分形市场下含交易费用的外汇欧式期权对冲研究  

Research on Foreign Exchange European Option Hedging with Transaction Costs in Fractal Market

作　　者：李志民[1] 侯婷婷 何瑞彬 程鹏翔[1] LI Zhimin;HOU Tingting;HE Ruibin;CHENG Pengxiang(School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China)

机构地区：[1]安徽工程大学数理与金融学院,安徽芜湖241000

出　　处：《运筹与管理》2024年第10期152-158,共7页Operations Research and Management Science

基　　金：国家自然科学基金面上项目(61873294);安徽高校省级自然科学研究重大项目(KJ2019ZD16)。

摘　　要：针对实际交易情形综合多个不完备市场因素,研究外汇欧式期权对冲交易过程,以切实提高风险识别和管理能力。首先基于外汇的分数布朗运动假设,分别采用即期和远期两种方式进行静态和动态的离散Delta对冲,推演考虑交易成本的离散对冲组合价值。其次,融合含摩擦系数的修正利率平价公式推导理论对冲误差公式。最后,实证模拟期权对冲过程并探寻最优对冲策略和最优对冲频率,检验说明误差公式具有合理性,每日对冲能够更好地平衡误差风险和成本支出之间的关系。This article focuses on actual trading situations and integrates multiple incomplete market factors,including the fusion of modified interest rate parity formulas,the use of fractal market assumptions to characterize asset return autocorrelation,and the adoption of discrete hedging methods that consider transaction costs.From the perspective of option sellers,it explores the hedging errors and strategies of foreign exchange European Options,in order to effectively improve risk identification and management capabilities.Firstly,based on the fractional Brownian motion assumption of foreign exchange,static and dynamic discrete Delta hedging are conducted using both spot and forward methods,and the value of the discrete hedging portfolio considering transaction costs is derived.Static hedging refers to only conducting Delta hedging once at the beginning of an option transaction.When the expected exchange rate price trend is stable,the static hedging strategy will be easy to operate and effectively save costs.Dynamic hedging strategy is to conduct multiple Delta hedging during the option term.When the expected trend fluctuates,the dynamic strategy can timely track the market situation and flexibly avoid risks.Secondly,by integrating the modified interest rate parity formula into the friction coefficientε,a theoretical hedging error formula is derived.In the fractal market,the friction coefficient in the modified interest rate parity formula is tested by the Monte Carlo simulation of the hedging process.In the fractal market,when considering transaction costs,it still has certain practical reference value for determining the optimal hedging method:when 0<ε<1,the expected return of forward hedging is greater than that of spot hedging;whenε<0,the expected return of spot hedging is greater than that of forward hedging;whenε=0,the two hedging methods are equally effective.At the same time,we adjust the hedging frequency by considering the discrete hedging method of transaction costs,and explore the optimal hedging stra

关 键 词：外汇欧式期权 分数布朗运动 交易费用 对冲误差 对冲机制 

分 类 号：F830.92[经济管理—金融学]