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I want to sketch a straddle and a butterfly payoff diagram when t tends to 0. I have searched and have been able to sketch both a butterfly and straddle diagram but fail to proceed when t tends to 0. Any help will be most appreciated. Thank you.

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what do you call T ? what do you call a diagram ? Have you tried to decompose both in put/call options ? –  lmorin May 8 at 17:09
    
I have drawn a short call and a short put with same strike price separately and then (add them) to obtain a straddle payoff diagram. Similarly i have drawn 2 long calls and2 short calls separately and then adding them up leads to the butterfly sketch. T is maturity (expiry) period. if t tends to 0, what will be the resulting sketch for the straddle and butterfly i have sketched. Thanks @ Imorin –  user3309969 May 9 at 8:21
    
At expiry the resulting sketch will be the payoff –  lmorin May 9 at 8:48
    
I am not sure I understand. Your straddle payoff diagram should be a sum of the two piecewise "hockeysticks" upon expiry, since there is no remaining time value of either option (as $t$ tends to $0$, as you say). Otherwise, the time value will smooth the payoff diagram, which, for the straddle will look curved like a branch of a hyperbola that approaches its asymptotes as $t$ tends to $0$. –  Jacob M. Morley May 12 at 6:17

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