The Deep Parametric PDE Method: Application to Option Pricing
The Deep Parametric PDE Method: Application to Option Pricing
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发表时间：
2020-12
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通讯作者：
K. Glau;Linus Wunderlich
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作者：
K. Glau;Linus Wunderlich
提出了求解高维参数偏微分方程的深度参数偏微分方程方法。单个神经网络在训练后逼近整个偏微分方程族的解，而不需要样本解。作为一个实际应用，我们计算了多变量Black-Scholes模型中的期权价格。在单个训练阶段之后，不同时间、状态和模型参数的价格以毫秒为单位。我们评估的准确性，在价格和概括的隐含波动率的例子多达25个维度。与其他机器学习方法的比较，证实了该方法的有效性。
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.