Binomial American Option Step

Problem

Take one backward-induction step for an American put in a binomial tree.

With up and down factors u, d, risk-neutral probability p, rate r, and step dt, the continuation value is exp(-r * dt) * (p * max(K - S * u, 0) + (1 - p) * max(K - S * d, 0)) and the exercise value is max(K - S, 0). Return [exercise, continuation, max(exercise, continuation)].

Hint

Early exercise has value when the immediate payoff exceeds the discounted continuation.

Test cases

case 1

in: [100,100,1.1,0.9,0.05,1,0.5]

expected: [0,4.75614712250357,4.75614712250357]

case 2

in: [80,100,1.1,0.9,0.05,1,0.5]

expected: [20,19.02458849001428,20]

case 3

in: [120,100,1.1,0.9,0.05,1,0.5]

expected: [0,0,0]

Starter codePython

def binomial_american_step(S, K, u, d, r, dt, p):
    # Returns [exercise, continuation, value]
    # Your code here
    pass

3 test cases · run your code against them in the editor