Parameter identification for the discretely observed geometric fractional Brownian motion

Xiao, Weilin; Zhang, Weiguo; Zhang, Xili

doi:10.1080/00949655.2013.814135

Cited by 19 publications

(18 citation statements)

References 26 publications

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“…Using that result we will show that in the diffusion driven by fBm with H < 3 4 with constant volatility, quadratic variation is asymptotically normal. For similar model and low frequency data with fixed time gap asymptotic normality for volatility estimator was obtained by Xiao et al(2013). In our paper we consider the estimator for high frequency data with time intervals decreasing to zero and show the asymptotic normality for the estimator.…”

Section: Introductionmentioning

confidence: 78%

Fractional Brownian markets with time-varying volatility and high-frequency data

Lahiri

Sen

2020

Econometrics and Statistics

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Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had been obtained by Necula (2002) under constant drift and volatility. We obtain option prices under time varying volatility model. The expression depends on volatility and the Hurst parameter in a complicated manner. We derive a central limit theorem for the quadratic variation as an estimator for volatility for both the cases, constant as well as time varying volatility. That will help us to find estimators of the option prices and to find their asymptotic distributions.

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Section: Introductionmentioning

confidence: 78%

Fractional Brownian markets with time-varying volatility and high-frequency data

Lahiri

Sen

2020

Econometrics and Statistics

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“…Moreover, in the study of Misiran et al [31], in which a general discrete-data complete maximumlikelihood-type procedure has been designed for estimating all the unknown parameters in gfBm, including the drift parameter, the diffusion coefficient and Hurst index, without the proof of asymptotic behavior. For the ground-breaking work of Xiao et al [43], all the unknown parameters of gfBm from discrete observations based on the quadratic variation and the maximum-likelihood approach have been well estimated, in particular, the asymptotic properties of the estimators have been provided in Xiao et al [43] as well. In addition, we also refer to a recent monograph, Kubilius et al [24], for a complete exposition on different approaches used in statistical inference for fractional diffusions.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for discretized geometric fractional Brownian motions with applications in Chinese financial markets

Sun

Chen

2022

Adv Cont Discr Mod

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It is widely accepted that financial data exhibit a long-memory property or a long-range dependence. In a continuous-time situation, the geometric fractional Brownian motion is an important model to characterize the long-memory property in finance. This paper thus considers the problem to estimate all unknown parameters in geometric fractional Brownian processes based on discrete observations. The estimation procedure is built upon the marriage between the bipower variation and the least-squares estimation. However, unlike the commonly used approximation of the likelihood and transition density methods, we do not require a small sampling interval. The strong consistency of these proposed estimators can be established as the sample size increases to infinity in a chosen sampling interval. A simulation study is also conducted to assess the performance of the derived method by comparing with two existing approaches proposed by Misiran et al. (International Conference on Optimization and Control 2010, pp. 573–586, 2010) and Xiao et al. (J. Stat. Comput. Simul. 85(2):269–283, 2015), respectively. Finally, we apply the proposed estimation approach in the analysis of Chinese financial markets to show the potential applications in realistic contexts.

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“…Xiao, W.G. Zhang, X. Zhang [11] (see also the references therein). If the driving process is a Lévy process, then see, for example, H. Long [5] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimations for linear parabolic fractional SPDEs with jumps

Grecksch¹,

Lisei

Lueddeckens³

2019

Stud. Univ. Babes-Bolyai Math.

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We give an unbiased and consistent estimator for the drift coefficient of a linear parabolic stochastic partial differential equation driven by a multiplicative cylindrical fractional Brownian motion with Hurst index 1/2 < h < 1 and a cylindrical centered Poisson process, if the observations of the solution process are given in discrete time points. The presented method is based on mean square estimations.

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Parameter identification for the discretely observed geometric fractional Brownian motion

Cited by 19 publications

References 26 publications

Fractional Brownian markets with time-varying volatility and high-frequency data

Fractional Brownian markets with time-varying volatility and high-frequency data

Parameter estimation for discretized geometric fractional Brownian motions with applications in Chinese financial markets

Parameter estimations for linear parabolic fractional SPDEs with jumps

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