A new method which combines numerical approximation techniques and artificial neural networks is used to approximate formulas for option prices and derivatives. Using this method, highly precise analytical formulas can be derived for option types (American, Asian, binaries,...) and models (GARCH, stochastic volatility,...) that are otherwise analytically intractable.
Using the formulas derived according to this new approach, option prices and greeks under these models can be computed instantaneously.