基于粗糙随机模型的参数校准与定价研究  

Research on Parameter Calibration and Pricing Based on Rough Stochastic Model

作　　者：凌倩瑜 刘宁 曾渝翔 陈晓鹏 Ling Qianyu;Liu Ning;Zeng Yuxiang;Chen Xiaopeng(Department of Mathematics,Shantou University,Shantou Guangdong 515063,China;Department of Computer Science,Shantou University,Shantou Guangdong 515063,China)

机构地区：[1]汕头大学数学系,广东汕头515063 [2]汕头大学计算机系,广东汕头515063

出　　处：《统计与决策》2025年第7期65-70,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(12271185);广东省普通高校特色创新项目(2022KTSCX037);广东省自然科学基金面上项目(2025A1515011188)。

摘　　要：传统Black-Scholes期权定价模型因假定波动率为常数,导致定价结果存在较大误差。文章采用分数布朗运动驱动的粗糙Bergomi随机波动率模型,针对国内金融市场进行波动率曲面刻画,并采用2022年1月4日至2022年12月30日的沪深300ETF期权的日交易数据进行实证分析,利用神经网络两步法进行参数校准,结果表明,粗糙Bergomi模型的定价精度优于Heston模型和BS模型,神经网络两步法在参数优化效果上优于差分进化算法。The traditional Black-Scholes option pricing model assumes volatility as a constant,which leads to large errors in pricing results.This paper adopts the rough Bergomi stochastic volatility model driven by fractional Brownian motion to characterize volatility surfaces in China’s financial market,then uses the daily trading data of CSI 300ETF options from January 4,2022 to December 30,2022 for empirical analysis,and finally employs neural network two-step method for parameter calibration.The results demonstrate that the pricing accuracy of Bergomi model is better than that of Heston model and BS model,while neural network two-step method outperforms the differential evolution algorithm in parameter optimization effect.

关 键 词：粗糙Bergomi模型 神经网络两步法 Heston模型 BS模型 差分进化算法 

分 类 号：F224.0[经济管理—国民经济] F830