Option pricing and trading with artificial neural networks and advanced parametric models with implied parameters

We combine parametric models and feedforward artificial neural networks to price and trade European S&P500 Index options. Artificial neural networks are optimized on a hybrid target function consisted by the standardized residual term between the actual market price and the option estimate of a certain parametric model. Parametric models include: (i) the Black and Scholes model that assumes a geometric Brownian motion process (GBM); (ii) the Corrado and Su that additionally allows for excess skewness and kurtosis via a Gram-Charlier series expansion; (iii) analytic models that extend the GBM by incorporating multiple sources of Poisson distributed jumps; and (vi) stochastic volatility and jump models. Daily average implied parameters of these models are estimated with options transaction data via an unconstraint process optimized by the non-linear least squares Levenberg-Marquardt algorithm. This structural average implied parameters are used to validate the out-of sample pricing and trading (with transaction costs) ability of all models developed.