Estimation of the instantaneous volatility

被引：2
|
作者：
Alexander Alvarez
Fabien Panloup
Monique Pontier
Nicolas Savy
机构：
[1] La Habana University,
[2] Institut de Mathématiques de Toulouse et INSA Toulouse,undefined
[3] Institut de Mathétiques de Toulouse et Université de Toulouse,undefined
来源：
Statistical Inference for Stochastic Processes | 2012年 / 15卷 / 1期
关键词：
Central limit theorem; Power variation; Semimartingale; Primary 60F05; Secondary 91B70; 91B82;
D O I：
10.1007/s11203-011-9062-2
中图分类号：
学科分类号：
摘要：
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: dXt =  atdt + σtdWt, where X denotes the log-price and σ is a càdlàg 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 power variations of the log-price. We provide central limit theorems with an optimal rate depending on the local behavior of σ. In particular, these theorems yield some confidence intervals for σt.
引用
收藏
页码：27 / 59
页数：32
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