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What Is the Maximum Value of a Put Option, and How Does This Relate to Early Exercise?

The maximum value of a put option is its strike price. This occurs if the underlying asset's price falls to zero, making the intrinsic value equal to the strike price.

This maximum value is relevant to early exercise because if the put is deep in-the-money and near its maximum value, the incentive to exercise early and lock in the profit is very high.

What Is an ‘Out-of-the-Money’ (OTM) Option?
How Does the Prevailing Interest Rate Environment Affect the Early Exercise Decision for a Put Option?
Does Theta Decay Affect In-the-Money, At-the-Money, and Out-of-the-Money Options Equally?
How Does the Concept of ‘In-the-Money’ Relate to the Decision to Exercise an American Put Option Early?