Modeling Asset Prices for Algorithmic and High Frequency Trading

Algorithmic Trading (AT) and High Frequency (HF) trading, which are responsible for over 70\% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this paper we employ a hidden Markov model to examine how the intra-day dynamics of the stock market have changed, and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit-orders to profit from the bid-ask spread and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intra-day states with shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with shortest average durations. Moreover, in 2008 the states with shortest durations have the smallest price impact as measured by the volatility of price innovations