关键词: 高频波动率矩阵模型, 网络关联性, 结构性降维, 波动溢出效应

Abstract:

Volatility matrix is the basis and core of quantitative analysis of many high-dimensional financial activities. Multivariate volatility models mainly include multivariate GARCH model， high-frequency volatility matrix model and network volatility model. There are three main difficulties in their modeling process， including the problem of dimensional disaster， meeting the requirements of the mathematical and empirical characteristics of volatility matrix， and the model has a certain economic interpretation. In order to alleviate these three kinds of problems， the integration of two kinds of modeling ideas is realized by utilizing the advantages of high frequency volatility model， which contains rich volatility information and flexible modeling， and the advantages of network volatility model， which has economic significance. Based on the traditional high-frequency CAW model， the conduction structure is presupposed between fluctuations by introducing positive and negative correlation networks with the characteristics of risk accumulation and risk dispersion， and further a two-layer network volatility matrix model （DNVM model） is established based on the heterogeneous market hypothesis. Under this framework， the network effects and spillover effects of asset volatility conduction along different network paths are derived. The model in this paper realizes the structural dimension reduction of parameters and the improvement of the economic significance of the model.The empirical research based on the 50 constituent stocks of Shanghai Stock Exchange in China shows that the correlation between assets is heterogeneous in time dimension， and there is significant positive and negative asymmetry in cross section. The volatility transmission between assets has a significant network effect， and the network effect is stronger in the short term than in the medium and long term. The short-term volatility spillover effect between assets is stronger than that in the medium and long term， and the positive volatility spillover effect is stronger than the negative volatility spillover effect on the whole， and the short-term positive volatility spillover plays a dominant role. Both the statistical prediction effect and the minimum variance portfolio strategy show that the DNVM model is better than the non-network high frequency model and the low frequency multivariate GARCH model such as BEKK model. DNVM model provides a new guidance and research method for the study of high-dimensional volatility matrix prediction of financial market， and also provides a new perspective for the expansion of traditional network econometric model based on vector data to matrix data.

Key words: high-frequency multivariate volatility matrix, network relevance, structural dimension reduction, volatility spillover effect