Probability of exercising European put option under Black-scholes model

Discussion in 'CT8' started by Chang Liu, Apr 19, 2017.

  1. Chang Liu

    Chang Liu Member

    Under black-scholes model, i know the probability of exercising European call option = Phi (d2)

    My question is : Is the probability of exercising European put option = Phi (-d2) ?
     
    Chang Liu, Apr 19, 2017
    #1
  2. Mark Mitchell

    Mark Mitchell Member

    P(exercising call option) = P(ST > K) = Phi(d2).

    P(exercising put option) = P(ST < K) = 1 - P(ST > K) = 1 - Phi(d2) = Phi(-d2).
     
    Mark Mitchell, Apr 19, 2017
    #2
  3. Cookie

    Cookie Member

    Where is this in the notes.
     
    Cookie, Sep 15, 2017
    #3
  4. John Potter

    John Potter ActEd Tutor Staff Member

    Hi Cookie,

    Chapter 16, Section 1.4
    Example: the Black-Scholes formula for a call option
    In the proof, look at the second integral - this is integrating the PDF from K to infinity. Well, that's PQ[S>K]

    Good luck!
    John
     
    John Potter, Sep 15, 2017
    #4
  5. Cookie

    Cookie Member

    Thanks
     
    Cookie, Sep 15, 2017
    #5

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