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

Option pricing model by applying hybrid neural network based on heston model and genetic algorithm

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。

Option is an important kind of derivative securities, and it has an unequivalent property of rights and obligations. Because of this, option is a very favorite investment instrument for investors. For other derivatives, option is also faced with the problem of pricing difficulty. In 1973, financial engineering field entered a golden age because developing the Black-Scholes option pricing formula was a major milestone. The number of studies on derivatives＇ pricing is increasing, and financial innovations are made one after another. These two trends have directly led to the rapid development of derivatives market in recent decades. However, how to price 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 open market. One side of reasons is the lack of sound market system and environment. The other side of reasons is the lack of an effective theory and pricing tools. In February 9, 2015, the Shanghai stock exchange carried out a pilot trading of stock option and started the transactions of Shanghai 50 ETF 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 transactions. With more and more frequent transactions, 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）. However, each of them has its advantages and disadvantages. Now the frontier theory combines 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 and use BP Artificial Neural Network to fit the difference between actual options data and option prices of Heston model in order to improve pricing accuracy. In addition, BP algorithm has the disadvantage of slow convergence and is easy to fall into local minima. Thus, we use genetic algorithm（GA） to optimize the structure of hybrid neural network. A new option pricing model is established by applying hybrid neural network and genetic algorithm based on Heston model. The pricing accuracy has been demonstrated using the actual Hongkong＇s Hang Sheng Index（HSI） options and Shanghai 50 ETF option. This hybrid approach is shown to provide greater accuracy than either conventional model or the hybrid neural network based on Black-Scholes model. It is a great valuable reference for China option market to trade option pricing. The article is organized as follows： The first chapter introduces the purpose and significance of the topic, studies results of domestic and foreign researchers, and discusses the main research content. The second chapter firstly introduces the Heston model and the derivation process of its closed-form solution, as well as the equivalent martingale measure. The number of model parameters is reduced from six to five. The third chapter describes the calibration theory for Heston model in detail, then compares the calibration--nonlinear least squares method with the adaptive simulated annealing method. Considering the computing time and accuracy, the nonlinear least squares method is finally selected. After 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 introduction of Hongkong＇s Hang Sheng index option and Shanghai 50 ETF option., including data description, selection of evaluating indicators, predicted results of the model, performance comparison between different models, and interpretation of results. The fifth chapter includes some analysis and discussion. Future researches are suggested in the end. In conclusion, Heston model is better than BS model. Thus, stochastic volatility assumption is more consistent with the actual market. A hybrid neural network model based on Heson model can receive higher pricing accuracy than other models.