Binomial trees in option pricing

In the binomial option 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 S₀ of the underlying security with a risk-neutral probability of increase q, and a risk-neutral probability of loss 1-q, at the next time step. 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...