摘要翻译:
本文讨论了一类随机波动率模型中波动率过程的估计问题:$dx_t=a_tdt+\sigma_tdw_t$,其中$x$表示对数价格,$sigma$是C\`adl\`ag半鞅。在最近关于累积波动率估计的一系列工作的精神下,我们在这里集中讨论瞬时波动率,对此我们研究建立在对数价格的textit{power variations}的有限差分上的估计量。我们给出了中心极限定理,其最优速率依赖于$\sigma$的局部行为。特别地,这些定理给出了$\sigma_t$的一些置信区间。
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英文标题:
《Estimation of the instantaneous volatility》
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作者:
A. Alvarez, F. Panloup, M. Pontier, N. Savy
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最新提交年份:
2010
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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:
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: $dX_t=a_tdt+\sigma_tdW_t$, where $X$ denotes the log-price and $\sigma$ is a c\`adl\`ag semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus on the instantaneous volatility for which we study estimators built as finite differences of the \textit{power variations} of the log-price. We provide central limit theorems with an optimal rate depending on the local behavior of $\sigma$. In particular, these theorems yield some confidence intervals for $\sigma_t$.
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PDF链接:
https://arxiv.org/pdf/0812.3538