  This paper is devoted to the price-storage dynamics in natural gas markets. A
novel stochastic path-dependent volatility model is introduced with
path-dependence in both price volatility and storage increments. Model
calibrations are conducted for both the price and storage dynamics. Further, we
discuss the pricing problem of discrete-time swing options using the dynamic
programming principle, and a deep learning-based method is proposed for
numerical approximations. A numerical algorithm is provided, followed by a
convergence analysis result for the deep-learning approach.
