The Deep Parametric PDE Method: Application to Option Pricing

Kathrin Glau; Linus Wunderlich

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arXiv · 2012.06211

The Deep Parametric PDE Method: Application to Option Pricing

Kathrin Glau·Linus Wunderlich

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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.

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BibTeX RIS

Kathrin Glau, Linus Wunderlich. 2020-12-11. The Deep Parametric PDE Method: Application to Option Pricing. https://arxiv.org/abs/2012.06211

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