Stock Index Futures Hedging Optimal Model Under Fuzzy Environment

Stock index futures are the stock index as the subject of the financial futures. Itis one of the hedging instruments to avoid the systemic risk in the capital market. Chinafirstly launch Hu-shen300stock index at April16. It has a major impact on China’sstock market. Hedging is one of the main functions of the stock index futures. Thefurther studies are how to us stock index futures on the hedging and how to determine amore reasonable hedge ratio to achieve the desired results.Since1952, Markowitz created portfolio theory by using the quantitativemethods, and the theory opened a new chapter in the filed of risk management. Afterquantitative research has been used in the financial fields, researchers had a series ofstudies on the theoretical model and financial econometrics. However, in fact, thehistorical data often have some limitations.Firstly, to consider that historical data are finite and discontinuity, we quote thefuzzy method under minimum variance hedging strategy and considered both the returnand risk hedging strategy, furthermore, we separately set the minimum variancehedging model and considered both the return and risk hedging model under the fuzzycircumstances. Empirical results show that the models are effective.Secondly, a hedger need to choose a hedging strategy based on some realisticrestriction, such as transaction cost, transaction restriction, capital restraint, and so on.Based on the former fuzzy method, we select the appropriate variables to portraythe transaction costs and capital constraints, thus, we establish two kinds of models:fuzzy hedging model based on transaction costs and fuzzy hedging model based oncapital constraints. We solve the models with mathematics methods and make somecomparative analysis.Finally, based on the minimum variance hedge model in front of single-stagefuzzy environment, we extend the single-period fuzzy hedge to fuzzy Multiperiodrolling hedge, so the series of rollover hedging model under the fuzzy environment isset.Empirical results show that the former models can provide not only an accurateprice of convertible bonds but also a flexible investment strategy, by then investorscould be with strong investment information.