摘要
把终期的期望亏损定义为风险,研究了标的资产价格服从跳扩散结构时的自筹资最小亏损风险套期保值.首先通过Monte-Carlo模拟生成标的资产若干条价格路径并用所有路径上的终期亏损平均值作为优化目标期望值的估计,然后引入基函数作为套期保值头寸的近似逼近,最后通过数值方法得到最优套期保值策略.最后通过实例分析表明:1)套期保值头寸调整的频率相对较高时,可以更好地应对市场出现的价格波动,从而降低可能面临的损失风险,达到较好的保值效果;2)欧式看涨期权的交割价格与对冲头寸呈反向变化,交割价格越高,可适当调低持有的对冲头寸,反之则反,这样,即对冲风险又节约成本.
Look on the terminal expected shortfall as risk, we study the optimal self-finance hedging strategy with minimum shortfall risk when the underlying asset＇s price obeys a jump-diffusion process. At first, by monte-carlo simulation, we generate thousands of the underlying asset＇s price paths and estimate the expected shortfall with averaged terminal shortfall on all simulated price paths; Then, basis functions are introduced to approximate the hedging positions and lastly, these optimal hedging positions are acquired by numerical method. Finally, demonstration shows that： higher strategy adjusting frequency may more excellently resist market＇s fluctuating and there is a reverse relationship between European call option＇s strike price and hedging position.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第7期41-50,共10页
Mathematics in Practice and Theory
基金
上海市重点学科建设资助项目(S30501)
关键词
套期保值
亏损风险
蒙特卡罗模拟
数值方法
跳扩散过程
hedging
shortfall risk
monte-carlo simulation
numerical methods
jumpdiffusion process
