基于机器学习的期权定价以及债务融资影响因素挖掘

随着大数据技术的发展、计算机性能的提高，人工智能进入了一个新时代。机器学习作为人工智能核心技术之一，在许多领域的应用中都取得了显著的成果。本文利用机器学习模型来研究和解决金融问题，包括金融衍生产品定价、公司债务融资影响因素挖掘并进行相关分析。

在金融衍生产品中，由于亚式期权的价格便宜、且其价格不易被操纵的优点，深受投资者的欢迎。但由于算术型亚式期权定价没有解析解，需要进行大量耗时的数值计算才能得到期权价格。因此，本文提出了一种基于反向传播的深度前馈神经网络模型的方法用于快速、精确地对亚式期权进行定价。该模型具有四层神经网络结构，同时采用了自适应矩估计优化算法（Adam）对模型参数进行优化。结果表明，该模型对于模拟期权价格以及实际期权价格预测均有良好的表现，在95%的真实亚式期权数据中的相对定价误差均值为2.015%，计算10000 个期权价格不超过1秒，远远快于蒙特卡洛模拟法的计算速度。

随着神经网络模型深度/层数的增加，会带来梯度消失的问题，导致模型预测精度下降。机器学习模型在期权定价中也存在着类似的问题。因此，本文提出了一个适用于欧式期权定价、具有灵活结构的残差神经网络（ResNet）模型。它由两个基本残差块构成，每个残差块包括三个一维卷积层和一个快速连接通道。该模型的优势在于它能拓展神经网络深度、提高预测精度，并且避免梯度消失。即便随着模型深度的增加，计算耗时会有所增加，但它计算大量的期权价格数据也仅需几秒。实验结果表明该模型在经过大量模拟期权数据的训练后，可以得到1.7%的样本外平均相对预测误差，这表明它能够很好地拟合BS 欧式期权定价公式。此外，该模型在中国上证50ETF 欧式期权真实数据中的定价误差要小于其他神经网络模型的误差。

以上的研究结果表明了机器学习模型能快速、准确地对期权进行定价，避免传统期权定价的理论模型与实际不符的假设。但存在的一个问题是，它们都是黑箱模型，无法解释模型结果。为了帮助决策者理解并信任机器学习模型的预测结果，本文以一个特定的残差神经网络模型为例，利用Gradient-SHAP 方法对它进行事后解释。它研究了上证50ETF 欧式期权价格的多个特征（比如前一期的期权结算价格、行权价格、隐含波动率等）如何影响当期欧式期权结算价格的预测结果。结果表明无论对于上证50ETF 欧式看涨期权还是看跌期权，影响期权结算价格特征的作用程度排序是一致的。尽管这些特征对于看涨或者看跌期权结算价格的边际影响不同，但它们对于期权价格的影响作用都符合看涨或看跌期权的特点，对预测结果能给出合理的解释，提高了机器学习模型的可信度。

机器学习模型不仅可以利用大量数据对金融产品的价格进行预测，还可以用于解析文本句法结构、提取文本特征。通过利用这些特征变量分析金融问题，能加深对金融问题的认识。因此，本文还基于神经网络的句法依存分析器以及实体关系抽取技术从16 万多条中国民营上市公司高管的简历文本中提取了高管背景特征指标。考虑到中国民营企业融资难问题、结合中国上市公司的双层董事会结构，本文研究不同高管职位下的高管政治背景、金融背景特征对中国民营企业的债务融资的影响。固定效应回归模型的结果表明，高管政治背景特征主要通过董事会对债务融资有积极影响，相反高管金融背景特征主要通过监事会对公司债务具有监督作用。此外，无条件分位数回归模型的结果表明，随着公司债务水平的增加，这两种特征对于公司债务水平的影响会逐渐减弱甚至消失。当公司处于较低的债务水平时，高管政治背景特征的积极作用会抑制金融背景特征作用，但它还是会随着公司债务分位数水平的增加而减弱。通过这些分析能够加深对上市民营企业债务融资问题的认识，进而可为解决民营企业债务融资难问题提供一些参考建议。

总之，拥有大量数据的金融行业中有许多问题和场景非常适合利用机器学习方法进行研究和分析。本文的研究很好地体现了这一点，也表明了机器学习在金融领域的应用具有突出意义和光明前景。

With the development of big data technology and the improvement of computer performance, artificial intelligence(AI) has entered a new era. Machine learning, as one of the core technologies of AI, has achieved remarkable results in many fields. This paper proposes and applies machine learning models to solve financial problems, including pricing of financial derivatives, mining the influencing factors of corporate debt financing and their related analysis.

