The Deep Parametric PDE Method: Application to Option Pricing
arXiv:2012.06211
Abstract
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.
arXiv commentSome examples can be reproduced in our Jupyter Notebook: https://github.com/LWunderlich/DeepPDE/blob/main/TwoAssetsExample/DeepParametricPDEExample.ipynb
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