【摘要】：股指期貨是以股票指數(shù)為標(biāo)的的期貨合約，它是資本市場(chǎng)中系統(tǒng)風(fēng)險(xiǎn)的主要避險(xiǎn)工具之一。2010年4月16日，我國(guó)正式推出滬深300股指期貨合約，它的推出將對(duì)我國(guó)股市產(chǎn)生重要影響。套期保值是股指期貨的主要功能之一，如何更好的運(yùn)用股指期貨套期保值，如何確定更加合理的套期保值比率達(dá)到預(yù)期效果仍需要進(jìn)一步的研究。 自1952年Markowitz運(yùn)用數(shù)量化方法創(chuàng)立了投資組合理論，為風(fēng)險(xiǎn)管理領(lǐng)域研究拉開(kāi)了新的篇章。數(shù)量化研究進(jìn)入金融領(lǐng)域以后，人們多采用隨機(jī)不確定性對(duì)套期保值過(guò)程進(jìn)行研究，但是市場(chǎng)參與者在套期保值過(guò)程中所面臨的不確定性還包括模糊不確定性，且現(xiàn)實(shí)世界中的不確定性大多數(shù)為模糊不確定性。針對(duì)現(xiàn)有問(wèn)題，本文主要工作從以下三個(gè)方面展開(kāi)： 首先，在最小方差和兼顧風(fēng)險(xiǎn)收益兩個(gè)套期保值策略下，考慮歷史數(shù)據(jù)的局限性，結(jié)合模糊方法，建立模糊環(huán)境下的最小方差套期保值模型和模糊環(huán)境下兼顧風(fēng)險(xiǎn)收益的套期保值模型。根據(jù)數(shù)理推導(dǎo)求解兩模型，并采用與套期保值策略相對(duì)應(yīng)的測(cè)度檢驗(yàn)套期保值效果。 其次，由于套期保值者需要在綜合考慮套期保值策略的交易成本、交易限制和資金約束等現(xiàn)實(shí)要求基礎(chǔ)上選擇相應(yīng)策略。這里在所建立的兩模糊套期保值優(yōu)化模型基礎(chǔ)之上，選擇適當(dāng)變量刻畫(huà)交易成本和資金約束，分別建立兩個(gè)模糊環(huán)境下考慮交易限制的套期保值調(diào)整模型和兩個(gè)模糊環(huán)境下考慮資金約束的套期保值調(diào)整模型。采用數(shù)理方法等方法進(jìn)行求解，并與不考慮這些限制的套期保值效果進(jìn)行對(duì)比。 最后，，基于前面單階段模糊環(huán)境下的套期保值模型，延展至多階段的模糊套期保值研究，給出了模糊環(huán)境下系列展期套期保值模型。通過(guò)建立交疊合約的風(fēng)險(xiǎn)函數(shù)以逆序遞推法求解期貨合約各個(gè)階段的最優(yōu)套期保值比率，檢驗(yàn)套期保值效果并對(duì)比分析。 算例結(jié)果表明，上述幾種套期保值模型能夠提供靈活的套期保值策略，從而為我國(guó)資本市場(chǎng)上的機(jī)構(gòu)投資者和個(gè)人投資者的投資決策提供有力的參考。
[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.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：F832.5;F224

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