Research On Dynamic Hedge Models Of Options And Their Applications

Option hedging means we can make up the possible loss of futures or spot with the gain of established option position to achieve the goal of locking price changes and other risks,which can be used to match futures or spot positions.Although the usage of option hedging is popular in the world,it is still new business in China.In February 9,2015,China’s first exchange traded options--Shanghai 50 ETF options came into the market.And in March 31,2017 the first domestic commodity options-meal options came out.With the development of China’s financial market,more options will appear in the future.More and more investors and enterprises will choose options as hedging tools to avoid the investment risks they face.Although options play an important role in risk management and asset allocation,their nonlinear characteristics also bring different experiences in hedging to people working on this,but it doesn’t mean option is a perfect tool in hedging.On the whole,as a new tool,although options are superior to futures or long-term in fitness and risk control,it’s hard to handle it in hedging.Improper use or rash participation is likely to cause huge losses for investors.When the hedgers face many real situations,such as different underlyings,different maturities,different options,and the cost contrant of the option,how to use options to hedge rationally has become a hot issue in both the theoretical and practical fields.This paper studies dynamic hedging options in theory and practice comprehensively,and constructs option dynamic hedging model,then figures out the option optimal hedging strategy,combined with the empirical analysis of the risk management decision reference for investors.The main work and the innovative parts are summarized as follows:(1)We propose the optimal options hedging models with portfolio of multi-underlying assets or multi-options for the risk management problem of a portfolio of various underlying assets.The uniqueness of optimal solutions of the models under the general risk aversion utility function is proven by constructing the equivalent martingale measure and the steps to calculate optimal hedging positions are given.Then,the explicit expressions of the optimal positions are obtained under the negative exponential utility function.The empirical analysis indicates that using options to hedge yields positive returns and decreases investment risk.(2)We propose the optimal dynamic hedging of options portfolio under quadratic utility function for the diversification selection of options.The uniqueness of the optimal solutions of the models is proven and the expressions of optimum positions of option are formed under two cases of reversible and irreversible covariance matrix.Based on four cases: first rising then falling,first falling then rising,falling and rising,the empirical analysis of different option portfolios shows that put options with different strike prices and different maturity dates have better effects on hedging on different market.The research in this paper provides reference to select options portfolio in hedging and solve problems in hedging researches of extendible option.(3)This paper puts forward the criterions of exiting investment and making adjustment on the problems existing in traditional option hedging strategy such as miss the best opportunity to exit investment or make too frequent relocations.It further optimizes the traditional strategy of option hedging.The optimal dynamic hedging model is established on the basis of VaR(Value at Risk)by fulfillment the conditions of enough budget,anticipated profit and good position.Traditional dynamic hedging strategy is formed.Based on the above,to quantize the value of risks and cost from the aspect of economic value of risks and formulate the criterion of exit investment and relocations by end-term performance evaluation.Option hedging strategy is further rectified.The result shows that the discretion criterion of exit will provide the reference timing to exit investment.Discretion criterion of relocation will decrease the cost of relocation by reducing the unnecessary relocations.Defects in traditional dynamic option hedging strategy is discovered through comparisons.Therefore,optimal hedging model which takes dual-discretion into consideration improved the single-discretion in traditional model.It proposes a more effective strategy in risk control.More importantly,it has more significance in practice when investors are making their decisions.(4)From the perspective of the portfolio of underlyings and options,this paper puts forward a dynamic hedging model with options based on Copula-GARCH method.At present,many researches have applied the Copula-GARCH method to portfolio selection or futures hedging models.Few methods have been applied to the study the problem of options hedging.Different from the existing literature that adopt the numerical simulation method,this paper deduces the distribution function of the hedged portfolio by using Copula-GARCH method.Based on improved lower partial moment(LPM)and the distribution function,we further calculates the extreme risk.The results show that setting the target return in LPM be the return median rather than the expected return is good for investors to prudent investment.For the purpose of reducing the extreme risk,investors with less budget should choose at-the-money put options hedging while those with higher budget can choose in-the-money put options.The latter shall consider an appropriate strike price which is comparatively lower than others.(5)From the angle of options and futures,the dynamic programming method is used to establish the multi-stage dynamic hedging model of options.Considering the common coexistence of linear and nonlinear investment risk in the reality,this paper proposes the dynamic hedging model of options and futures and proves the necessity of hedging nonlinear risk by options.Furthermore,under the quadratic utility,we present the optimal positions of options and futures by the dynamic programming method.The empirical study results show that relative to no hedging,the risk of loss is reduced by futures and options hedging and the volatility in the process of wealth accumulation is also effectively controlled.