A derivative[dɪˈrɪvətɪv](金融)衍生工具(产品)  is a contract whose payoff depends on the value of some underlying asset. In cases where closed-form derivative pricing may be complex or even impossible, numerical procedures excel. A numerical procedure is the use of iterative computational methods in attempting to converge to a solution. One such basic implementation is a binomial tree. In a binomial tree, a node represents the state of an asset at a certain point of time associated with a price. Each node leads to two other nodes in the next time step. Similarly, in a trinomial tree, each node leads to three other nodes in the next ti