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 ultra-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 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 fastest states have the smallest price impact as measured by the volatility of price innovationsHigh frequency traders; Algorithmic trading; Durations; Hidden Markov model;

Deep Q-Learning for Nash Equilibria: Nash-DQN

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a local linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets.Comment: 16 pages, 4 figure