白糖期权因其独特的市场特征和定价难度,成为期权定价研究的重要对象。本文基于郑州商品交易所公布的2023年白糖期权数据,利用二叉树定价模型对白糖期权进行定价研究。同时,将基于二叉树模型所计算出的白糖期权理论价格与市场真实期权价格进行对比分析。研究发现:一是二叉树模型能够较为精准地反映白糖期权的定价趋势,但通过该模型计算得到的理论价格与实际市场价格之间仍存在一定的差异;二是白糖看涨期权的MAPE和MAE较白糖看跌期权的MAPE和MAE低;三是以白糖看涨期权为例,随着行权价格的逐步提高,其MAE和MAPE的曲线偏离程度增加。通过本研究,期望能为白糖期权市场的定价提供理论支持,并为相关金融产品的创新和发展贡献力量。Due to its unique market characteristics and pricing difficulty, white sugar option has become its important object of option pricing research. Based on the data of sugar options in 2023 released by Zhengzhou Commodity Exchange, this paper studies the pricing of white sugar options by using the binary tree pricing model. Meanwhile, the theoretical price of sugar option based on the binary tree model and the real option price in the market are analyzed. The study shows that the binary tree model can accurately reflect the pricing trend of sugar option, but there is still some difference between the theoretical price calculated by the model and the actual market price;second, the MAPE and MAE of sugar call option are lower than the MAPE and MAE of sugar put option;and with sugar call option as an example, the curve deviation of MAE and MAPE increases with the gradual increase of the exercise price. Through this study, it is expected to provide theoretical support for the pricing of the white sugar options market, and to contribute to the innovation and development of related financial products.
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.
