%0 Book Section %1 statphys23_0931 %A Kenta, K.Y. %A Hideki, H.T. %A Misako, M.T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K artificial brownian dynamics market motion statphys23 threshold topic-11 %T A minimal stochastic dealer model of financial markets %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=931 %X Just like Boltzmann's ideal gas model that reproduces basic properties of real gas, we expect that we can construct a minimal dealer model reproducing most of the empirical laws of market fluctuations. This approach is promising as we have already introduced a deterministic dealer model with threshold dynamics that satisfies major known empirical laws 1. In this paper we introduce a set of stochastic version of dealer models with threshold dynamics and report their validity. In the first stochastic model we consider two dealers whose bid and ask prices move randomly in each time step keeping each dealer’s spread constant. This diffusion effect spontaneously causes transaction as depicted in Fig.1. Namely, They move their prices either up or down with probability 1/2. In the left figure the dealers’ bid and ask prices are different and no transaction occurs. In the right figure the left dealer’s ask price and the right dealer’s bid price take the same value and a transaction is taking place.Analyzing this simple model we can show that transaction intervals follow a discrete Poisson process and the price changes follow an independent symmetric exponential distribution. When the number of dealers is more than three we have a negative value in the autocorrelation function of price change at time difference 1 tick, that is consistent with the real market’s autocorrelation. This result implies that a kind of attractive potential force appears in the market in view of the market potential theory developed by Misako Takayasu et al 2. In order to make the price change distribution to follow a power law like real markets we introduce a trend-follow effect. We assume that each dealer adds a term proportional to the past market price change to his bid and ask prices. This is a kind of indirect interaction among dealers through the market and we can reproduce most of market potentials by chaging dealers' trend follow effect. 1) Kenta Yamada, Hideki Takayasu, Misako Takayasu, Physica A, to appear.\\ 2) Misako Takayasu, Takayuki Mizuno and Hideki Takayasu, Physica A \bf 370 (2006), 91-97.

@incollection{statphys23_0931, abstract = {Just like Boltzmann's ideal gas model that reproduces basic properties of real gas, we expect that we can construct a minimal dealer model reproducing most of the empirical laws of market fluctuations. This approach is promising as we have already introduced a deterministic dealer model with threshold dynamics that satisfies major known empirical laws [1]. In this paper we introduce a set of stochastic version of dealer models with threshold dynamics and report their validity. In the first stochastic model we consider two dealers whose bid and ask prices move randomly in each time step keeping each dealer’s spread constant. This diffusion effect spontaneously causes transaction as depicted in Fig.1. Namely, They move their prices either up or down with probability 1/2. In the left figure the dealers’ bid and ask prices are different and no transaction occurs. In the right figure the left dealer’s ask price and the right dealer’s bid price take the same value and a transaction is taking place.Analyzing this simple model we can show that transaction intervals follow a discrete Poisson process and the price changes follow an independent symmetric exponential distribution. When the number of dealers is more than three we have a negative value in the autocorrelation function of price change at time difference 1 tick, that is consistent with the real market’s autocorrelation. This result implies that a kind of attractive potential force appears in the market in view of the market potential theory developed by Misako Takayasu et al [2]. In order to make the price change distribution to follow a power law like real markets we introduce a trend-follow effect. We assume that each dealer adds a term proportional to the past market price change to his bid and ask prices. This is a kind of indirect interaction among dealers through the market and we can reproduce most of market potentials by chaging dealers' trend follow effect. 1) Kenta Yamada, Hideki Takayasu, Misako Takayasu, Physica A, to appear.\\ 2) Misako Takayasu, Takayuki Mizuno and Hideki Takayasu, Physica A {\bf 370} (2006), 91-97.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Kenta, K.Y. and Hideki, H.T. and Misako, M.T.}, biburl = {https://www.bibsonomy.org/bibtex/226d4b6e1d2385474ee953ca034faa521/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {7480186af82a9f7f89134b793e0deb5c}, intrahash = {26d4b6e1d2385474ee953ca034faa521}, keywords = {artificial brownian dynamics market motion statphys23 threshold topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:34.000+0200}, title = {A minimal stochastic dealer model of financial markets}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=931}, year = 2007 }