Abstract
We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent 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.
Highlights
The continuous double auction is the trading system used by most regulated equity markets
When the rate of market orders is larger than the rate of limit orders, the number of orders in the book remains finite and prices are free to fluctuate over the whole available range
In this paper we have shown that a symmetric continuous double auction model has three regimes depending on the value of the parameter r
Summary
The continuous double auction is the trading system used by most regulated equity markets. A market order may take place, when a trader accepts a best bid or best ask price from the book, and the i-th trade occurs at the epoch ti. We shall further assume that limit ask orders are uniformly placed in the price classes from pbz to pbzn, where pb is the class of the current best bids. The trade price process P(t) is a continuous-time random walk that we wish to characterize as Cont and de Larrard did in Sections 3 and 4 of [9] They considered fixed bid-ask spread equal to one tick, whereas in our case the bid-ask spread is a random variable. It turns out that the behaviour of Ri crucially depends on the presence or absence of statistical equilibrium in the supply mechanism
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