Put Option Exercise

An investor will likely exercise a put option when the price of the stock is:

A) Above the strike price

B) Below the strike price plus the premium

C) Below the strike price

A) is clearly incorrect. I picked B), but the answer is C). The explanation is that the premium is used to determine the net profit to each party.

Is this because the long put investor will still exercise the option when the stock price is below the strike price but not below the strike price with the premium? Since the long put investor will lose less if he exercises below the strike price than if he wouldn’t (ie. if premium is $5, strike price = 50, stock price = 48, the investor will still exercise because he would lose 3 instead of 5?)?

Yup, exactly that. If the investor waits until the spot price goes below the strike + prem, he could lose the opportunity to save part of the prem paid.

Don’t forget most options related questions concern European options. There is only one chance to exercise-at expiration. At expiration if spot is less than strike price the put option will be exercised 100% of the time.

Option B is meant to mislead you.

It’s a long put => breakeven is strike price minus premium, not plus premium.

ToughProgram, I think premium is a sunk cost and is not relevant in this question. Whenever the stock price is less than the strike price, it is beneficial for the investor to exercise the put option at the given time, since the benefit is greater from exercising.



The premium is, indeed, a sunk cost.

Think of it this way: you paid $5 for a put option with a strike price of $40, and when it expires the stock is selling for $38. If you don’t exercise the option, you’ve lost $5. If you do exercise the option, you’ve lost only $3.

Exercise the option when it’s in the money; ignore the option cost.

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The question is insufficient.If the option is American,the investor will likely exercise when the strike price+premium is above the stock price whereas if the option is European,he/she has to exercise it even if the stock price is one penny less than the strike price(the word likely is inappropriate as well if the option is European).There shouldn’t be any doubt on the questions.

An investor will almost never exercise an American option early. By exercising it the investor will gain only the intrinsic value of the option. By selling it the investor will gain both the intrinsic value and the time value.

Only in rare circumstances (e.g., a call option on a stock that is about to go ex-dividend, or a deep in-the-money put option for which the time value is negative) will it be beneficial to exercise an American option early.

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In what case can the tine-value of an option be -ve, I was under the impression that its always +ve? i.e how does one calculate time-value of money?
(my inclination is towards that time-value of an option is market determined)

It’s not the time value of money; options aren’t money.

The time value of deep in-the-money puts can be negative. The idea is that because the price of the underlying is bounded below by zero, at some point it’s more likely to go up than down, so if you wait the price of the underlying will likely increase and the intrinsic value of the option will therefore likely decrease.

It’s easy to see with a B-S-M model. For example, if:

  • S_0 = \$40.00
  • X = \$30.00
  • r_{rf_{effective}} = 2\%
  • T = 0.5
  • \sigma = 20\%

then the value of the put option is \$9.65, so the time value is -\$0.35.

Cool, eh?

(When S_0 = \$34.15, the time value is zero. Above that it’s positive and below that it’s negative.)