European call price modelling using neural networks in considering volatility as stochastic with comparison to the Heston model

摘要

The aim of this paper is to model the European call price using neural networks (NNs). Many existing works have treated the problem as Hutchinson et al. [(1994). A nonparametric approach to pricing and hedging derivative securities via learning networks. J Finance. 49(3):851-889] Compared to these previous studies, the originality of our work consists in considering the volatility as stochastic and then to compare the NN's results to those of Heston (1993) model rather than to those of Black and Scholes [(1973 May-Jun). The pricing of options and corporate liabilities. J Polit Econ. 81(3):637-654)] as Hutchinson et al. did. We base our empirical work on real data (12 contracts on CAC40 index from the period January 2005 to January 2007). We found that the NNs approach gives better performances than the Heston's, in terms of accuracy and convergence speed.