基于O-U特征的Bachelier模型的期权定价  

Option Pricing of Bachelier Model Based on O-U Characteristics

作　　者：钱维佳 陈海枫 陈安钢 吕照进 奚雷[2] QIAN Weijia;CHEN Haifeng;CHEN Angang;LV Zhaojin;XI Lei(GuotaiJunan Securities Co.,Ltd,Shanghai 200042,China;College of Management,Anhui Science and Technology University,Chuzhou 233100,China)

机构地区：[1]国泰君安证券股份有限公司,上海200042 [2]安徽科技学院管理学院,滁州233100

出　　处：《中国证券期货》2023年第4期38-46,共9页Securities & Futures of China

摘　　要：随着“负油价”现象的出现,对于期权等衍生产品来说,标的资产负价格意味着经典Black-Scholes模型失效。本文对原始的Bachelier模型进行修改,保留标的资产价格可以为负的特点,并且使其具有Ornstein-Uhlenbeck随机过程特征。基于修正的Bachelier模型结合蒙特卡洛数值算法对欧式期权、美式期权以及障碍期权进行定价,进一步扩展其期权定价应用范围。通过数值模拟,基于修正的Bachelier模型在期权定价上表现出很高的计算精度,基于O-U特征的Bachelier模型的期权定价可以作为Black-Scholes模型期权定价的替代方案,指导期权等衍生品定价决策。With the emergence of“negative oil prices”,the negative price of underlying assets for options and other derivatives means the failure of the classic Black-Scholes model.The original Bachelier model is modified in this paper to preserve the feature that the underlying asset price can be negative and make it have the Ornstein-Uhlenbeck stochastic process feature.Based on the modified Bachelier model combined with Monte Carlo numerical algorithm to price European option,American option and Barrier option,further expand its application range of option pricing.Through numerical simulation,the modified Bachelier model shows high computational accuracy in option pricing.The option pricing of the Bachelier model based on O-U characteristics can be used as an alternative to the Black-Scholes model and guide the pricing decisions of options and other derivatives.

关 键 词：BLACK-SCHOLES模型 Bachelier模型 期权定价 障碍期权 负标的资产 

分 类 号：F83[经济管理—金融学]