论文标题
部分可观测时空混沌系统的无模型预测
Interpolation of Missing Swaption Volatility Data using Gibbs Sampling on Variational Autoencoders
论文作者
论文摘要
尽管对金融从业者和研究人员都有关键的兴趣，但由于各种潜在的交换工具的流动性不足，欧洲交换的市场刻薄波动性数据通常会显示出很大一部分缺失的报价。在这种情况下，由于数据仅适用于相应的基本交换的货币报价，因此通常无法将标准随机插值工具（如常见的SABR模型）校准为隐含的波动性微笑。在这里，我们建议通过通过变异自动编码器学习隐含波动率立方体的随机潜在表示，从而推断出全面未知的隐含波动率立方体的几何形状，从而通过近似GIBBS采样方法对观察到的数据有条件地对观察到的数据有条件地进行推断。随后可以使用估计缺失引号的估计值来拟合标准的随机波动率模型。 Since training data for the employed variational autoencoder model is usually sparsely available, we test the robustness of the approach for a model trained on synthetic data on real market quotes and we show that SABR interpolated volatilites calibrated to reconstructed volatility cubes with artificially imputed missing values differ by not much more than two basis points compared to SABR fits calibrated to the complete cube.此外，我们展示了如何用于成功设置Delta-Sundral投资组合以进行对冲目的。
Albeit of crucial interest for both financial practitioners and researchers, market-implied volatility data of European swaptions often exhibit large portions of missing quotes due to illiquidity of the various underlying swaption instruments. In this case, standard stochastic interpolation tools like the common SABR model often cannot be calibrated to observed implied volatility smiles, due to data being only available for the at-the-money quote of the respective underlying swaption. Here, we propose to infer the geometry of the full unknown implied volatility cube by learning stochastic latent representations of implied volatility cubes via variational autoencoders, enabling inference about the missing volatility data conditional on the observed data by an approximate Gibbs sampling approach. Imputed estimates of missing quotes can afterwards be used to fit a standard stochastic volatility model. Since training data for the employed variational autoencoder model is usually sparsely available, we test the robustness of the approach for a model trained on synthetic data on real market quotes and we show that SABR interpolated volatilites calibrated to reconstructed volatility cubes with artificially imputed missing values differ by not much more than two basis points compared to SABR fits calibrated to the complete cube. Moreover, we show how the imputation can be used to successfully set up delta-neutral portfolios for hedging purposes.
