有效价差的极大似然估计

Maximum Likelihood Estimator of Effective Spread

有效价差是刻画金融资产交易成本的一种重要度量。本文基于Roll的价格模型,利用对数价格极差分布的近似正态特征,提出了一种有效价差的近似极大似然估计,并通过数值模拟比较了这一新的估计与以往文献中提出的Roll的协方差估计、贝叶斯估计以及High-LOW估计在各种不同状况下的精度。模拟的结果表明,无论是在连续交易的理想状态还是交易不连续且价格不能被完全观测到的非理想状态下,极大似然估计和High-Low估计的精度均高于协方差和贝叶斯估计;当波动率相对较小的时候,极大似然估计的精度优于High-Low估计;另外,在非理想情形下,极大似然估计要比High-Low估计更加稳健。

Effective spread is an important measure of the transaction cost of fi- nancial asset. Based on Roll＇s price formation model, this paper puts forward a quasi maximum likelihood estimator for effective spread by approximating the dis- tribution of the logarithm of price range with a normal distribution. Monte Carlo simulation studies have been conducted to make a comparison of the accuracy be- tween the MLE and other three estimators proposed in early literature. Simulation results reveals that, both in the ideal case when the prices can be observed continu- ously and in the more realistic case when the trading is not consecutive, the MLE and High-Low estimator are more accurate than the other two estimators. If the volatility is relatively smaller than the spread, the performance of MLE will be su- perior to the High-Low method. Moreover, the MLE is obviously more robust than the High-Low estimator to the practical problems.