Patience vs. impatience of traders: Formation of the value-at-price distribution through competition for liquidity

Abstract

An ability to postpone one's execution without much penalty provides an important strategic advantage in high-frequency trading. To quantify competition between traders one has to resort to a consistent 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 my modification of the Foucault, Kadan and Kandel dynamic Limit Order Book (LOB) model.My modification 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.Keywords: Limit order book (LOB), Foucault, Kadan and Kandel model, bid-ask spread, market microstructure. JEL: G14, G12, C63.

Fourier Integral Operator Model of Market Liquidity: The Chinese Experience 2009–2010

“…Many semi-empirical measures have been used to describe market behavior on a microstructure level [11]. The most popular or theoretically well-researched are the ones called VPIN (Volume-Synchronized Probability of Informed Trading [12], volume imbalances [13][14][15], VWAP and its modifications (Volume at Weighted Average Price, [16][17][18][19]), and all the different versions of Amihud measure [20,21]. Note that VPIN or VWAP measures do not distinguish particular stocks, placing them in uniform price buckets.…”