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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 11: Poster Session

SOE 11.10: Poster

Dienstag, 15. März 2011, 18:05–18:45, P2

relationship between ARCH model and stochastic dealer model — •Kenta Yamada¹, Sidney Redner², Hideki Takayasu³, and Misako Takayasu¹ — ¹Tokyo Institute of Technology, Japan — ²Boston University, USA — ³Sony CSL, Japan

In order to understand statistical properties of time series of market prices from the viewpoint of microscopic dealers' action, we clarify a relationship between ARCH model and stochastic dealer models. ARCH model is an autoregressive type of time series model developed in the field of financial technology which reproduces the empirically known power law distribution of price changes, and there are many derived models such as GARCH model. On the other hand stochastic dealer model, which is studied mostly by physicists, is consisted of minimal configuration of dealers in an artificial market, and by tuning the parameters the models reproduce most of empirically stylized facts of financial markets including the power law distribution of price changes.

A. Sato and H. Takayasu showed that ARCH model can be derived from a deterministic dealer model in the special case that dealers have tendency of following trends of price changes. In this presentation we pay attention to the dealer's spread, that is, the price difference between the dealer's buying and selling prices, which has been set as a constant in the dealer model. By taking into account a feedback effect of volatility to the dealer's spread, we can theoretically derive ARCH model from the dealer model with fluctuation of spread.