Determining the Volatility of a Price Process in The Presence of Rounding Errors
Determining the Volatility of a Price Process in The Presence of Rounding Errors
复制标题
确定存在舍入误差时价格过程的波动性
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
P. Mykland
中科院分区：
文献类型：
--
作者：
Yingying Li;P. Mykland
设S表示证券的价格过程，并假设S服从波动率为a2的几何布朗运动：我们考虑在离散时间点0；1=n；2=n；1是取整后的-o值S(Fi)i=n=finbSi=n=finc(i=0；研究了“已实现波动率”Vn=Pn=1(log(S(Fi)i=n)ilog(S(Fin)(Ii1)=n))2的渐近行为，它通常被用作波动率ae 2的估计量。我们证明了Vn或Scaled Vn在FIN上的不同条件下的收敛。给出了波动率的偏差修正估计量，并证明了相应的中心极限定理。仿真结果表明，统计特性的改善是显著的。
Let S denote the price process of a security, and suppose that S follow a geometric Brownian motion with volatility ae 2 : We consider the case when the observations at the discrete time points 0; 1=n; 2=n; ¢¢¢ ; 1 are the rounded-o values S (fi n) i=n = finbSi=n=finc (i = 0;¢¢¢ ;n); where fin > 0 is the round-o level corresponding to the sample frequency n. We investigate the asymptotic behavior of the “Realized Volatility” V n = Pn=1 (log(S (fi n) i=n ) i log(S (fin) (ii1)=n )) 2 , which is commonly used as an estimator of the volatility ae 2 . We prove the convergence of V n or scaled V n under dierent conditions on fin. A bias corrected estimator of the volatility is proposed and an associated central limit theorem is shown. Simulation results show that improvement in statistical properties can be substantial.