Modeling of Gold coin futures with stochastic differential equations

The capital market is one of the financial markets that in a dynamic economy can pave the way for long-term economic growth.Futures contracts that derive their values from an underlying asset, are included these financial instruments.To enter the futures market, the investor needs to anticipate future trends to cover his risk. For this purpose, the appropriate random differential equation has been selected to model the prediction of future coin contracts in the present study. Thus, after providing the necessary explanations about the necessity of using random models and as a result of new principles called random accounts, to introduce the most important stochastic differential equation in financial sciences including geometric Brownian, geometric Brownian with jump term, Heston and the explained model are discussed. Then, the appropriate model is selected, with a practical approach and based on the ability of each model to predict the price of futures contracts by assembling the Monte Carlo. The results of the fitness criteria regarding the predictive power indicate the superiority of the model explained in these contracts.