Among financial derivative products, Asian option is popular among investors because of its cheap price and the advantage that its price is not easily manipulated. However, since there is no analytical solution for the arithmetic Asian option pricing, a lot of time-consuming numerical calculations are required to obtain the option price. Therefore, this paper proposes a deep feed-forward neural network model based on back-propagation for fast and accurate pricing of the arithmetic Asian option. The model has a four-layer neural network structure, and an optimization algorithm based on adaptive moment estimation(Adam) is used to optimize the model parameters. The results show that the model performs well for simulated option price forecasts as well as for actual option price forecasts. It has a mean relative pricing error of 2.015% over 95% of the real Asian option data and calculates 10,000 option prices in less than 1 second, much faster than the Monte Carlo simulation method.

As the depth of the neural network model increases, the problem of gradient disappearance is introduced, resulting in a decrease in prediction accuracy. A similar problem exists in the application of machine learning models to option pricing. Therefore, this paper also proposes a residual neural network (ResNet) model with a flexible structure suitable for European option pricing. It consists of two basic residual blocks, each of which includes three one-dimensional convolutional layers and a fast connection channel. The advantage of this model is that it can extend the depth of the neural network, improving the prediction accuracy of the model, and avoiding gradient disappearance. Even though its computation time increases as the depth of the model increases, it takes only a few seconds to compute a large amount of option price data. The experimental results show that the model can obtain an out-of-sample relative prediction error of 1.7% after being trained with a large amount of simulated option data, which means it can fit the BS European option pricing formula very well. In addition, the prediction errors of the model in the real data of European option on the Shanghai Stock Exchange(SSE) 50ETF are smaller than those of other neural network models.

The above findings show that machine learning models can price options quickly and accurately, avoiding the reality-inconsistent assumptions of traditional option pricing theory. However, one problem is they are black-box models. To help decision makers understand and trust the prediction results of machine learning models, this paper takes a specific residual neural network model as an example and interprets it ex-post by using the Gradient-SHAP method. It investigates how multiple features of the SSE 50 ETF European option price (e.g., the option settlement price of the previous period, the strike price, the implied volatility of the proximity, etc.) affect the prediction of the current European option settlement price. The results show that the importance ranking of these features affecting option prices is the same for the SSE 50 ETF European call and put options. These features have different marginal effects on call and put option prices. And the findings are consistent with the characteristics of the options and also provide a reasonable explanation for the prediction results, improving the credibility of the machine learning model.

Besides, machine learning model can not only predict the price of financial products, but also analyze the syntactic structure of text and extract text features. By using these characteristic variables to analyze financial problems, it can deepen the understanding of financial problems. Therefore, based on the dependency analyzer of neural network and entity relationship extraction technology, this paper extracts the features of executives from more than 160000 resumes of executives of Chinese private listed companies. Considering the financing problem of for Chinese private firms and the two-tier board structure of Chinese listed companies, this paper investigates the impacts of the political and financial background characteristics of executives under different executive positions on the financing of Chinese private firms. The results of the fixed-effects regression model indicate that executive political background characteristics have a positive impact on debt financing mainly through the board of directors. While on the contrary, executive financial background characteristics have a supervisory role on corporate debt mainly through the board of supervisors. The results of the unconditional quantile regression model indicate that the effect of both characteristics on the level of corporate debt diminishes or even disappears as the level of corporate debt increases. When the companies are at low debt levels, the positive effect of the political background characteristics suppresses the negative effect of the financial background characteristics, but it still diminishes with the increase of the debt level. These analyses can deepen the understanding of debt financing research problems of listed private enterprises, and then provide references to solve the problem of debt financing difficulties of private enterprises.

In conclusion, there are many problems and scenarios in the financial industry with a large number of data that are well suited for research and analysis using machine learning method. This study reflects this well, and also shows that the application of machine learning in finance is important in practice and has a bright future.

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