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Pricing Variance Swaps Under Stochastic Volatility with an ornstein-uhlenbeck process

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Journal of Systems Science & Complexity 2015年第6期28卷 1412-1425页

作者： JIA Zhaoli BI Xiuchun ZHANG Shuguang School of Mathematics Hefei University of Technology Department of Statistics and Finance University of Science and Technology of China

Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an ornstein-uhlenbeck(OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.

关键词： Closed-form solution ornstein-uhlenbeck process stochastic volatility variance swaps

MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ornstein-uhlenbeck process

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Acta Mathematica Scientia 2010年第4期30卷 1125-1133页

作者：高付清蒋辉汪宝彬 School of Mathematics and Statistics Wuhan University Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences

We study moderate deviations for estimators of the drift parameter of the fractional ornstein-uhlenbeck process. Two moderate deviation principles are obtained.

关键词： Large deviations moderate deviations ornstein-uhlenbeck process

PARAMETER ESTIMATION FOR AN ornstein-uhlenbeck process DRIVEN BY A GENERAL GAUSSIAN NOISE

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Acta Mathematica Scientia 2021年第2期41卷 573-595页

作者： Yong CHEN Hongjuan ZHOU School of Mathematics and Statistics Jiangxi Normal UniversityNanchang 330022China School of Mathematical and Statistical Sciences Arizona State UniversityArizona 85287USA

In this paper,we consider an inference problem for an ornstein-uhlenbeck process driven by a general one-dimensional centered Gaussian process(G_(t))t≥*** second order mixed partial derivative of the covariance function R(t,s)=E[GtGs]can be decomposed into two parts,one of which coincides with that of fractional Brownian motion and the other of which is bounded by(ts)^(β-1)up to a constant *** condition is valid for a class of continuous Gaussian processes that fails to be self-similar or to have stationary increments;some examples of this include the subfractional Brownian motion and the bi-fractional Brownian *** this assumption,we study the parameter estimation for a drift parameter in the ornstein-uhlenbeck process driven by the Gaussian noise(G_(t))t≥*** the least squares estimator and the second moment estimator constructed from the continuous observations,we prove the strong consistency and the asympotic normality,and obtain the Berry-Esséen *** proof is based on the inner product's representation of the Hilbert space(h)associated with the Gaussian noise(G_(t))t≥0,and the estimation of the inner product based on the results of the Hilbert space associated with the fractional Brownian motion.

关键词： Fourth moment theorem ornstein-uhlenbeck process Gaussian process Malliavin calculus

Minimum contrast estimator for fractional ornstein-uhlenbeck processes

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Science China Mathematics 2012年第7期55卷 1497-1511页

作者： XIAOWeiLin ZHANGWeiGUO ZHANGXiLi SchoolofBusinessandAdministration SouthChinaUniversityofTechnologyGuangzhou510640China DepartmentofAccountingandFinance SchoolofManagementZh iangUniversityHangzhou310006China

This paper proposes a minimum contrast methodology to estimate the drift parameter for the ornstein-uhlenbeck process driven by fractional Brownian motion of Hurst index, which is greater than one half. Both the strong consistency and the asymptotic normality of this minimum contrast estimator are studied based on the Laplace transform. The numerical simulation results confirm the theoretical analysis and show that the minimum contrast technique is effective and efficient.

关键词： minimum contrast estimator fractional Brownian motions ornstein-uhlenbeck process strongconsistency asymptotic normality

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ornstein-uhlenbeck processES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2）：394-408）

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Acta Mathematica Scientia 2017年第4期37卷 1173-1176页

作者：申广君尹修伟闫理坦 Department of Mathematics Anhui Normal University Wuhu 241000 China Department of Mathematics Donghua University Shanghai 201620 China

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

关键词： weighted fractional Brownian motion least squares estimator ornstein-uhlenbeck process

Asymptotic Properties of Estimators for ornstein-uhlenbeck processes with Small Symmetricα-Stable Motions

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Journal of Donghua University(English Edition) 2020年第4期37卷 357-364页

作者： PAN Yurong JIA Chaoyong LIU Xiaoyan School of Science Bengbu UniversityBengbu 233030China College of Arts and Sciences University of La VerneLa Verne 91750USA

The asymptotic behaviors for estimators of the drift parameters in the ornstein-uhlenbeck process driven by small symmetricα-stable motion are studied in this *** on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the ornstein–uhlenbeck process are *** establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.

关键词： ornstein-uhlenbeck process symmetricα-stable motion conditional least squares estimator(CLSE) consistency asymptotic distribution

Global Random Attractors for the Stochastic Dissipative Zakharov Equations

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 289-304页

作者： Yan-feng GUO Bo-ling GUO Dong-long LI College of Science Guangxi University of Science and Technology Institute of Applied Physics and Computational Mathematics

The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by ornstein-uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.

关键词： stochastic dissipative Zakharov equations global random attractors ornstein-uhlenbeck process compactness

Random Attractors of Stochastic Non-Newtonian Fluids

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 165-180页

作者： Chun-xiao GUO Bo-ling GUO Yong-qian HAN Department of Mathematics China University of Mining and Technology BeijingBeijing 100083China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors AH （w） in H; Secondly, we prove the existence of random attractors Ay（w） in V. Then we verify regularity of the random attractors by showing that AH（W） = Ay（w）, which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.

关键词： random attractors non-Newtonian fluids additive noise ornstein-uhlenbeck process

Estimation for nearly unit root processes with GARCH errors

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Applied Mathematics(A Journal of Chinese Universities) 2010年第3期25卷 297-306页

作者： YUAN Yu-ze ZHANG Rong-mao Department of Mathematics, Zhejiang University, Hangzhou 310027, China Department of Mathematics Zhejiang University Hangzhou China

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.

关键词： Nearly unit root GARCH error least square estimation ornstein-uhlenbeck process empirical likelihood.