Patience vs. Impatience of Traders : Formation of the Value-at-Price Distribution Through Competition for Liquidity

An ability to postpone one's execution without penalty provides an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution price from market expectations and quotes. This theory was provided in 2005 by Foucault, Kadan and Kandel. I derive asymptotic distribution of the bids/offers as a function of the ratio of patient and impatient traders using the dynamic version of the Foucault, Kadan and Kandel dynamic Limit Order Book (LOB) model. Dynamic version of the LOB model allows stylized but sufficiently realistic representation of the trading markets. In particular, dynamic LOB allows simulation of the distribution of execution times and spreads from high-frequency quotes. Significant analytic progress is made towards understanding of trading as competition for immediacy of execution between traders. The results are qualitatively compared with empirical volume-at-price distribution of highly liquid stocks