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

Abstract: 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 coefficient ε, 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; when ε<0, the expected return of spot hedging is greater than that of forward hedging; when ε=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 strategy. The empirical evidence shows that asset returns will have strong autocorrelation when the time span is around one month, which may be related to investor sentiment, market expectations, or policies. When the market is volatile, dynamic hedging can adjust the proportion of assets in the portfolio in a timely manner according to market changes, effectively hedging the risks brought by market fluctuations. However, when frequent hedging is required while considering transaction costs, this article empirically suggests that daily hedging can maximize the return on the hedging portfolio.
Against the backdrop of fluctuating international epidemics and turbulent global layout, the foreign exchange and foreign trade markets have been greatly affected. The options market in our country is still in an emerging stage, and various incomplete factors add pressure to hedging. In order to effectively reduce hedging errors and improve risk management capabilities, it is urgent to focus on the actual situation of the financial market, study foreign exchange option hedging transactions, improve and innovate hedging mechanisms. The transformation of the influencing factors of incomplete markets from qualitative description to quantitative description will be a very practical research point for future options hedging and hedging error issues.

Key words: European Options on foreign exchange, fractional Brownian motion, transaction cost, hedging error, hedging mechanism