基于Heston模型和遗传算法优化的混合神经网络期权定价研究 本期目录 >>
Title: Option Pricing Model by Applying Hybrid Neural Network based on Heston Model and Genetic Algorithm
作者 张丽娟;张文勇
Author(s): zhang lijuan; zhang wenyong
摘要: 本文以Heston模型取代传统混合神经网络期权定价模型中的Black-Scholes(BS)模型,通过Back Propagation (BP)神经网络来拟合实际市场期权价格和Heston模型的期权价格的差值,并运用遗传算法来优化整个神经网络,建立了基于Heston模型和遗传算法的混合神经网络期权定价模型。应用这一模型,通过对香港恒生指数期权和上证50ETF期权的实证研究,结果表明:该模型相对于基于BS模型的混合神经网络模型和其他传统定价模型,有着更高的精确度,而且运用上证50ETF期权的Heston神经网络定价模型要比运用香港恒生指数期权的定价模型定价效果好,说明基于Heston神经网络期权定价模型在中国期权市场上有更好的适应性,为未来的期权定价提供新的模型指导,具有较大的参考价值。
Abstract: Abstract: Option is an important kind of derivative securities, and it has the unequivalent property of rights and obligations. Because of this, option is a very favorite investment instrument for investors. But as other derivatives, option is also faced with the problem of difficulty to pricing. In 1973, developing the Black-Scholes option pricing formula is a landmark, and then financial engineering has entered a golden age. The research on derivatives’ pricing is increasing, and financial innovations are made one after another, which directly lead to the rapid development of derivatives market in recent decades. But how to pricing efficiently and accurately is still the consistent goal for financial experts. The innovation of financial tools in China has long been inadequate, particularly in the trading of financial derivatives, which directly affects the pace of financial reforms and opening up. The reasons are on one side due to the lack of sound market system and environment, on other side also with the lack of an effective theory and the pricing tools. In February 9, 2015, the Shanghai stock exchange carried out stock option trading pilot and started the transactions of Shanghai 50ETF option. This means that Chinese investors will have a new hedging investment--option. In options trading, the options’ fair value is very important for both sides of the transactions. With the transactions more and more frequent, the accurate pricing model is very important for the validity of the options market. The traditional method of pricing is divided into parameter models(such as BS model, Cev model, Heston model, etc.) and non-parameter models(such as artificial neural network model). But each of them has its advantages and disadvantages. Now the frontier theory combines the parameter models and non-parameter models to design a hybrid neural network model. The conventional hybrid neural network for option pricing is based on Black-Scholes model. While the Black-Scholes model has very strict assumptions, it does not accord with the actual situations of financial market. In this paper, we use Heston model (a kind of stochastic volatility models) to replace BS model in the hybrid neural network, use BP Artificial Neural Network to fit the difference between actual options data and option prices of Heston model in order to get better pricing accuracy. In addition, BP algorithm has the disadvantage of slow convergence and easy to fall into local minima, so we use genetic algorithm (GA) to optimize the structure of hybrid neural network. A new option pricing model by applying hybrid neural network and genetic algorithm based on Heston model is established. The pricing accuracy has been demonstrated using the actual Hongkong's Hang Sheng Index (HSI) options and Shanghai 50ETF option . This hybrid approach is shown to provide greater accuracy than either conventional model or the hybrid neural network based on Black-Scholes model. And it is a great valuable reference for China option market on option pricing. The article is organized as follows: The first chapter introduces the purpose and significance of the topic, study results of domestic and foreign researcher, and the main research content of this paper. In the second chapter,it first briefly introduces the Heston model and the derivation process of its closed-form solution, and through the equivalent martingale measure. The number of model parameters is reduced from six to five。 In the third chapter,it firstly describes the calibration theory for Heston model in detail, then compares the two methods of calibration--nonlinear least squares method and adaptive simulated annealing method. Considering the computing time and accuracy, finally the nonlinear least squares method is selected. Later combining the calibrated Heston model with BP neural network and genetic algorithm, we establish a BP hybrid neural network based on Heston model and a BP hybrid neural network based on Heston model optimized by genetic algorithm. The fourth chapter is an empirical study of Hongkong's Hang Sheng index option and Shanghai 50ETF option., including data description, selection of evaluating indicators, predicted results of the model, performance comparison between different models, and interpretation of results. In the fifth chapter there are some analysis and discussion, and future researches are prospected in the end. In conclusion, the Heston model is better than BS model, so stochastic volatility assumption is more consistent with the actual market; and a hybrid neural network model based on Heson model can get higher pricing accuracy than other models. Keywords: Heston model; Black-Scholes model; hybrid neural network; genetic algorithm; option pricing
关键词: Heston模型;Black-Scholes模型;遗传算法;混合神经网络;期权定价
Keywords: Heston mode; Black-Scholes model; genetic algorithm;; hybrid neural network;; option pricing
基金项目: 教育部人文社会科学青年基金项目;上海哲学社会科学规划青年项目;上海市教委研创新项目
发表期数: 2018年 第3期
中图分类号: 文献标识码: 文章编号:
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