Abstract
Recent research on the response of stock prices to trading activity revealed long-lasting effects, even across stocks of different companies. These results imply non-Markovian effects in price formation and when trading many stocks at the same time, in particular trading costs and price correlations. How the price response is measured depends on data set and research focus. However, it is important to clarify how the details of the price response definition modify the results. Here, we evaluate different price response implementations for the Trades and Quotes (TAQ) data set from the NASDAQ stock market and find that the results are qualitatively the same for two different definitions of time scale, but the response can vary by up to a factor of two. Furthermore, we show the key importance of the order between trade signs and returns, displaying the changes in the signal strength. Moreover, we confirm the dominating contribution of immediate price response directly after a trade, as we find that delayed responses are suppressed. Finally, we test the impact of the spread in the price response, detecting that large spreads have stronger impact.
Highlights
While the definition of complexity varies, it is widely agreed upon that a system is referred to as complex if it, first, consists of a large number of interacting agents or constituents, respectively, second, is nonstationary, i.e., cannot be described by standard equilibrium approaches, and, third, its interactions are typically not captured by microscopic governing equations, rather, by statistical rules
We evaluate different price response implementations for the Trades and Quotes (TAQ) data set from the NASDAQ stock market and find that the results are qualitatively the same for two different definitions of time scale, but the response can vary by up to a factor of two
We select the last midpoint price of every second and compute them. We use this strategy with the TAQ data set considering that the price response in trade time scale cannot be directly compared with the price response in physical time scale
Summary
While the definition of complexity varies, it is widely agreed upon that a system is referred to as complex if it, first, consists of a large number of interacting agents or constituents, respectively, second, is nonstationary, i.e., cannot be described by standard equilibrium approaches, and, third, its interactions are typically not captured by microscopic governing equations, rather, by statistical rules. The present interdisciplinary contribution studies financial markets, and it is put forward in the proven physics spirit: first, that every quantity which is used has to be a measurable observable; second, that the results given are quantitative and statistically sound; and third, that the methods are carefully and critically checked and verified. In view of an increasing interest in the analysis of response functions, we feel that this is a rewarding effort. It helps to answer the highly relevant question of the extent to which financial markets deviate from the largely Markovian behavior. It is supposed that their actions are interpreted by other agents as potentially containing some information [5,7,35,44] In both cases, the outcome is the same, and the prices follow a random walk. In Ref. [29], it is found that the impact of small trades on the price is, in relative terms, much larger than that of large trades and the impact of trading on the price is quasi-permanent
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