Terminal Payoff Calculation

Terminal payoff calculation is the initial step in valuing a derivative, involving the determination of the contract's value at the exact moment of expiration. At this final time point, the option's value is purely intrinsic, meaning it is simply the difference between the strike price and the underlying asset price, or zero if the option is out of the money.

This value serves as the boundary condition for all subsequent backward induction steps. By establishing these terminal values across all possible price scenarios at expiration, the model creates a baseline from which the values at earlier time steps are derived.

This process is critical because the accuracy of the entire pricing model depends on the correct specification of these final outcomes. It represents the ultimate resolution of uncertainty, where the path taken to reach that point is no longer relevant, only the final relationship between the asset price and the strike price.