A closed-form solution for the stochastic volatility model with applications on international stock markets
提出随机波动率模型的闭式估计量，无需数值优化或初始值，易于实现；结合新拉普拉斯近似的极大似然估计（MLE-C）优于MCMC等方法，实证表明该模型在拟合和预测上普遍胜过GARCH模型，并有效描述尾部风险。
This paper proposes a closed-form estimator for the stochastic volatility (SV) model. Compared to the usual maximum likelihood estimation (MLE), which is difficult to perform without appropriate approximations, the proposed method can be easily implemented and does not require the use of any numerical optimizer or starting values for iterations. Moreover, closed-form estimates can be supplied as initial values to MLE, for instance, conducted with a novel Laplace approximation. Denoted by MLE-C, this method consistently outperforms other estimators including the Markov chain Monte Carlo (MCMC). This is confirmed with simulation studies consisting of various combinations of true parameters and sample sizes. Our empirical data include daily returns of S&P 500, Nikkei 225 and DAX 100 over 2011–2020. The SV model estimated by MLE-C almost uniformly beats the popular GARCH counterparty, based on both the in-sample fit and out-of-sample forecasting criteria. Value-at-Risk analyses further demonstrate the capability of the SV model to accurately describe the tail behaviors of negative returns.