The deep parametric PDE method and applications to option pricing

We propose, formalise and analyse the deep parametric PDE method to solve high-dimensional partial differential equations with a focus on financial applications. A single neural network approximates solution of whole family PDEs after being trained without need sample solutions. As practical application, we compute option prices Greeks in multivariate Black–Scholes model as there is an urgent for highly efficient methods. After training phase, sensitivities different times, states parameters are available milliseconds. Exploiting framework incorporating a-priori knowledge no-arbitrage bounds improves performance significantly. evaluate accuracy price, implied volatility examples up 25 dimensions. comparison alternative machine learning methods confirms effectiveness new approach reveals advantages underlying formulation.