"Cash or nothing" and "Asset or Nothing" binary on shares

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by Oracleyoda, Apr 25, 2010.

  1. Oracleyoda

    Oracleyoda New Member

    I am trying to use the relevant formula from Black Scholes to value both of these digitals on a common stock


    Option type = Put

    Strike = 50
    S = 50
    CC Dividend Yield = 0.75
  2. Oracleyoda

    Oracleyoda New Member

    And Standard Deviation for the Stock is 20%
  3. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member


    This is belated, but i was developing a binary XLS for our library, so maybe you'd find helpful. Here is a copy of rough with your numbers input, please see rows 28 to 31:


    My references (including Culp) and my intuition, like yours, suggest that dividend should be treated the same way. And the theory, too: specifically, the cash or nothing is a special case of BSM.

    And the test, it seems, is to compute the cash-or-nothing call and the cash-or-nothing put. The combination of the positions--note the elegance of this(!)--must be $1; i.e., at strike = $1, the payoff is a certain $1.

    And so, using your numbers:
    cash-or-nothing call = $0.5101 (note this is a d2 that is influenced by d1; by my d1 = 0.1945 per the -div. Please note that subtracting the dividend outright is equivalent to the alternative of embedding it inside the LN(). That is: LN(S*EXP[-q*T]/K) = LN(S) + LN(EXP[-q*T]) - LN(K) = LN(S/K) + (-qT) = LN(S/K) - qT ... so just a reminder the "adjustment" can be found in one of two places and your texts may not explicitly refer to that....or perhaps they merely assume a non-dividend paying stock

    In this case, I get:
    cash-or-nothing call = $0.5101
    cash or nothing put = $0.46878
    and sum of cash or nothing put and call = $0.97897 (cell C31) which should equals the discounted value of a certain $1 to be received in 0.5 years(!) = EXP(-4.25%*0.5), which it does.
    ... so this would appear to validate your intuition that the treatment of dividends is the same

  4. Oracleyoda

    Oracleyoda New Member


    One of the things that sent me in the wrong direction was a model published by one of the very prominent US business schools.

    I could not get their answer without making some unnatural assumptions. I eventually contacted them and it turns out their model was wrong and has since been corrected.

    The lesson there I guess is not to place blind trust everything that is in the public domain.

    Many thanks
  5. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    I think they probably deploy initially a non-dividend model (it's always the first learning step) then maybe they forget to adjust when dividends are layered in - David

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