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on Market Microstructure |
| By: | Felix Patzelt; Jean-Philippe Bouchaud |
| Abstract: | How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price impact has a universal non-linear shape for trades aggregated on any intra-day scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order flow imbalance is not associated with large returns. To the contrary, it is observed when the price is "pinned" to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the mid-price falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intra-day scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intra-day timescales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking. |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1706.04163&r=mst |
| By: | Massil Achab; Emmanuel Bacry; Jean-Fran\c{c}ois Muzy; Marcello Rambaldi |
| Abstract: | We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics. |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1706.03411&r=mst |
| By: | S\"uhan Altay; Katia Colaneri; Zehra Eksi |
| Abstract: | We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piecewise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases. |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1706.03567&r=mst |