Study On Futures Pricing And Long-term Contracts Hedging Strategy Of Commodity

In economics,a commodity is a marketable item produced to satisfy wants or needs.Often the item is fungible.Economic commodity comprise goods and services.Commodity,which plays a key role for developing industry and agricultural,is the foundation of economics.Usually,commodity trading mainly depend on long-term contracts and futures contracts for convenience and stability of trading.Long-term contracts lasts several years or even several decades,this comes with a huge risk due to the volatility of market price of commodity.So,making scientific pricing mechanism of long-term contracts of commodity is a challenging problem.There is a huge risk comes with long-term contracts because of the irrationality of pricing and volatility of market price,futures becomes an useful tool for hedging.Seeking for the optimal hedging strategy is the core for controlling risk of hedging long-term exposures.Choosing the optimal hedging strategy which can keep the terminal risk at a safe leval and control cask flow risk to minimum is the most important part in hedging long-term contracts.Our country makes influence on the word economic landscape a lot since we are a big producing,consuming and trading country of commodity.Unfortunately,we don't have much right on pricing of commodity world wide.This is a big problem in our country for development of economy.So,making scientific pricing and hedging mechanism of long-term contracts are important for our country.Based on analysis above,we focus on commodity derivatives pricing under assumptions of stochastic return and stochastic convenience yield with co-integration,and study the optimal heding strategy with short-term futures contracts for hedging long-term commodity contracts.Furthermore,we find a method to approximate the optimal hedging strategy with discrete functions,there generate the theory of commodity derivatives pricing and hedging.The results in this dissertation are as follow:First,aiming at the problem of pricing long-term contracts,we construct multi-assets pricing model and get the closed form solution.Most of the studies until now of pricing commodity futures assume that the return is a constant,and use risk free rate to represent commodity return.This assumption can 't reveal the uncertainty of payoff and substitutability of commodity.Under the assumptions of stochastic return,stochastic convenience yield and co-integration,we propose GSCR model and get the analytical solution of multi-assets of commodity derivatives pricing.Numerical results show that there is a positive relationship between the underlying asset return and its derivatives price,and a negative relationship with its substitutability derivatives price;there is a negative relationship between convenience yield and derivatives price,and a positive relationship with substitutability derivatives price.Second,since the difficulty of sloving the optimal hedging strategy for long-term contracts of commodity,we propose a discrete approximating algorithm for the approximation of the optimal hedging strategy of hedging long-term contracts.Aiming at minimizing the maximum of cash flow risk,we propose an algorithm based on approximating continuous function with discrete function,and prove the convergence of this algorithm.The result shows that we can approximate the optimal hedging strategy with this algorithm.Third,we design a multi-dimensional Newton Method for approximating the optimal hedging strategy,this unpgrading the convergencing speed heavily.Based on Newton Method and approximating continuous function with discrete function,we propose a method of finding the fast decreasing direction by gradient for approximating the optimal hedging strategy,and prove the convergence of this algorithm.The results reveals that this algorithm can approximate the optimal hedging strategy better than the former one;Fourth,analysis the optimal hedging strategy under the assumptions of Geometric Brownian Motion and Mean Reverting Process(Ornstein-Uhlenbeck Process).Assume that the underlying asset price follows the Geometric Brownian Motion and Mean Reverting Process respectively,we analysis the cash flow risk of long-term contracts hedging problem with short-term futures contracts.Results shows that the optimal hedging strategy is different from that under the assumption of Arithmetic Brownian Motion.Fifth,study the performance of several hedging strategy on commodity long-term contracts hedging.Aiming at the risk of international oil long-term contracts,we study the performance of full hedging strategy,OLS hedging strategy,VAR hedging strategy,FIVEC hedging strategy,BEKK hedging strategy,CCC-GARCH hedging strategy,DCC-GARCH hedging strategy,Copula-GARCH hedging strategy,RS-OLS hedging strategy,RS-VAR hedging strategy,RS-VEC hedging strategy and the optimal hedging strategy of minimizing the maximum of cash flow risk,based on the results of cumulative cash flow,decrease ratio of variance,average hedging ratio and sharp ratio,we find that the optimal hedging strategy of minimizing the maximum of cash flow risk can decrease cash flow risk,meanwhile,it performs well on controlling the terminal risk.