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Full-Text Articles in Physical Sciences and Mathematics
Bayesian Posterior Inference And Lan For L̩Vy Models Under High-Frequency Data, Qi Wang
Bayesian Posterior Inference And Lan For L̩Vy Models Under High-Frequency Data, Qi Wang
Arts & Sciences Electronic Theses and Dissertations
Parameter estimation and inference for L̩vy models under high-frequency data has been an exciting and important task in the field of financial mathematics and has been found practically useful when analyzing real financial data. One feature of L̩vy models is the allowance of jumps to model the abrupt changes sometimes observed in the market. In this thesis, we discuss some problems related to the statistical inference of L̩vy models based on high-frequency data emphasizing on the presence of the jumps. The first problem we consider focuses on the estimation of the volatility, which is critical to measure and control the …
Spot Volatility Estimation Of Ito Semimartingales Using Delta Sequences, Weixuan Gao
Spot Volatility Estimation Of Ito Semimartingales Using Delta Sequences, Weixuan Gao
Arts & Sciences Electronic Theses and Dissertations
This thesis studies a unifying class of nonparametric spot volatility estimators proposed by Mancini et. al.(2013). This method is based on delta sequences and is conceived to include many of the existing estimators in the field as special cases. The thesis first surveys the asymptotic theory of the proposed estimators under an infill asymptotic scheme and fixed time horizon, when the state variable follows a Brownian semimartingale. Then, some extensions to include jumps and financial microstructure noise in the observed price process are also presented. The main goal of the thesis is to assess the suitability of the proposed methods …