Volatility Model Calibration With Convolutional Neural Networks

We use a supervised deep convolution neural network to replicate the calibration of the Heston model to equity volatility surfaces. For this purpose we treat the implied volatility surface together with some auxiliary data, namely the strikes and moneyness of the corresponding options and the equity forwards, as a 3-dimensional input tensor for the neural network, in analogy to a colour channel image representation like the RGB. To extract the main features of the input data we are using inception layers with (1;1), (1;3) and (2;1) dimensional kernels. The specific choice is motivated by the no-arbitrage conditions on the call price surface. In terms of a local surface modelling the (1;3) filters with different weights can model the position, slope and curvature in the moneyness direction while the (2;1) filters can model Position and slope in the maturity direction. The neural network has been implemented using the open source library tensorflow.