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Statistical Methods in Financial Markets

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This dissertation focuses on applications of statistical methods in nancial markets and isdivided into three parts. The rst part proposes an accurate variable-order cumulant approximation method for Black-style shadow interest rate models respecting the zero lower bound and estimates the interest rates models on historical bond yield data using the extended Kalman Filter. The second part focuses on the problem of market making, starting with empirical tests of the recent work of Chakraborty & Kearns (2011) and propose various generalizations. The third part proposes a new method to estimate and predict adverse selection cost using book exhaustion rate (BER), tests the theoretical relationship between BER and empirical adverse selection risk, and uses reinforcement learning to show BER can signicantly improve the performance of market making.

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