A Modelling of Bitcoin Price Dynamics by the Artificial Market Algorithm

Abstract

A famous crypto-currency “Bitcoin” was invented in 2009. Since then, we have observed dramatic fluctuation of its price due to the nature of crypto-currency. In other words, the level of the fluctuation seems totally different from the ordinary financial assets like equities, interest rates and foreign exchange rates. Therefore it is afraid that the well-known framework of PDE used for those financial assets, is not suitable to express Bitcoin’s dynamics. In this article, an algorithm of artificial market simulation model, so called “150 Agents Model” is proposed to express the fluctuation of Bitcoin price. The model is composed of two types of agents, Traders and Non-Traders, who trade Bitcoin through “itayose” method. The aim of the model is not pricing Bitcoin exactly for trading. Rather it could visualize the structure implied behind the price actions. By calibrating the model to actual price fluctuation of Bitcoin, we are able to see the overall market picture composed of agents to recognize their target prices and price sensitivities as the driver of the price dynamics, to predict the range of next big fluctuation and to recognize how the change of agent’s target price and its sensitivity to the price change, affect the landscape of the price range. This model is versatile and flexible. We could add new agents, take new issued amount into consideration, express flash crush and also simulate fluctuation of ordinary financial assets like foreign exchange rates by applying a moderate range of the parameters, which could produce a kind of Elliot Wave dynamics.