  In this paper we study the continuum time dynamics of a stock in a market
where agents behavior is modeled by a Minority Game and a Grand Canonical
Minority Game. The dynamics derived is a generalized geometric Brownian motion;
from the Black & Scholes formula the calibration of both the Minority Game and
the Grand Canonical Minority Game, by means of their characteristic parameters,
is performed. We conclude that for both games the asymmetric phase with
characteristic parameters close to critical ones is coherent with options
implied volatility market.
