混合次分数布朗运动下的欧式外汇期权定价  

Pricing of European Foreign Exchange Options Under Mixed Sub-fractional Brownian Motion

作　　者：王欣怡 李其珂 王威 WANG Xinyi;LI Qike;WANG Wei(School of General Education,Nantong Institute of Technology,226002,Nantong,Jiangsu,China)

机构地区：[1]南通理工学院基础教学学院,江苏南通226002

出　　处：《淮北师范大学学报（自然科学版）》2024年第4期13-18,共6页Journal of Huaibei Normal University：Natural Sciences

基　　金：江苏高校哲学社会科学研究项目(2022SJYB1750,2023SJYB1714)。

摘　　要：相较于传统分数布朗运动,混合次分数布朗运动能够更好地刻画标的资产价格长程相关性的特征。以混合次分数布朗运动作为随机驱动源建立欧式外汇期权定价模型,利用Delta对冲技巧,得到该模型下欧式外汇期权所满足的混合次分数阶偏微分方程,最后给出外汇期权定价的解析公式和数值计算。计算结果表明:欧式看涨外汇期权在布朗运动下的价格较高;当敲定价格和到期日增大时,混合次分数布朗运动模型与G-K模型下的期权价格之差也在不断增大。该定价模型具有一定的合理性,投资者可以通过优化投资策略以降低潜在风险。Compared with the traditional fractional Brownian motion,the mixed sub-fractional Brownian mo-tion can better capture the long-range correlations of the underlying asset price.In this paper,the mixed sub-fractional Brownian motion is used as the random driving source to establish a pricing model for Europe-an foreign exchange options.By using the Delta hedging technique,the mixed sub-fractional partial differen-tial equation for European foreign exchange options under our model is obtained.Finally,the analytical for-mula and numerical calculation for foreign exchange options are given.The calculation results show that the price of European call foreign exchange options is higher under Brownian motion.Moreover,the difference in price between the mixed sub-fractional model and the G-K model is also increasing with the exercise date increase.Therefore,the pricing model has certain rationality,and investors can reduce potential risks by optimizing their investment strategies.

关 键 词：期权定价 混合次分数布朗运动 欧式外汇期权 数值模拟 

分 类 号：F830.9[经济管理—金融学]