Binomial trees in options pricing

In the binomial options pricing model, the underlying security at one time period, represented as a node with a given price, is assumed to traverse to two other nodes in the next time step, representing an up state and a down state. Since options are derivatives of the underlying asset, the binomial pricing model tracks the underlying conditions on a discrete-time basis. Binomial option pricing can be used to value European options, American options, as well as Bermudan options.

The initial value of the root node is the spot price of the underlying security with a given probability of returns should its value increase, and a probability of loss should its value decrease. Based on these probabilities, the expected values of the security are calculated for each state of price increase or decrease for every time step. The terminal nodes represent every value of the expected security prices for every combination of up states and down states. We can then calculate...