Asymptotic expansion for Barndorff-Nielsen and Shephard ’ s stochastic volatility model $
Asymptotic expansion for Barndorff-Nielsen and Shephard ’ s stochastic volatility model $
复制标题
Barndorff-Nielsen 和 Shephard 随机波动率模型的渐近展开 $
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
N. Yoshidab
中科院分区：
文献类型：
--
作者：
H. Masudaa;N. Yoshidab
利用混合过程渐近展开的一般方法，得到了Barndorff-Nielsen和Shephard随机波动率模型中股票价格对数收益率的Edgeworth展开式，其中潜在波动率过程是一个平稳的非高斯Ornstein-Uhlenbeck过程（R过程）在R上具有不变的自分解分布：目前的结果使我们能够同时解释非高斯短时间滞后以及近似高斯长时间滞后。由Bichteler，Gravereaux和Jacod为带跳过程所建立的Malliavin演算和带跳过程的指数混合性质在保证条件型Cramér条件下的截断中起着重要的作用。由于双曲过程的一些固有性质，展开式的正则性条件可以毫无困难地被验证，并且可以显式地计算直到任何阶的展开式的系数。r 2005 Elsevier B. V.保留所有权利。
With the help of a general methodology of asymptotic expansions for mixing processes, we obtain the Edgeworth expansion for log-returns of a stock price process in Barndorff-Nielsen and Shephard’s stochastic volatility model, in which the latent volatility process is described by a stationary non-Gaussian Ornstein–Uhlenbeck process (OU process) with invariant selfdecomposable distribution on Rþ: The present result enables us to simultaneously explain non-Gaussianity for short time-lags as well as approximate Gaussianity for long time-lags. The Malliavin calculus formulated by Bichteler, Gravereaux and Jacod for processes with jumps and the exponential mixing property of the OU process play substantial roles in order to ensure a conditional type Cramér condition under a certain truncation. Owing to several inherent properties of OU processes, the regularity conditions for the expansions can be verified without any difficulty, and the coefficients of the expansions up to any order can be explicitly computed. r 2005 Elsevier B.V. All rights reserved.