How do I price an American put option using a binomial tree?

Question

AcadiFi · Accepted Answer

American put pricing on a binomial tree requires checking the early exercise condition at every node during backward induction. Consider a 3-month put on Ironwood Energy at $58, strike $60, volatility 32%, risk-free rate 4.2%, and three time steps. The up factor u = exp(0.32*sqrt(0.0833)) = 1.097, down factor d = 0.911, and risk-neutral probability p = (exp(0.042*0.0833) - 0.911) / (1.097 - 0.911) = 0.497. Build the stock tree, compute terminal payoffs max(60 - S_T, 0), then at each earlier node compute the continuation value as exp(-r*dt)*[p*V_up + (1-p)*V_down] and compare to immediate exercise max(60 - S, 0). The node value is the maximum. For deep in-the-money nodes, early exercise often dominates because you capture intrinsic value and earn interest on the strike. Without early exercise check, you'd underprice the American put by 3-8% depending on moneyness and maturity. ```mermaid graph TD A[Node
S=58] --> B[V_cont] A --> C[V_exercise
max K-S,0] B --> D[Take max] C --> D ``` For more tree-based pricing, explore our FRM Part I derivatives course.

How do I price an American put option using a binomial tree?

Master Part I with our FRM Course

Related Questions

Practice Questions