The Black-Scholes type financial models and the arbitrage opportunities

Abstract

By using the conservation laws concept, we study certain financial models similar tothe Black–Scholes model. We show that without complement limitations such modelscan have two or more volatilities. This fact imposes several intrinsic limitations forthe dynamical system parameters in order to guarantee the correct definition.Keywords: Black–Scholes model, volatility, laws of conservation.

Usando el concepto de leyes de conservaci´on, estudiamos ciertos modelos financierossimilares al modelo de Black–Scholes. Demostramos que sin limitaciones complementariastales modelos pueden tener dos o m´as volatilidades. Este hecho impone variaslimitaciones intr´?nsecas para los par´ametros de sistemas din´amicos con fines de garantizarla definici´on correcta de dichos sistemas.Palabras clave: Modelo de Black–Scholes, volatilidad, leyes de conservaci´on.