From Minority Game to Black & Scholes pricing
Trading and Market Microstructure
2013-05-17 v2 Probability
Pricing of Securities
Statistical Finance
Abstract
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.
Keywords
Cite
@article{arxiv.1205.2521,
title = {From Minority Game to Black & Scholes pricing},
author = {Matteo Ortisi and Valerio Zuccolo},
journal= {arXiv preprint arXiv:1205.2521},
year = {2013}
}
Comments
Extended to the Grand Canonical Minority Game 20 pages, 18 figure