An Analysis of the Financial Market Volatility via Nonlinear Time Series Models

本研究基于离散时间随机过程和连续时间随机过程的弱收敛理论，对金融市场波动的时间序列行为进行了实证研究，发展了标准GARCH(1，1)模型的各种扩展，包括具有神经网络型灵活条件方差函数的非线性模型，并将其应用于包括发达市场和新兴市场在内的主要股市指数的每日数据。得到的经验结果表明，对于大多数指数而言，波动率相对于当前波动率水平的弹性比以前认为的要高得多，这意味着金融市场的波动性对冲击的反应非常迅速。这一发现对风险管理、衍生品定价和对冲以及货币政策具有重要影响。在项目的第二部分，ARFIMA-GARCH模型被应用于所谓的每日已实现波动率(RV)，该波动率由日经225指数5分钟高频回报的平方每日总和构成。与现有文献一致的是，日经225房车具有高度可预测性和长记忆性，这意味着其自相关性衰减非常缓慢。ARFIMA GARCH模型的GARCH分量表明，波动率的波动性，更具体地说，日经225房车的条件方差，是随时间随机变化的，其分量在某种程度上是可预测的。研究了RV的连续样本路径变化分量，该分量在指标值中不存在大跳跃的贡献。其结果与标准房车的结果相似。

This research project empirically investigates the time series behavior of financial market volatility Based on the weak convergence theory that approximately links discrete-time and continuous-time stochastic processes, various extensions of the standard GARCH(1,1) model, including nonlinear models with flexible conditional variance functions of a neural network type, are newly developed and applied to daily data of major stock market indices including both developed markets and emerging markets. The obtained empirical results indicate that the elasticity of volatility of volatility with respect to the current level of volatility is much higher than previously believed for most indices, implying that financial market volatility increases very rapidly in response to shocks. This finding has important implications for risk management, derivatives pricing and hedging, and monetary policy. In the second part of the project, the ARFIMA-GARCH model is applied to the so-called daily realized volatility (RV) constructed as a daily sum of squared five-minute high-frequency returns on the Nikkei 225 stock market index. Consistent with the extant literature, it is found that the Nikkei 225 RV is highly predictable with a long-memory property, meaning that its autocorrelations decay very slowly. The GARCH component of the ARFIMA GARCH model reveals that the volatility of volatility, more specifically the conditional variance of the Nikkei 225 RV, is stochastically changing through time with a component that is to some extent predictable. The continuous sample path variation component of the RV, which is free of the contributions of large jumps in the index value, is also studied. The results are similar to those for the standard RV.