积分波动率二阶变差估计量分析:鞍点算法

Analysis of Variational Estimator for Integrated Volatility:Saddlepoint Algorithm

本文利用鞍点逼近方法对Black-Scholes模型的积分波动率的二阶变差估计量的估计误差进行分析,得到了相对于中心极限定理更为精细的结果,并且给出了逼近的鞍点算法。结果表明鞍点逼近是中心极限定理的纠正。模拟结果表明鞍点算法给出的估计误差分布相对于正态逼近更合理。该结果在对积分波动率进行统计假设检验时是有意义的。

This paper analyzes the estimation error of the variational estimator for integrated volatility of the Black-Scholes model by using saddlepoint approximation method. A much more accurate result compared with central limit theorem is established, and the saddlepoint algorithm is presented. It turns out that saddlepoint approximation is a correction of normal approximation. Simulation provides evidence of more rationality of the estimation error distribution calculated by saddlepoint algorithm. This is of significance in statistical test for integrated volatility.