[Verse 1] Start with one period, now we extend the tree Two steps forward, more complexity Up and down movements, prices can go Building our branches, watch the model grow From today's value, we map each path Working with probabilities, doing the math [Chorus] Two periods forward, then backwards we go From final to first, let the values flow Up-up, up-down, down-up, down-down Four possible endings when we break it down Backward induction, that's the key From leaves to the root of our pricing tree [Verse 2] At each final node, we know the price Calculate payoffs, roll the dice European style means wait till the end But American options have rules that bend At every node we must compare Exercise now or wait and bear [Chorus] Two periods forward, then backwards we go From final to first, let the values flow Up-up, up-down, down-up, down-down Four possible endings when we break it down Backward induction, that's the key From leaves to the root of our pricing tree [Bridge] Early exercise, check at each step Compare intrinsic value, which one to accept Present value of waiting or exercise today The higher value shows us the way Risk-free rate for discounting back Keep the tree balanced, stay on track [Verse 3] From period two back to period one Weight by probabilities till we're done Each node's value is crystal clear Discount and weight as we draw near The root reveals our option's worth Two-period model, for what it's worth [Final Chorus] Two periods forward, then backwards we go From final to first, let the values flow Up-up, up-down, down-up, down-down Four possible endings when we break it down Backward induction, that's the key From leaves to the root of our pricing tree Master the model, now you can see The power of binomial pricing, set yourself free
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