2020/12/11 by Kathrin Glau, Glau, Kathrin, Linus Wunderlich +1
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Computational Finance (q-fin.CP) #FOS: Economics and business #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2012.06211
openalex publication_date 2020/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample solutions. As a practical application, we compute option prices in the multivariate Black-Scholes model. After a single training phase, the prices for different time, state and model parameters are available in milliseconds. We evaluate the accuracy in the price and a generalisation of the implied volatility with examples of up to 25 dimensions. A comparison with alternative machine learning approaches, confirms the effectiveness of the approach.