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Why Early Exercise Can Benefit an American Put Despite Time Value

Article Quant Q&A · Author: Alec
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Summary

The question asks how early exercise of an American put can be optimal when the option has nonnegative time value. The answer distinguishes the time value surrendered on exercise from the benefit of receiving the strike sooner. With positive interest rates, receiving that cash earlier can earn interest or otherwise avoid waiting for payment.

Early exercise is therefore rational when the value of the earlier receipt of the strike exceeds the time value lost. The document gives this as a conceptual comparison rather than a numerical example or a full exercise-boundary analysis. It does not specify the underlying price, remaining maturity, volatility, or other conditions needed to decide whether exercise is optimal in a particular case.

Key ideas

  • An American put can be exercised before expiry even when it has positive time value.
  • Early exercise provides the strike proceeds sooner.
  • Exercise is favorable when the financing benefit outweighs the time value surrendered.
  • The explanation is qualitative and does not determine an exercise boundary for a specific contract.

Tags

OptionsDerivatives pricingRisk management
Full text
# If American Options always have positive time value, how can it be optimal to exercise an American Put early?


# If American Options always have positive time value, how can it be optimal to exercise an American Put early?












r > 0. I understand that money today is worth more than money tomorrow. So if volatility is 0, it's better to take the money today. But I don't understand how to square away the following:

- Time value for American Options is always nonnegative

- Value = Time Value + Intrinsic Value

How is it ever optimal to throw away positive time value?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/75034

“How is it ever optimal to throw away positive time value?”

Answer: when the thing you are throwing away is less than what you are gaining through the early exercise . What is that ? Interest you receive on the strike price by receiving it earlier.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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