金融资产价格具有“尖峰厚尾”和长期记忆等分形特征,采用具有GARCH结构的时变混合双分数Brown运动可以描述其动态变化过程。首先,构建混合双分数Brown运动下的期权定价模型和时变参数模型;再选取上证50ETF指数、香港恒生指数、日本东证指数的历史收盘价进行实证分析,并与传统的BS模型、混合双分数Brown运动定价等模型进行对比研究。结果发现:时变混合双分数Brown运动下的欧式期权定价模型在期权定价精度方面具有明显优势,特别是在发达证券市场上表现更好,同时具有较强的预测能力。对金融衍生品、风险管理、投资管理等方面都具有一定的参考意义和实用价值。Financial asset prices have fractal characteristics such as “sharp peaks and thick tails” and long-term memory, and its dynamic process can be described by the time-varying mixed double-fractional Brownian motion with GARCH structure. Firstly, the option pricing model and the time-varying parameter model are constructed under the hybrid two-fractional Brown’s motion;then, the historical closing prices of SSE 50 ETF index, Hong Kong Hang Seng index, and Japan TSE index are selected for the empirical analysis, and compared with the traditional BS model and the hybrid two-fractional Brown’s motion pricing model. The results show that the European option pricing model with time-varying hybrid bifractional Brownian motion has obvious advantages in terms of option pricing accuracy, especially in the developed stock markets, and has strong forecasting ability. It has certain reference significance and practical value for financial derivatives, risk management and investment management.
