Ergodic transition in a simple model of the continuous double auction
Tijana Radivojević1, Jonatha Anselmi1, Enrico Scalas2
1BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.
Plos One
|February 22, 2014
Summary
This study models the continuous double auction using M/M/1 queues, revealing three distinct price and return behaviors. Ergodic conditions lead to unstable prices and heteroskedastic returns, while non-ergodicity offers price stability.
Area of Science:
- Quantitative Finance
- Market Microstructure
- Stochastic Processes
Background:
- The continuous double auction is a fundamental trading mechanism.
- Understanding price dynamics and return behavior is crucial for market analysis.
- Previous models often simplify the aggregate order process.
Purpose of the Study:
- To develop a phenomenological model for the continuous double auction.
- To analyze the conditions for ergodicity in this auction model.
- To identify and characterize different regimes of price and return behavior.
Main Methods:
- Modeling the aggregate order process as two independent M/M/1 queues.
- Defining the continuous double auction as a continuous-time random walk for trade prices.
- Deriving conditions for the ergodicity of the auction process.
Main Results:
- Identified three distinct regimes governing prices and logarithmic returns.
- In the ergodic regime, prices exhibit instability and logarithmic returns show heteroskedasticity.
- Non-ergodicity leads to price stability, with two observable sub-regimes.
Conclusions:
- The model provides insights into the complex behavior of prices in continuous double auctions.
- Ergodicity is a key factor determining price stability and return characteristics.
- The findings have implications for understanding market dynamics and risk management.
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