Deriving vega for call option

Discussion in 'CT8' started by r_v.s, Apr 16, 2014.

  1. r_v.s

    r_v.s Ton up Member

    q9 september 2008

    (ii).

    How did the K disappear from the penultimate step in the solution?
     
  2. John Potter

    John Potter ActEd Tutor Staff Member

    I'm not quite sure which bit you're talking about but it's probably down to the fact that

    S phi(d1) = K exp(-r(T-t)) phi (d2)

    where phi( ) is the PDF of a standard normal distribution..

    phi(x) = exp(-x^2 / 2)/sqrt(2Pi) (see page 10 Tables)

    It's worth knowing this result, really useful for deriving the Greeks in the BS formula.

    John

    PS have you considered buying ASET? It contains all the explanations to the many questions on the past papers that you have been asking. I would definitely recommend it for your future exams.
     
  3. r_v.s

    r_v.s Ton up Member

    Thanks John!
    For my future exams I'd definitely start working on the question papers along with the ASET!! but now I'd hv to wait atleast another week to be able get it! :(
     
  4. skhurana

    skhurana Very Active Member

    I would recommend ActEd online tutorials..they are really good.
     
  5. Actu09

    Actu09 Keen member

    Hello...regarding the calculations for Sept.2008,question 9(iii), could someone enlighten me how to proceed with the required calculations??

    Kind Regards,
     
  6. Graham Aylott

    Graham Aylott Member

    In this tricky and non-standard question, you need to partially differentiate the Black-Scholes PDE with respect to sigma.

    You can then rewrite the resulting formula in terms of partial derivatives with respect to vega and so obtain an equation that is similar to the Black-Sholes PDE, but with vega taking the place of the derivative price f.

    I've attached the relevant two pages from an old ASET that covered this question, which I hope will make clear what was required.

    Graham
     

    Attached Files:

  7. Actu09

    Actu09 Keen member

    Thank you so much Graham..Now it does make sense.
     
  8. Tele76

    Tele76 Member

    Wow, the ASET looks really helpful. Wish I had ordered them for CT8 this time, have been struggling with some of the solutions in the examiners reports.

    Oh well, too late now.
     
  9. Hi,

    Not obvious to me where the above result is from:

    S phi(d1) = K exp(-r(T-t)) phi (d2)

    Please could anyone shed some light?
     
    Last edited by a moderator: Aug 28, 2018

Share This Page