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  • March 20, 2019
  • Liu, Yunxiao
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
  • With the advent of intraday high-frequency data of financial assets since the late 1990s, the research of financial econometrics has entered into a "big data" era. New theoretical techniques using the theory of continuous time stochastic processes has been extensively developed, and new empirical evidence has been documented. In particular, due to its far-reaching applications in various fields such as risk management and option pricing, the study of volatility, which quantitatively measures the uncertainty of prices of financial assets, has drawn substantial attention from researchers and there has been a large amount of literature devoted to this topic, including both modelling and prediction. In this dissertation, we are firstly concerned with the statistical inference of the so-called integrated volatility functionals, which is a general class of quantities that are computed from volatility. Secondly, we also devise a simulation method to recover the probability distribution of prices of financial assets by taking advantage of the information contained in sampled price data. Accordingly, the dissertation consists of two parts. In the first part, we focus on the estimation of integrated volatility functionals, where the volatility process is assumed to be a long memory Ito semimartingale (LMIS), which is defined as the sum of an Ito semimartingale and a process satisfying certain regularity assumptions that in particular is able to capture the long memory property of financial volatility that has been vastly documented in literature. We provide central limit theorem (CLT) in such context. Furthermore, under the such LMIS assumption, we consider both parametric and nonparametric bootstrap inference methods of integrated volatility functionals, and we show the validity of both bootstrap methods by providing CLTs. Furthermore, with the usual assumption of volatility being Ito semimartingale, we consider an empirical-process form of integrated volatility functionals, and offer functional CLTs when the indexing parameter is of arbitrary finite dimensions. We also consider bootstrap inference in this empirical-process setting. In the second part, we consider Euler method with estimated spot volatility, from which we are able to regenerate and realize the stochastic dynamics of price of financial asset by taking advantage of the information contained in the observed prices. We provide both theoretical foundation and empirical application of this method.
Date of publication
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Rights statement
  • In Copyright
  • Budhiraja, Amarjit
  • Tauchen, George
  • Bhamidi, Shankar
  • Pipiras, Vladas
  • Ji, Chuanshu
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2017

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