Commodity Futures Options Pricing Model With Double-Exponential Jump And Convenience Yield And Its Application

With the rapid development of China commodity futures trading market in the last two years,relevant risk management is becoming more and more prominent.Owing to the effectiveness of commodity futures options to avoid the varying basis risk,how to construct an effective commodity price model to realize accurate futures options pricing and risk hedging has become one of the most challenging and practical research topics in financial academic and industrial world.The construction of commodity price model needs to be realistic.The stochastic phenomena and mean recovery of commodity convenience yield have become the consensus in the field of commodity derivatives pricing.At the same time,jump as an observable and interpretable price behavior,is also favored by scholars.Most of the existing studies have added Merton jump to the Schwartz(1997)two factor model to describe the mean recovery of convenience yield and the discontinuous change of price.However,the model can't explain the asymmetry jump of commodity price and the distribution features of commodity returns such as peak,fat tail and skewness.In this paper,we introduce the stochastic convenience yield following the OU Process(Ornstein-Uhlenbeck Process,short of OU Process),to depict the incomplete basis between commodity futures price and commodity price,and combines the double-exponential jump to describe the jump behavior,then,the Two Factor model with double-exponential jump(short of Two-Factor-DBEJ model)is constructed.Further,the expression of commodity futures price and the characteristic function of log-asset price are obtained by mathematical derivation.Furthermore,the quasi-analytical expression of commodity futures options price under the Two-Factor-DBEJ model is derived according to the Fourier-Cosine method.To verify the pricing performance and practical value of the Two-Factor-DBEJ model,in this paper,the prices of copper futures options is used to correct the parameters,calculate the theoretical prices and design corresponding Delta hedging strategy.Empirical results show that,Two-Factor-DBEJ model outperforms other models,especially for out-of-money options,asymmetric double-exponential jump can significantly improve the pricing effect of two factor model with stochastic convenience yield.Furthermore,the Delta hedging strategy based on the Two-Factor-DBEJ model shows superior hedging performance.This paper is expected to provide new risk management ideas and pricing tools for commodity futures and commodity futures options markets in China.