INVESTOR'S SENTIMENT IN MULTI-AGENT MODEL OF THE CONTINUOUS DOUBLE AUCTION

Alexander Lykov (), Stepan Muzychka () and Kirill Vaninsky
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Alexander Lykov: Faculty of Mathematics and Mechanics, Moscow State University, Vorobjevy Gory 1, Moscow, Russian Federation
Stepan Muzychka: Faculty of Mathematics and Mechanics, Moscow State University, Vorobjevy Gory 1, Moscow, Russian Federation
Kirill Vaninsky: Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 06, 1-29

Abstract: We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behavior of the market when new information affecting the market arrives. The novel feature of the model is two additional slow changing parameters, the so-called sentiment functions. These sentiment functions measure the conception of the fair price of two groups of investors, namely, bulls and bears.Our model specifies differential equations for the time evolution of sentiment functions and constitutes a nonlinear Markov process which exhibits long-term correlations. We explain the intuition behind equations for sentiment functions and present numerical simulations which show that the behavior of our model is similar to the behavior of the real market. We also obtain a diffusion limit of the model, the Ornstein–Uhlenbeck type process with variable volatility. The volatility is proportional to the difference of opinions of bulls and bears about the fair price of a security.

Keywords: Behavioral finance; continuous double auction; diffusion with variable volatility (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219024916500400

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