论文标题
使用深度学习在随机波动下解决障碍选项
Solving barrier options under stochastic volatility using deep learning
论文作者
论文摘要
我们开发了一种无监督的深度学习方法，以解决伯戈米模型下的障碍选项。神经网络充当近似选项表面，并经过训练以满足PDE和边界条件。在神经网络中添加了两个单一的术语，以在罢工和障碍水平上处理非平滑和不连续的回报，以便神经网络可以在短暂到期时复制屏障选项的不对称行为。之后，在一个框架中定价香草选项和障碍选项。同样，使用神经网络来处理Bergomi模型中功能输入的高维度。一旦训练，神经网络解决方案就会产生快速准确的选项值。
We develop an unsupervised deep learning method to solve the barrier options under the Bergomi model. The neural networks serve as the approximate option surfaces and are trained to satisfy the PDE as well as the boundary conditions. Two singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of barrier options at short maturities. After that, vanilla options and barrier options are priced in a single framework. Also, neural networks are employed to deal with the high dimensionality of the function input in the Bergomi model. Once trained, the neural network solution yields fast and accurate option values.
