模糊环境下的股指期货套期保值优化模型

发布时间：2018-08-27 15:23

【摘要】：股指期货是以股票指数为标的的期货合约，它是资本市场中系统风险的主要避险工具之一。2010年4月16日，我国正式推出沪深300股指期货合约，它的推出将对我国股市产生重要影响。套期保值是股指期货的主要功能之一，如何更好的运用股指期货套期保值，如何确定更加合理的套期保值比率达到预期效果仍需要进一步的研究。自1952年Markowitz运用数量化方法创立了投资组合理论，为风险管理领域研究拉开了新的篇章。数量化研究进入金融领域以后，人们多采用随机不确定性对套期保值过程进行研究，但是市场参与者在套期保值过程中所面临的不确定性还包括模糊不确定性，且现实世界中的不确定性大多数为模糊不确定性。针对现有问题，本文主要工作从以下三个方面展开：首先，在最小方差和兼顾风险收益两个套期保值策略下，考虑历史数据的局限性，结合模糊方法，建立模糊环境下的最小方差套期保值模型和模糊环境下兼顾风险收益的套期保值模型。根据数理推导求解两模型，并采用与套期保值策略相对应的测度检验套期保值效果。其次，由于套期保值者需要在综合考虑套期保值策略的交易成本、交易限制和资金约束等现实要求基础上选择相应策略。这里在所建立的两模糊套期保值优化模型基础之上，选择适当变量刻画交易成本和资金约束，分别建立两个模糊环境下考虑交易限制的套期保值调整模型和两个模糊环境下考虑资金约束的套期保值调整模型。采用数理方法等方法进行求解，并与不考虑这些限制的套期保值效果进行对比。最后，，基于前面单阶段模糊环境下的套期保值模型，延展至多阶段的模糊套期保值研究，给出了模糊环境下系列展期套期保值模型。通过建立交叠合约的风险函数以逆序递推法求解期货合约各个阶段的最优套期保值比率，检验套期保值效果并对比分析。算例结果表明，上述几种套期保值模型能够提供灵活的套期保值策略，从而为我国资本市场上的机构投资者和个人投资者的投资决策提供有力的参考。
[Abstract]:Stock index futures is a futures contract with stock index as its target. It is one of the main hedging tools for systematic risk in the capital market. On April 16, 2010, China officially launched the Shanghai and Shenzhen 300 stock index futures contract. Its introduction will have an important impact on China's stock market. Hedging is one of the main functions of stock index futures, how to better use stock index futures hedging, how to determine a more reasonable hedge ratio to achieve the desired results still need further research. Since 1952, Markowitz has established portfolio theory by quantitative method, which has opened a new chapter for the research of risk management. After quantitative research has entered the financial field, people often use random uncertainty to study the hedging process, but the uncertainty that market participants face in the hedging process also includes fuzzy uncertainty. And the uncertainty in the real world is mostly fuzzy uncertainty. Aiming at the existing problems, the main work of this paper is as follows: firstly, considering the limitations of historical data and combining the fuzzy method with the minimum variance and the risk-return hedging strategy, The minimum variance hedging model in fuzzy environment and the hedging model in fuzzy environment are established. The two models are solved by mathematical derivation, and the hedging effect is tested by the measure corresponding to the hedging strategy. Secondly, the hedgers need to choose the corresponding strategies on the basis of considering the transaction costs, transaction constraints and capital constraints of the hedging strategy. Based on the two fuzzy hedging optimization models, the appropriate variables are selected to describe transaction costs and capital constraints. A hedging adjustment model with transaction constraints under two fuzzy environments and a hedging adjustment model with capital constraints under two fuzzy environments are established respectively. The numerical method is used to solve the problem, and the results are compared with those without these limitations. Finally, a series of extended hedging models are proposed based on the previous one-stage fuzzy hedging model, which extends the fuzzy hedging model at most stages. By establishing the risk function of overlapping contracts and solving the optimal hedging ratio in each stage of futures contracts by inverse order recursive method, the effectiveness of hedging is tested and compared. The numerical results show that the above models can provide flexible hedging strategies and provide a powerful reference for institutional and individual investors in China's capital market.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.5;F224

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