A new logistic-type model for pricing European options

Abstract

We propose a family of models for the evolution of the price process St of a financial market. We model share price and volatility using a two-dimensional system of stochastic differential equations (SDEs) driven by a single Wiener process. We prove that this family of models is well defined and that each model from this family is free of arbitrage opportunities, and it is (state) complete. We use option prices written over the S&P500 from December 2007 to December 2008 to calibrate a model of the proposed family and compare the calibration results with results of the Heston Model for the same data set. The empirical results achieved in both models show similarities for periods of low volatility, but the model studied shows a better performance during the period of higher volatility.