Why an American Put Can Be Worth More Than Its Exercise Payoff

Summary

The note explains why an American put’s value can exceed the amount available from exercising it immediately. The payoff is a lower bound: the holder can exercise and receive that amount, or keep the option alive. The right to choose later has value because the underlying price may move further in a favorable direction before expiration.

The answer compares early exercise with the option’s terminal payoff and emphasizes that the extra value comes from retaining the choice to wait. At expiration, that choice disappears, so the option’s value is its payoff. The explanation is intuitive rather than a formal valuation proof; it does not quantify the value of waiting or discuss when early exercise is optimal.

Key ideas

• An American put’s value cannot fall below its immediate exercise payoff.
• The holder can exercise now or retain the option for a possible future benefit.
• The ability to wait contributes time value that vanishes at expiration.

Tags

# Put price, payoff, how come?


# Put price, payoff, how come?












From Merton (1973) the following boundary condition is valid for an American put.

```
G(S,t:E) >= Max [0,E-S]
```

I dont understand how the Rational put price can be greater than the potential payoff? You may pay for something that will always yield you less right?

Could you think of this as - European put payoff sets the lower floor of and american put?

## Answer by davidhigh (score 1)

https://quant.stackexchange.com/a/37837

When you exercise at any moment prior to expiry, you obtain the price at payoff, i.e. the same as you would get when you hold it till expiry and the price stayed constant.

What makes your pur more valuable than the price at expiry is the right to hold it further -- that is your free choice to exercise it now or hold it for some more time. At expiry this right vanishes.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.