Ensemble deep neural network method for solving free boundary American style stochastic volatility models

Abstract We present an ensemble deep learning method for solving free boundary American style stochastic volatility models. To this end, we cast our solution framework as a free boundary problem where the early exercise boundary surface, as a function of time and volatility, is approximated simultaneously with the value function and Greeks. For precise computation of the free boundary plane, we first use the Landau transformation to fix the free boundary and normalize the value function and the time domain. We then develop a novel ensemble auxiliary operator (EANO) involving suite of configurations based on the ensemble neural network output (ENNO). The early exercise boundary surface, value function, delta sensitivity, vega, gamma, vomma and vanna are predicted from the EENO, EANO, and the derivatives of EANO after training. The performance of our neural network configuration is verified and validated by comparison with some existing methods and examples. It provides an alternative approach for solving free boundary stochastic volatility models