Artificial neural network for option pricing with and without asymptotic correction
Artificial neural network for option pricing with and without asymptotic correction
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DOI：
10.1080/14697688.2020.1812702
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发表时间：
2020-10
影响因子：
1.3
通讯作者：
Hideharu Funahashi
中科院分区：
文献类型：
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作者：
Hideharu Funahashi
为了提高计算速度、稳定性和逼近精度，提出了一种渐近展开(AE)和人工神经网络(ANN)相结合的期权定价方法。在实践中，复杂的随机波动率模型(SVM)被广泛使用，它可以考虑倾斜和微笑的形状。然而，在这些模型下，通常很难获得写在资产价格上的期权的解析解。AE可以有效地计算期权价格及其敏感性，但它通常只能计算完整解的有限项和，因为随着展开阶数的增加，解析和数值计算都变得乏味和混乱，计算成本呈指数级增长。另一方面，使用人工神经网络可以将定价过程分为两个步骤：(1)逼近可离线训练的人工神经网络；(2)使用在线获得的神经网络预测期权价格。离线过程具有极高的计算成本，因为它需要数万到数十万的蒙特卡罗(MC)或PDE数值模拟来训练几个隐藏层和几十个节点。此外，期权定价的深度学习(DL)表现出不稳定的行为和较差的质量，因为衍生品价格对投入的敏感性通常呈钟形，这会导致价值的快速变化。通过结合两种方法的优点和缺点，我们的新方法提供了以下改进：(1)需要更少的训练数据、层和节点：(2)离线训练变得更健壮，在线预测产生更稳定和准确的结果：(3)显著加快离线计算速度。
This paper proposes a mixed approach of asymptotic expansion (AE) and artificial neural network (ANN) methods for option pricing in order to improve computational speed, stability, and approximation accuracy. In practice, there is wide use of complex stochastic volatility models (SVMs) which can allow for skew and smile shapes. However, under these models, it is usually hard to obtain analytical solutions for options written on the asset price. AE can compute option prices and their sensitivities effectively, but it can usually only compute a finite sum of terms of the complete solution because, as the expansion order increases, both analytical and numerical calculations become tedious and messy and the computational cost grows exponentially. On the other hand, using ANN one can separate the pricing procedure into two steps: (1) approximating ANN that can be trained offline and (2) using the ANN predicted option price obtained online. The offline procedure has an extremely high-computational cost because it requires tens to hundreds of thousands of Monte Carlo (MC) or PDE numerical simulations in order to train several hidden layers and several dozens of nodes. Moreover, deep learning (DL) for option pricing shows unstable behaviour and poor quality because the sensitivity of the derivatives price with respect to the input often takes a bell-shape, which induces rapid changes in value. By combining the strong points and making up for the weak points of the two methods, our new approach offers the following improvements: (1) much less training data, layers, and nodes are required: (2) the offline training becomes more robust and the online predictions produce more stable and accurate results: and (3) it significantly speeds up the offline calculations.