeck process with linear drift. Pdf parameter estimation for the nonstationary ornstein. Long, ma studied parameter estimation for ornstein uhlenbeck processes driven by small levy noises for discrete observations when. Kutoyants le mans university, le mans, france abstract we consider the problem of parameter estimation for the partially observed linear stochastic di. Shen and yu obtained consistency and the asymptotic distribution of the estimator for ornstein uhlenbeck processes with small fractional levy noises. The parameter estimation theory for stochastic di erential equations drivenby brownianmotions orgenerall evy processes with nite second moments has been well developed.
Estimation and inference in fractional ornstein uhlenbeck model with discretesampled data. We prove the strong consistence of the almost surely. Drift parameter estimation for fractional ornstein. Request pdf on parameter estimation of the hidden ornsteinuhlenbeck process this paper considers parameter estimation in the. For a ornstein uhlenbeck process, the maximum likelihood parameters are the ones from least squares regression.
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