独立增量过程下亚式期权的方差最优对冲策略  

Variance-optimal Hedging for Asian Options under Independent Increments Processes

作　　者：贾兆丽[1] 杨舒荃 吴霍俊 JIA Zhaoli;YANG Shuquan;WU Huojun(School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《应用数学学报》2022年第5期767-780,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上资助项目(72071068)。

摘　　要：方差最优对冲策略是金融市场中控制风险的重要工具.文章以几何平均亚式看涨期权为例,假设标的资产的价格服从离散时间下的独立增量过程,得到了标的资产价格的F?llmerSchweizer分解,进而推导出了亚式期权的方差最优对冲策略,以及相应的方差最优对冲误差.该方法可以应用于二因子模型等独立非平稳增量的情况,为投资者、金融机构提供了更有效的计量模型,同时加深了人们对风险管理的认识.Variance-optimal hedging is a vital tool to manage risks in the financial market.This paper takes the geometric average Asian option as an example,assuming that the price of the underlying assent follows the discrete time process with independent increments,and a.Follmer-Schweizer decomposition of the price of the underlying assent is presented.In this way,we derive variance optimal hedging strategies of Asian options,and the corresponding variance optimal hedging error respectively.Furthermore,this method can be used in the two factors model and other non-stationary independent increments processes.It will be provided for investors and financial institutes with more efficient measurement models,and enhance people’s understanding on risk management.

关 键 词：方差最优对冲 亚式期权 F?llmer-Schweizer分解 独立增量 

分 类 号：O211.63[理学—概率论与数理统计]