基于动态规划原理的平方套期保值策略研究

运筹与管理 ›› 2011, Vol. 20 ›› Issue (5): 135-142.

基于动态规划原理的平方套期保值策略研究

郭建华, 肖庆宪

上海理工大学管理学院,上海 200093

收稿日期:2010-03-20 出版日期:2011-10-25
作者简介:郭建华(1975-),男,湖南邵阳人,博士研究生,研究方向:金融工程;肖庆宪(1956-),男,河南信阳人,教授,博士生导师,从事金融工程方向研究。
基金资助:
上海市重点学科建设资助项目(S30501);上海市哲学社会科学规划项目(2009BJ001)

Research on Quadratic Hedging Based on Dynamic Programming

GUO Jian-hua, XIAO Qing-xian

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2010-03-20 Online:2011-10-25

摘要/Abstract

摘要： 在自融资约束下研究了标的资产价格服从跳扩散过程时欧式未定权益的平方套期保值问题。假定套期保值者用与未定权益相关的风险资产和另一种无风险资产来进行套期保值,利用动态规划原理,得到了离散时间集上均方最优套期保值策略的显式解。文章最后通过对比分析不同期限、不同策略调整频率的欧式看涨期权的套期保值结果表明:(1)对冲头寸与期限具有相依关系,期限越长,头寸比例通常也高;(2)对冲头寸与标的资产价格呈同向变化,标的资产价格越高,可以持有的头寸比例也高;(3)对冲头寸与交割价格呈反向变化,交割价格越高,可以适当降低头寸比例。

关键词: 未定权益, 动态规划, 套期保值, 平方标准, 跳扩散过程

Abstract: Under the constraint of self-financing, this paper assumes that the underlying price obeys a jump-diffusion process and studies the quadratic hedging for European style contingent claims. During the hedging horizon[0,T], by using dynamic programming method, we first get the explicit expression of hedging strategies, which can minimize the terminal risk. Then, by comparison of all hedging results under different settings, the dependent relationship between the hedging position and the hedging horizon, the direct proportion relationship between the hedging position and the underlying asset’s price ,the inverse proportion relationship between the hedging position and the exercise price are acquired.

Key words: contingent claim, dynamic programming, hedgingl, quadratic criteria, jump-diffusion process

中图分类号:

F830.9

郭建华, 肖庆宪. 基于动态规划原理的平方套期保值策略研究[J]. 运筹与管理, 2011, 20(5): 135-142.

GUO Jian-hua, XIAO Qing-xian. Research on Quadratic Hedging Based on Dynamic Programming[J]. Operations Research and Management Science, 2011, 20(5): 135-142.

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