Silvia Lavagnini

Abstract

We price European type options having forward contracts in the commodity market as underlying, which we model by the HJM approach with stochastic volatility operator. As stochastic volatility models are cost demanding in terms of Monte Carlo simulations, in a first step we train a neural network as function of the parameters of the HJM model plus the features of the option, such as strike and time to maturity, in order to approximate the option price functional. Once trained the neural network with data obtained by cost demanding simulations of an SPDE, we get a deterministic function capable to price options. In a second step, we use this function together with options market data to calibrate the HJM model and get the forward curve parameters. Since only the second step is using market data, and it is based on a deterministic function that is the neural network, no simulations are required and the approach allows to fast parameters calibration. Indeed, the first step being off-line, this does not need to be trained frequently, while the second step is less cost demanding and can be run, e.g., daily, in order the HJM model to reflect the current market data.