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Call Option S=100 K=100 Payoff=1 (option is not available) How can i replicate this (payoff) with calls and puts with strike prices with multiples of 5$

Thanks for help

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I'm actually not convinced that you can replicate a binary option with vanilla options, even with arbitrary strike prices. Reasoning: a binary option's payout graph has an infinite slope at the strike price, whereas all vanilla options (and underlyings) have finite-slope graphs. I don't think you can add finite-slope combinations to get infinite slope, unless you use an infinite number of them. – barrycarter Oct 15 '11 at 19:37
The payout is discontinuous, it's the delta that has extreme slope around the strike. – Joshua Sep 24 '13 at 21:44

use a vertical spread and delta hedge it.


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A digital call option (cash-or-nothing) can be replicated with two call options with different maturity. When we make the delta infinitely small and assume we have arbitrary strike prices. We get:

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