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摘要翻译：
对离散观测的Barndorff-Nielsen和Shephard模型给出了一个简单的显式估计，在方差过程平稳分布的所有矩都是有限的单一假设下，证明了严格的相合性和渐近正态性，并给出了渐近协方差矩阵的显式表达式。我们详细地发展了一个二元模型的鞅估计函数方法，它不是一个扩散，但允许跳跃。我们不使用遍历性参数。我们假设在固定宽度的离散网格上观测到对数收益和瞬时方差，且观测视界趋于无穷大。由于瞬时方差在实际中是不可观测的，我们的结果不能立即应用。我们的目的是提供一个理论分析，作为关于最优鞅估计函数的进一步发展的起点和基准，并为理论和实证研究提供一个起点和基准，以替代方差过程，如交易数量或交易量或期权数据的隐含方差。
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英文标题：
《Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen
and Shephard stochastic volatility models》
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作者：
Friedrich Hubalek and Petra Posedel
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function approach for a bivariate model, that is not a diffusion, but admits jumps. We do not use ergodicity arguments. We assume that both, logarithmic returns and instantaneous variance are observed on a discrete grid of fixed width, and the observation horizon tends to infinity. As the instantaneous variance is not observable in practice, our results cannot be applied immediately. Our purpose is to provide a theoretical analysis as a starting point and benchmark for further developments concerning optimal martingale estimating functions, and for theoretical and empirical investigations, that replace the variance process with a substitute, such as number or volume of trades or implied variance from option data.
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PDF链接：
https://arxiv.org/pdf/0807.3479
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