根据实际投资中投资者可以选择不同到期日、不同敲定价格的期权组合进行套期保值的现实,本文建立了二次效用函数下期权组合最优动态套期保值模型,证明了该模型最优解存在的唯一性,并在协方差矩阵可逆和不可逆两种情形下分别给出了期权最优头寸的显式表达式.在50ETF价格先升后降、先降后升、下降和上升四种情形下,对上证50ETF期权的多种期权组合套期保值问题进行实证分析.研究结果表明:不同到期日不同敲定价格的看跌期权组合具有较好的套期保值效果.本文的研究为选择期权组合进行套期保值和解决展期期权套期保值问题提供了借鉴.%The investors in practice are flexible to choose options portfolio with different maturity dates or strike prices to hedge risk.This paper proposes the optimal dynamic hedging of options portfolio under quadratic utility function.Unique existence of the optimal solutions to the models are proved and the expressions of optimum posi-tions of option are formed under two cases of reversible and irreversible covariance matrix.Empirical analysis of different option portfolios on Shanghai 50ETF are implemented under four market conditions(i.e.first rising then falling,first falling then rising, falling and rising).The research results indicate that it has better effects using options portfolio with different maturity dates and strike prices.The research in this paper provides refer-ence for the selection of options portfolio in hedging and hedging researches of extendible option.
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