Deep learning, utilizing artificial neural networks, offers capabilities in solving parametric Black-Scholes Equations under local volatility models. This study introduces dual-training methodology to calculate option price and implied volatility simultaneously, utilizing market data. For that, we use the Physics-Informed Neural Network as a deep learning, a novel approach harnessing physical information to efficiently solve parametric partial differential equations. The network provides two key advantages: construction of implied volatility surface on continuous state set, and allowing predictions at unobserved market values. This study presents a refined tool to practitioners in analyzing the local volatility model.
