高频数据波动率统计推断、预测与应用

波动率统计推断与预测在投资组合分析、市场风险管理、衍生产品定价等领域具有重要应用价值，其严格数理结论的建立将丰富管理统计理论和方法。相较低频离散时间序列，高频数据因包含丰富的市场信息而为波动率的精准统计推断、预测与应用提供了数据基础。基于高频数据，本项目拟在带跳扩散过程框架下结合市场微观结构特征研究波动率的统计推断与预测的严格数理统计大样本理论，并应用于市场指数的实证分析和跨式期权复制。重点研究的数理统计问题包括：1）估计瞬时波动率的分布并进行统计推断以了解瞬时波动率的分位数等随机性特征；2）研究波动率的多元相依性和高维波动率的因子结构；3）给出波动率的日内效应（diurnal-effect）曲线的函数展开估计并检验日内效应的乘积模型（multiplicative model）；4）利用市场微观结构特征研究瞬时波动率和积分波动率的更有效估计和预测。

Statistical inference and prediction on volatility is of great importance in a broad applications, such as portfolio allocation, market risk management, derivative pricing. The establishment of theoretical results can renew the management statistics theory and method. Compared with low-frequency time series, high-frequency data contains abundant of market information and hence facilitates more accurate statistical inference and prediction of volatility. With high-frequency data and under the framework of jump-diffusion process, this project plans to give a solid mathematical statistics theory on statistical inference and prediction of the volatility by taking the market microstructure features into consideration, and then apply the theory to the empirical studies on the market indices and duplication of straddle option. The key mathematical statistics problems include: 1) estimating the distribution of spot volatility and do statistical inference to master stochastic volatility’s randomness, such as the quantiles; 2) investigating the correlation of multivariate volatility process and the factor structure of the high-dimensional volatility process; 3) estimating the diurnal effect curve using functional expansion and testing the multiplicative model of the intraday volatility; 4) providing more efficient estimator and predictor of the volatility using the market microstructure features.