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Thread: Written Put Options Question

  1. #1
    Actuary.com - Level I Poster
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    Written Put Options Question

    For a Writer of a Put,

    They want the (Future) Spot price to increase so that
    [(Future) Spot Price > Strike Price]

    And if that happens, then the Purchaser of the Put will sell at the (Future) Spot Price, and the Writer of the Put needs to buy that asset at the (Future) Spot Price.


    So technically the Writer of the Put should want the (Future) Spot Price to increase to a point higher than the Strike Price...
    But lower than the Strike Price + the premium


    For example-
    Premium for Put= 100, i= 5%......(At t=1, Premium with interest = 105)
    Strike Price for t=1 is 1750
    -------

    Writer of the Put should want the (Future) Spot Price to be in between
    1750 < (Future) Spot Price < 1855


    If the (Future) Spot Price =1855
    then he technically lost $105 from making the Put Option deal, However will gain it back from the $105 Premium.

    If the (Future) Spot Price =1856
    then he lost $106 from making the Put Option Deal, and will only gain $105 back...So he will be losing a dollar


    Am I wrong to think of it like this?

  2. #2
    Actuary.com - Level IV Poster
    Join Date
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    KS
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    I think your making it more complicated than needs to be. These are options, which means the purchaser of an option has the "option" but not the obligation to buy or sell.

    From the perspective of someone writing a put option, they want the spot price at expiration to be higher than the strike. This will mean it is not beneficial to the buyer of the put to exercise it. Thus, the most the writer of the put can make, is the future value of the put premium.

    There is no range like you are describing for the written put payoff. It doesn't matter if the spot price at expiration is 1000 times the strike price, or $.01 above the strike price. The purchaser won't exercise it, and again the amount the writer of the put option makes is the future value of the premium.

    The writer however can still make a profit if the spot price at expiration is lower than the strike, meaning he must pay K-S(t).
    If FV(premium)>K-S(t) he still turns a profit, but his profit is maxed at FV(premium) when S(t)>K.
    Last edited by brandond; August 11th 2010 at 12:29 PM.

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