  We propose an innovative data-driven option pricing methodology that relies
exclusively on the dataset of historical underlying asset prices. While the
dataset is rooted in the objective world, option prices are commonly expressed
as discounted expectations of their terminal payoffs in a risk-neutral world.
Bridging this gap motivates us to identify a pricing kernel process,
transforming option pricing into evaluating expectations in the objective
world. We recover the pricing kernel by solving a utility maximization problem,
and evaluate the expectations in terms of a functional optimization problem.
Leveraging the deep learning technique, we design data-driven algorithms to
solve both optimization problems over the dataset. Numerical experiments are
presented to demonstrate the efficiency of our methodology.
