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Risk Evaluation and Portfolio Allocation in the Context of High Frequency Trading
High frequency trading of financial assets such as stocks and commodities are transactions that may occur a few seconds apart. Trading at this scale requires not only sophisticated technology to extract and process real time information, but also sophisticated mathematical and statistical tools for risk management. In this particular context, observed trades for a set of assets do not take place all at the same time, i.e. the trades are not synchronized and therefore, the volatility or covariance estimation becomes very challenging. In this dissertation, the first article surveys the literature of different synchronization methods and covariance estimators used in high frequency trading. The common criticism of commonly used synchronization methods is that they discard many observations. Therefore, the second article of this dissertation suggests a synchronization method, called the pseudo-refresh method that does not discard any observations, provides a better convergence rate of the most current covariance estimator called the Two Scales Covariance (Fan, Li, & Yu, 2012), and provides a portfolio risk closer to the true portfolio risk. Unfortunately, the TSCV produces non positive definite matrices. In article 3, we prove that forcing non positive definite matrices to be positive definite has negative consequences on estimating the true portfolio risk. We suggest a restricted TSCV risk estimator by insuring positive definite covariance matrices. However that risk is not unbiased and an expression of that bias is proposed, resulting in a corrected portfolio risk estimator which is unbiased and based on positive definite covariance matrices.
Nzouda, Cyrille, "Risk Evaluation and Portfolio Allocation in the Context of High Frequency Trading" (2017). ETD collection for University of Nebraska - Lincoln. AAI10266503.