Filtering with Counting Process Observations and Other Factors: Applications to Bond Price Tick Data

Abstract

In this paper, we propose an extended filtering micromovement model. The model captures the two main stylized facts of the bond price tick data: random trading times and trading noises. In the intrinsic value process for the transaction price of 5-year U.S. Treasury note, we extend the volatility part by adding the buyer-seller initiation dummy. For the extended model, we present the normalized and un-normalized filtering equations, a robustness theorem and the consistency of Bayes estimates. Based on the robustness theorem, we employ the Markov chain approximation method to construct a robust recursive algorithm for computing the posteriors and Bayes estimates. We present a Monte Carlo example to demonstrate that the computed Bayes estimates converge to their true values. The algorithm is applied to one and an half month of intraday transaction prices of 5-year Treasury notes. Bayes estimates are obtained. Especially, the sign of the buyer-seller initiation dummy is significantly negative, supporting that the inventory theory dominates in the bond trading. Read More: http://www.worldscientific.com/doi/abs/10.1142/9789814355711_0006