Backward Induction

Backward induction is a recursive optimization method used in game theory and financial modeling to determine the optimal strategy or value by starting from the final state of a process and working backward to the present. In the context of options pricing, it involves calculating the option payoff at the expiration date for all possible asset prices at that final time step.

Once these terminal values are known, the model moves one step back in time to compute the value of the option at the preceding nodes, typically by calculating the discounted expected value of the future payoffs. This process repeats until the current time is reached, yielding the theoretical fair value of the derivative today.

This technique is essential for valuing American options, where the model compares the value of holding the option against the value of exercising it immediately at each node. By systematically evaluating future possibilities, it ensures that optimal decision-making is captured throughout the life of the instrument.