Abstract

The paper illustrates a new procedure for estimating asymmetric stochastic volatility models. These models shape the asymmetric effect of negative and positive financial returns on the expected volatility, behaviour often observed in the stock prices, and known as “leverage effect”. The procedure is based on the iterative application of the quasi-maximum likelihood (QML) method and is proposed as an alternative to the procedure presented by Harvey and Shephard in 1996 and based on the application of the QML method on a modified auxiliary model. The estimation results generally converge to constant values after a few iterations. The volatility predictor provided by the new method is conceptually similar to the EGARCH predictor and different from the predictor of the other procedure. A simulation study shows that the iterative QML method provides parameter estimators with RMSEs decreasing as series length increases. The distribution of the estimates is approximately normal, and the approximation improves as the series size increases. Empirical applications of the method provide results similar to ones of the method known in literature. However, the two methods provide two different predictors and smoothers of volatility, which should be compared on a case-by-case basis.

中文翻译：

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非对称随机波动率模型的迭代 QML 估计

摘要

本文阐述了估计非对称随机波动率模型的新程序。这些模型塑造了负财务回报和正财务回报对预期波动性的不对称影响，这种行为经常在股票价格中观察到，被称为“杠杆效应”。该过程基于准最大似然 (QML) 方法的迭代应用，并被提议作为 Harvey 和 Shephard 于 1996 年提出的过程的替代方案，并且基于 QML 方法在修改后的辅助模型上的应用。经过几次迭代后，估计结果通常会收敛到恒定值。新方法提供的波动率预测器在概念上与 EGARCH 预测器相似，但与其他过程的预测器不同。仿真研究表明，迭代 QML 方法提供的参数估计量的 RMSE 随着序列长度的增加而减小。估计值的分布近似正态，并且近似值随着序列大小的增加而改善。该方法的经验应用提供了与文献中已知的方法类似的结果。然而，这两种方法提供了两种不同的波动率预测器和平滑器，应根据具体情况进行比较。