论文标题
超越替代建模：通过形状约束学习局部波动率
Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints
论文作者
论文摘要
我们探讨了两种机器学习方法的能力，即欧洲香草期权价格的无契约插值，它们共同产生相应的局部波动性表面：基于价格的无标准限制下的有限维度高斯流程（GP）回归方法，基于价格，以及一种基于神经网络（NN）的方法，并基于隐性波动性的仲裁。我们证明了这些方法相对于SSVI行业标准的性能。 GP方法是无套利的，而套利仅在SSVI和NN方法下受到惩罚。 GP方法获得了最佳的样本外校准误差，并提供了不确定性量化。NN方法可以使局部波动更平滑，并且更好地进行了测试性能，因为其训练标准包含了局部波动性的正规化项。
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP) regression approach under no-arbitrage constraints based on prices, and a neural net (NN) approach with penalization of arbitrages based on implied volatilities. We demonstrate the performance of these approaches relative to the SSVI industry standard. The GP approach is proven arbitrage-free, whereas arbitrages are only penalized under the SSVI and NN approaches. The GP approach obtains the best out-of-sample calibration error and provides uncertainty quantification.The NN approach yields a smoother local volatility and a better backtesting performance, as its training criterion incorporates a local volatility regularization term.
