论文标题
一种生成的对抗网络方法，用于校准局部随机波动率模型
A generative adversarial network approach to calibration of local stochastic volatility models
论文作者
论文摘要
我们提出了一种完全数据驱动的方法来校准局部随机波动率（LSV）模型，尤其规定了波动率表面的临时插值。为了实现这一目标，我们通过馈送前馈神经网络家族的杠杆功能参数，并直接从可用的市场期权价格中学习它们的参数。这应该在神经SDE和（因果）生成对抗网络的背景下可以看出：我们通过特定的神经SDE产生波动表面，这些神经SDE的质量是通过量化的，可能是以对抗性方式来评估的。校准功能的最小化强烈依赖于基于对冲和深度对冲的方差降低技术，这本身就是有趣的：它允许仅使用小型样品路径集的准确方式计算模型价格和模型的隐含方式。对于数值说明，我们实施了SABR型LSV模型，并对许多隐含波动性微笑样本进行了彻底的统计性能分析，显示了该方法的准确性和稳定性。
We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed-forward neural networks and learn their parameters directly from the available market option prices. This should be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by specific neural SDEs, whose quality is assessed by quantifying, possibly in an adversarial manner, distances to market prices. The minimization of the calibration functional relies strongly on a variance reduction technique based on hedging and deep hedging, which is interesting in its own right: it allows the calculation of model prices and model implied volatilities in an accurate way using only small sets of sample paths. For numerical illustration we implement a SABR-type LSV model and conduct a thorough statistical performance analysis on many samples of implied volatility smiles, showing the accuracy and stability of the method.
