scholarly journals A MATHEMATICAL APPROACH TO ORDER BOOK MODELING

2013 ◽  
Vol 16 (05) ◽  
pp. 1350025 ◽  
Author(s):  
FRÉDÉRIC ABERGEL ◽  
AYMEN JEDIDI
Keyword(s):  
Exponential Convergence ◽  
Agent Based Modeling ◽  
Price Formation ◽  
Order Book ◽  
Continuous Time Markov Chain ◽  
Mathematical Study ◽  
Microscopic Description ◽  
Arrival Times ◽  
Agent Based ◽  
Functional Central Limit

Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data.

scholarly journals Investor Sentiment in an Artificial Limit Order Market

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lijian Wei ◽  
Lei Shi
Keyword(s):  
Regime Switching ◽  
Trading Volume ◽  
Bayesian Learning ◽  
Investor Sentiment ◽  
Agent Based Modeling ◽  
Order Book ◽  
Limit Order ◽  
Agent Based ◽  
Bid Ask Spread ◽  
Limit Order Market

This paper examines the under/overreaction effect driven by sentiment belief in an artificial limit order market when agents are risk averse and arrive in the market with different time horizons. We employ agent-based modeling to build up an artificial stock market with order book and model a type of sentiment belief display over/underreaction by following a Bayesian learning scheme with a Markov regime switching between conservative bias and representative bias. Simulations show that when compared with classic noise belief without learning, sentiment belief gives rise to short-term intraday return predictability. In particular, under/overreaction trading strategies are profitable under sentiment beliefs, but not under noise belief. Moreover, we find that sentiment belief leads to significantly lower volatility, lower bid-ask spread, and larger order book depth near the best quotes but lower trading volume when compared with noise belief.

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