Dresden 2011 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 11: Poster Session
SOE 11.10: Poster
Tuesday, March 15, 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.