基于动态规划原理的平方套期保值策略研究

Research on Quadratic Hedging Based on Dynamic Programming

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。

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,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.