基于FFT与Transformer算法的混合期权定价模型研究  

Research on hybrid option pricing model based on FFT and Transformer algorithm

作　　者：温伟 付志远 张艳慧[2] WEN Wei;FU Zhiyuan;ZHANG Yanhui(School of Economics,Beijing Technology and Business University,Beijing 100048,China;School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China)

机构地区：[1]北京工商大学经济学院,北京100048 [2]北京工商大学数学与统计学院,北京100048

出　　处：《河北科技大学学报》2024年第5期562-572,共11页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11971042)。

摘　　要：为解决经典期权定价模型与实际价格数据偏差较大的问题,选取BS期权定价模型,采用快速傅里叶变换(Fast Fourier Transform,FFT)结合Transformer多头注意力机制深度学习算法,对上证300ETF期权与上海期货交易所黄金期权数据进行实证研究,通过改进的Transformer算法对基于FFT算法的期权定价模型与实际金融市场期权价格数据之间的残差值进行二次训练。结果表明,与其他算法(BS、FFT-BS)及其他混合算法(FFT-BS+ARIMA、FFT-BS+LSTM)模型相比,基于FFT-BS+Transformer的算法在R^(2)、MSE、NRMSE以及MAE等统计指标上均有很好的表现,且针对不同波动、不同品种的期权,该混合算法模型均取得了较好的结果。将改进后的Transformer算法应用到期权定价中,可弥补经典期权定价模型的不足,提供了更加精确的期权定价模型。In order to solve the problem of the large deviation between the classical option pricing model and the actual price data,based on the BS option pricing model,the Fast Fourier Transform(FFT)combined with the Transformer's multi-head attention mechanism of deep learning algorithm was used to conductthe empirical research on the 300ETF options and Shanghai gold options data.The model was quadratically trained by the improved Transformer algorithm on the residual values between the option pricing model based on the FFT algorithm and the option price data of the actual financial market.The results show that compared with other algorithms(BS model,FFT-BS model)and other hybrid algorithm models(FFT-BS+ARIMA model,FFT-BS+LSTM model),the proposed model has a good performance in the statistical indexes such as R^(2),MSE,NRMSE and MAE,and the hybrid algorithm model achieves a better performance for different volatilitiesand different varieties of options.The study innovatively applies the improved Transformer algorithm to option pricing,which compensates for the shortcomings of the classical option pricing model and provides a more accurate option pricing model.

关 键 词：计算机神经网络 金融市场 期权定价 深度学习 混合模型 多头注意力机制 

分 类 号：F830.91[经济管理—金融学]