摘要：We review a recently proposed general partially-observed framework of Markov processes with marked point process observations for financial ultra-high frequency (UHF) data, and the related Bayes estimation via filtering equation (BEFE), a stochastic PDE approach. In this paper, we show how the BEFE through explicit recursive algorithms becomes bottlenecked when the tick size is reduced from $\$1/8$ to $\$1/100$, and we develop the BEFE through implicit recursive algorithms, greatly improving the computational efficiency. We demonstrate the substantial computation gained in implementing real-time BEFE for an illustrating but practical model using simulated data. The new implicit recursive algorithm is applied to a real stock price UHF data set, and is capable of producing real time Bayes parameter estimates of the model.
关键词：Bayes estimation; implicit methods; marked point process; market microstructure noise; Markov chain approximation method; nonlinear filtering; partially observed model; ultra-high frequency data
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