分别考虑期货机会成本和期权预算约束，建立最优期货和期权套期保值模型.通过构造等价鞅测度，在风险厌恶型一般效用函数下证明了模型最优解是唯一存在的，给出了求解模型的算法步骤；并在负指数效用函数下得到期货和期权最优头寸的显式表达式.实证研究表明：为规避上证50ETF价格风险，期货和期权套期保值都获得了正收益.期货（权）套期保值收益随着投资者风险厌恶系数的增加而增加（减少）.通过分析预算的影响建议风险厌恶系数较小的投资者在预算较大时选择期货套期保值，而风险厌恶系数小预算较少或风险厌恶系数较大的投资者选择期权套期保值；通过模拟金融危机情景发现随着标的价格波动的增大，期货套期保值收益增大、期权套保收益减少，建议投资者在现货价格波动较大时优先采取期货套期保值.
Abstract
Considering the opportunity cost of futures and budget constraints of options respectively, this paper establishes the optimal futures and options dynamic hedging models. By constructing the equivalent martingale measure, the optimal solutions of the models are proved to be unique under the general risk aversion utility function, then the steps of calculating optimal hedging positions are given. Furthermore, the explicit expressions of the optimal positions are obtained under the negative exponential utility function. Empirical study results indicate that:To avoid the decline risk of Shanghai 50ETF price, both futures hedging and options hedging have yielded positive returns. Meanwhile, investors' futures hedging profit increases when risk aversion coefficient increases, while options hedging profit deceases. By analyzing the impact of the budget, it is suggested that investors with smaller risk aversion coefficient and larger budget could choose futures hedging; ones with smaller risk aversion coefficient and smaller budget or with larger risk aversion coefficient could choose options hedging. According to the simulation results of a financial crisis scenario, it finds that futures hedging income increases and options hedging income decreases along with the volatility of the underlying asset price. Investors are suggested to take priority in futures hedging to match a financial turmoil scenario.
关键词
期货套期保值 /
期权套期保值 /
等价鞅测度 /
负指数效用
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Key words
futures hedging /
options hedging /
equivalent martingale measure /
negative exponential utility function
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中图分类号：
F830.9
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基金
国家自然科学基金国际（地区）合作与交流项目（71720107002）；广东省自然科学基金（2017A030312001，2014A030310454）；广州市金融服务创新与风险管理研究基地（N5150800）
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