微观结构噪声下高频金融时间序列Lévy跳跃的非参数统计推断与应用研究

Asset prices we observe in the financial markets combine two unobservable components: equilibrium prices and market microstructure noise. The objective of this proposal is to develop nonparametric statistic inference for Levy jump in semimartingales sampled at high frequency, which are contaminated by a market microstructure noise.Firstly, based on the theory of financial engineering and financial econometrics, we study how to tell apart large shifts in underlying equilibrium prices from noise using high frequency financial time series, and measure the precise level of noise, so we can evaluate the complete situation of the financial market. Then, we will propose a robust test for jump and estimation of Levy measure by nonparametric methods for the presence of market microstructure noise in high frequency financial time series, based on the pre-averaging method. So we will know what are some of the finer characteristics of the jump components, such as the degree of activity of jumps, whether they have finite or infinite activity, etc.Finally, based on a comprehensive study of noise, stochastic volatility, levy measure, jump activity index，time-varying intensity of levy jump etc, we then examine whether these factors can uncover the information shocks, premium of different risk factor such as liquidity etc.The research will not only promote the corresponding methods of the test for jump and the estimation for Levy jump, but also have theoretical and practical value.

通常我们观测到的金融资产价格由未观测的均衡价格和微观结构噪音组成。本项目将金融工程原理和金融计量经济学方法相结合，引入高频和超高频数据，研究如何对市场噪音水平进行准确的度量与估计，以评价市场的运行状况，并在此基础上还原市场的真实面貌。在微观结构噪音下，基于非参数方法，建立对噪音稳健的高频金融时间序列Levy跳跃检测方法。这种检测方法不仅能识别有限活动大跳跃，同时能识别无限活动小跳跃。在微观结构噪音下，建立对噪音稳健的Lévy跳跃非参数估计方法，以便更精确反映金融资产价格的Lévy跳跃特征和行为。通过对高频金融时间序列微观结构噪音、随机波动、Levy跳跃密度、跳跃活动指数、时变Levy跳跃强度和流动性研究，揭示这些变量所反映的关于金融资产的信息冲击、不同风险因子的风险溢价、风险市场价格等方面信息。研究成果不仅会推动Levy跳跃检验和参数估计的相关方法，而且具有重要的理论和实际应用价值。

通常我们观测到的金融资产价格由未观测的均衡价格和微观结构噪音组成。本项目将金融工程原理和金融计量经济学方法相结合，引入高频和超高频数据，研究如何对市场噪音水平进行准确的度量与估计，以评价市场的运行状况，并在此基础上还原市场的真实面貌。在微观结构噪音下，基于非参数方法，建立对噪音稳健的高频金融时间序列Levy 跳跃检测方法。这种检测方法不仅能识别有限活动大跳跃，同时能识别无限活动小跳跃。在微观结构噪音下，建立对噪音稳健的Lévy 跳跃非参数估计方法，以便更精确反映金融资产价格的Lévy 跳跃特征和行为。通过对高频金融时间序列微观结构噪音、随机波动、Levy 跳跃密度、跳跃活动指数、时变Levy 跳跃强度和流动性研究，揭示这些变量所反映的关于金融资产的信息冲击、不同风险因子的风险溢价、风险市场价格等方面信息。研究成果不仅会改进Levy 跳跃检验和参数估计的相关理论和方法，而且具有重要的理论和实际应用价值。