146 research outputs found
Ergodic transition in a simple model of the continuous double auction
We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen
"Market making" behaviour in an order book model and its impact on the bid-ask spread
It has been suggested that marked point processes might be good candidates
for the modelling of financial high-frequency data. A special class of point
processes, Hawkes processes, has been the subject of various investigations in
the financial community. In this paper, we propose to enhance a basic
zero-intelligence order book simulator with arrival times of limit and market
orders following mutually (asymmetrically) exciting Hawkes processes. Modelling
is based on empirical observations on time intervals between orders that we
verify on several markets (equity, bond futures, index futures). We show that
this simple feature enables a much more realistic treatment of the bid-ask
spread of the simulated order book.Comment: 17 pages, 9 figure
Price dynamics in a Markovian limit order market
We propose and study a simple stochastic model for the dynamics of a limit
order book, in which arrivals of market order, limit orders and order
cancellations are described in terms of a Markovian queueing system. Through
its analytical tractability, the model allows to obtain analytical expressions
for various quantities of interest such as the distribution of the duration
between price changes, the distribution and autocorrelation of price changes,
and the probability of an upward move in the price, {\it conditional} on the
state of the order book. We study the diffusion limit of the price process and
express the volatility of price changes in terms of parameters describing the
arrival rates of buy and sell orders and cancelations. These analytical results
provide some insight into the relation between order flow and price dynamics in
order-driven markets.Comment: 18 pages, 5 figure
Reduced form modeling of limit order markets
This paper proposes a parametric approach for stochastic modeling of limit
order markets. The models are obtained by augmenting classical perfectly liquid
market models by few additional risk factors that describe liquidity properties
of the order book. The resulting models are easy to calibrate and to analyze
using standard techniques for multivariate stochastic processes. Despite their
simplicity, the models are able to capture several properties that have been
found in microstructural analysis of limit order markets. Calibration of a
continuous-time three-factor model to Copenhagen Stock Exchange data exhibits
e.g.\ mean reversion in liquidity as well as the so called crowding out effect
which influences subsequent mid-price moves. Our dynamic models are well suited
also for analyzing market resiliency after liquidity shocks
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