In this talk we will discuss a data-driven approach based on neural networks (NN) for calibrating financial asset price models. Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The framework consists of two parts: a forward pass in which we train the weights of the NN off-line, valuing options under many different asset model parameter settings; and a backward pass, in which we evaluate the trained NN-solver on-line, aiming to find the weights of the neurons in the input layer. We will show how the same data-driven approach can be used to estimate the Black-Scholes implied volatility and dividend yield for American options in a fast and robust way. We then discuss the complexity of the optimization problem through an analysis of the loss surface of the neural network. We finally will present some numerical examples which show that neural networks can be an efficient and reliable technique for the calibration of financial assets and the extraction of implied information.
