论文标题
通过人工神经网络进行无监督学习的财务期权评估
Financial option valuation by unsupervised learning with artificial neural networks
论文作者
论文摘要
最近还将人工神经网络（ANN）应用于求解部分微分方程（PDE）。在这项工作中，研究了基于相应的PDE配方定价的经典问题。我们不使用基于有限元或差异方法的数值技术，而是在无监督学习的背景下使用ANN解决了问题。结果，根据合适的损失函数的最小化，ANN在将来时间点了解所有可能的基础库存值的期权值。对于欧洲选项，我们解决了线性黑色 - choles方程，而对于美国选项，我们解决了线性互补性问题的制定。还计算了两个资产的外来期权值，因为ANN可以准确地估值高维期权。通过与分析选项值或数值参考解决方案进行比较（对于美国选项，由有限元素计算）来评估ANN方法的结果错误。
Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black-Scholes equation, whereas for the American option, we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements).
