Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling
提出一个离散时间简化模型，通过引入持久杠杆效应显著改进标普500波动率预测，并估计能复制这些特征的连续时间随机波动率模型，发现多因子马尔可夫模型优于单因子分数布朗运动模型。
We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly.We then estimate continuous-time stochastic volatility models that are able to reproduce the statistical features captured by the discrete-time model.We show that a single-factormodel driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multifactor Markovian model fully replicates the persistence of both volatility and leverage effect. The impact of jumps can be associated with a common jump component in price and volatility. This article has online supplementary materials. © 2012 American Statistical Association.