Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has G...Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.展开更多
This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized var...This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized variance is a consistent estimator of quadratic variation under mild regularity conditions.Other variation concepts,such as power variation and bipower variation,are useful and important for analyzing high frequency data when jumps are present.High frequency data can also be used to test jumps in asset prices.We discuss three jump tests:bipower variation test,power variation test,and variance swap test in this study.The presence of market microstructure noise complicates the analysis of high frequency data.The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise.Finally,some applications of jump tests in asset pricing are discussed in this article.展开更多
基金Supported by ZJNSF(Grant No.LY20A010020)NSFC(Grant No.11671115)。
文摘Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.
文摘This study examines the use of high frequency data in finance,including volatility estimation and jump tests.High frequency data allows the construction of model-free volatility measures for asset returns.Realized variance is a consistent estimator of quadratic variation under mild regularity conditions.Other variation concepts,such as power variation and bipower variation,are useful and important for analyzing high frequency data when jumps are present.High frequency data can also be used to test jumps in asset prices.We discuss three jump tests:bipower variation test,power variation test,and variance swap test in this study.The presence of market microstructure noise complicates the analysis of high frequency data.The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise.Finally,some applications of jump tests in asset pricing are discussed in this article.
