外汇欧式期权在市场不完备下的对冲误差分析  

Hedging error analysis of foreign exchange European options under incomplete market

作　　者：彭程 李爽 包莹 赵延龙[1,2] PENG Cheng;LI Shuang;BAO Ying;ZHAO Yanlong(The Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Risk Management Department,Industrial and Commercial Bank of China,Beijing 100032,China)

机构地区：[1]中国科学院数学与系统科学研究院系统控制重点实验室,北京100190 [2]中国科学院大学数学科学学院,北京100049 [3]中国工商银行总行风险管理部,北京100032

出　　处：《系统工程理论与实践》2019年第11期2739-2749,共11页Systems Engineering-Theory & Practice

基　　金：国家重点研发计划项目(2018YFA0703800);国家自然科学基金(61622309)~~

摘　　要：本文研究了外汇欧式期权的对冲误差问题,针对典型的静态和动态Delta对冲策略,在对冲过程不连续和利率平价公式不成立的市场不完备情形下,给出了即期对冲和远期对冲的对冲误差公式,从而能够更准确地衡量实际对冲组合产生的风险.在研究Delta对冲策略过程中,本文提出了一个包含摩擦系数ε的外汇远期汇率模型,并通过分析即期对冲和远期对冲的差异,给出了最优对冲方式的判别条件.该判别条件依赖于摩擦系数ε,做市商仅通过对摩擦系数ε实时的监控,便可以选择最优的风险对冲方式,从而提高了对冲效率.本文提出的对冲误差的具体解析式和最优对冲方式的判别条件为外汇期权对冲及其风险管理提供了理论依据.实证结果表明,本文提出的期望收益差与实际对冲组合的收益差基本一致,从而验证了判别条件的合理性.This paper studies the hedging error of foreign exchange options.In respect of the typical static and dynamic Delta hedging strategies,under the circumstance of incomplete market,in which hedging process is discontinuous and interest rate parity theory is not established,the hedging error formulas of spot hedging and forward hedging are given,which can be used to measure the risk of actual hedging portfolio more accurately.In the process of studying Delta hedging strategies,this paper presents a forward exchange rate model including the friction coefficientε.And by analyzing the difference between the spot hedging and forward hedging,a criterion for choosing the optimal hedging method is given.The criterion depends on the friction coefficientε,so the market maker can choose the optimal risk hedging method only through real-time monitoring of friction coefficientε,thus improving the hedging efficiency.The specific analytic formula of hedging error and the criterion of optimal hedging method proposed in this paper provide theoretical basis for foreign exchange option hedging and its risk management.The empirical results show that,the expected return difference proposed in this paper is basically consistent with the actual hedging portfolio,which verifies the rationality of the criterion.

关 键 词：外汇欧式期权 Delta对冲 对冲误差 摩擦系数 

分 类 号：F830.92[经济管理—金融学]