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Math Help - Does this 'put on a call' question actually make sense?

  1. #1
    Super Member Deadstar's Avatar
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    Does this 'put on a call' question actually make sense?

    Let T_1 and T_2 be two positive constants such that T_2 > T_1.
    Suppose S_t denotes the price of a risky asset at time t and consider a filtered probability space (\Omega, F, \{F_t\}_{0 \leq t \leq T_2} , \mathbb{P}) such that F_t := \sigma(S_u : 0 \leq u \leq T_2) for every t \in [0, T_2].
    Then, one may consider a (European-type) option written on another (European-type) option, i.e. a compound option.
    A typical example of a compound option is `a put on a call', where both put and call are European-type options with maturity dates T_1 and T_2 (respectively) and strike prices K_1 and K_2 (respectively).

    Question.

    Suppose the (effective) rate of interest is constant and equal to 2% (per time step), the initial stock price is S_0 = $50 and it can rise by 5% or fall by 2% at time 1, and again also at time 2.

    Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call').



    The italic bit is the bit I can't understand, it doesn't seem to make any grammatical sense. Someone fancy translating it? This was an exam question as well, I would've surely kicked up fuss about it afterwards.
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  2. #2
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    'Put on a call'

    No. But puts and calls in relationship to stock options does make sense.
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  3. #3
    Super Member Deadstar's Avatar
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    Quote Originally Posted by wonderboy1953 View Post
    No. But puts and calls in relationship to stock options does make sense.
    Yeah I know what a put and a call are and how they relate to finance etc... But the question just seemed to make so sense.
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    I would ask a broker

    Sounds like you have a very technical term you're dealing with.
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  5. #5
    Super Member Deadstar's Avatar
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    Quote Originally Posted by wonderboy1953 View Post
    Sounds like you have a very technical term you're dealing with.
    I think you might be misunderstanding. This isn't about my understanding of mathematical finance (though it is not great). This is about the wording of the question.

    Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call')

    This reads horribly and no-one that I have shown it to can make head nor tail of it.
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  6. #6
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    Quote Originally Posted by Deadstar View Post
    I think you might be misunderstanding. This isn't about my understanding of mathematical finance (though it is not great). This is about the wording of the question.

    Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call')

    This reads horribly and no-one that I have shown it to can make head nor tail of it.
    I am not sure if we could show that. (1) 73p tends to mean 73pence, we don't know currency conversion values for the problem at hand, and we have quotes in dollars (2) you are going to have to construct binomial trees of up 5% down 2% and determine sigma(volatility) (3) when is expiry for both?

    It seems like we don't have enough information.
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  7. #7
    Super Member Deadstar's Avatar
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    Quote Originally Posted by dwsmith View Post
    I am not sure if we could show that. (1) 73p tends to mean 73pence, we don't know currency conversion values for the problem at hand, and we have quotes in dollars (2) you are going to have to construct binomial trees of up 5% down 2% and determine sigma(volatility) (3) when is expiry for both?

    It seems like we don't have enough information.
    Lol... No one seems to understand my problem...

    I never even noticed that.


    This...

    Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call')

    Does not make any grammatical sense. I was kinda hoping someone would be able to untangle what the question was asking...

    This part in particular... It's does not make sense (NOT mathematically, just as a sentence).
    ...sell for $2 at time 1 an (European) option to buy one unit of stock...

    Can't believe this was a past exam question lol. I woulda raged I would say.
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    If you want a better answer, post your question at Quant Network
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  9. #9
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    Quote Originally Posted by Deadstar View Post
    Show that the value at time 0 of an (European) option to sell for $2 at time 1 an (European) option to buy one unit of stock for $51 at time 2 is about 73p (this is a simple example of `a put on a call').

    The italic bit is the bit I can't understand, it doesn't seem to make any grammatical sense. Someone fancy translating it?
    Agree, no grammatical sense whatsoever...or any other sense
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