基于RBF神经网络的期权定价研究

发布时间：2018-10-25 18:22

【摘要】：在现代金融市场中,期权是一种重要的基础性金融衍生产品。如何准确地为期权定价一直是众多学者研究的重要课题。本文主要研究RBF神经网络在期权定价中的应用。主要工作如下： 1.构建模型。在文献[15]中,尽管杨梁玉利用RBF神经网络对七只权证进行定价研究,并取得了较好结果,但其仅考虑了标的股票波动率为历史波动率的情况,而未考虑标的股票波动率为隐含波动率的情况。我们在此基础上,以国电CWB1权证为研究对象,将历史波动率和隐含波动率同时作为输入变量构建了基于RBF神经网络的期权定价模型。与B-S定价模型相比,基于RBF神经网络的期权定价模型模型无任何假设和限制,而且没有任何参数,只需利用已有数据,合理确定输入输出变量,即可进行期权定价。与BP模型相比,基于RBF神经网络的期权定价模型收敛速度更快,而且不存在局部极小的问题。 2.模型的算法实现及实证分析。我们基于Matlab工具箱、K-均值聚类算法、梯度下降法和粒子群算法优化(PSO-RBF)的RBF网络模型进行仿真,得到了比较好的实验结果。通过算法参数和仿真结果的比较发现,利用隐含波动率的RBF网络模型要优于利用历史波动率的RBF网络模型,且前者所选取的神经元个数要多于后者所选取的。基于Matlab工具箱的RBF网络的泛化能力较弱。基于K-均值聚类算法、梯度下降算法和PSO算法优化的RBF网络模型计算的权证理论价格与实际价格的趋势基本一致。 3.模型的比较。首先,我们采用ME、MSE、MAE和MRE四种误差指标对分别使用历史波动率和隐含波动率的基于四种RBF网络算法的定价模型进行评价。结果表明,PSO-RBF仿真精度较高,效果优于其他三种算法模型。其次,通过对比RBF网络模型与B-S模型、BP模型,发现不论是使用历史波动率还是隐含波动率,RBF网络模型都要优于B-S模型、BP模型。
[Abstract]:Option is an important basic financial derivative in modern financial market. How to accurately price options has been an important research topic for many scholars. This paper mainly studies the application of RBF neural network in option pricing. The main work is as follows: 1. Build the model. In reference [15], although Yang Liangyu used RBF neural network to study the pricing of seven warrants and obtained good results, it only considered that the volatility of underlying stocks was historical volatility. But does not consider the underlying stock volatility is the implied volatility situation. On this basis, we take the CWB1 warrant of Guodian Power as the research object, and take both historical volatility and implied volatility as input variables to construct the option pricing model based on RBF neural network. Compared with the B-S pricing model, the option pricing model based on RBF neural network has no assumptions and restrictions, and has no parameters. The option pricing can be carried out by making use of the existing data and reasonably determining the input and output variables. Compared with BP model, the option pricing model based on RBF neural network converges faster and does not have the problem of local minima. 2. Algorithm implementation and empirical analysis of the model. Based on Matlab toolbox, K-means clustering algorithm, gradient descent method and particle swarm optimization (PSO-RBF), we simulate the RBF network model and obtain good experimental results. By comparing the algorithm parameters with the simulation results, it is found that the RBF network model based on implicit volatility is better than the RBF network model using historical volatility, and the number of neurons selected by the former is more than that by the latter. The generalization ability of RBF network based on Matlab toolbox is weak. Based on the K-means clustering algorithm, gradient descent algorithm and PSO algorithm, the theoretical price of warrant is basically consistent with the actual price. 3. Comparison of models. Firstly, we use ME,MSE,MAE and MRE to evaluate the pricing model based on four RBF network algorithms using historical volatility and implicit volatility, respectively. The results show that the simulation accuracy of PSO-RBF is higher than that of other three algorithms. Secondly, by comparing RBF network model with B-S model and BP model, it is found that RBF network model is superior to B-S model and BP model, regardless of using historical volatility or implied volatility.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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