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I've been studying how to replicate different payoffs using options and zero-coupon bonds, and each time there's a different approach to solving the problem. I've been wondering if there's a general approach that would apply to any given payoff?

Thanks.

Metrician
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  • Thanks for the response ! Will that work on any arbitrary payoff ? – Metrician Sep 28 '20 at 17:52
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    When the payoff is not piecewise linear then you’d approximate as such. Letting the intervals of your strike grid become smaller you’d get better approximations that in the limit need a continuum of strikes. – LocalVolatility Sep 28 '20 at 18:00
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    For an arbitrary payoff $P$, one could replicate any european option whose payoff is $P$ as a continum of calls and puts using Carr-Madan Formula, see here : https://quant.stackexchange.com/questions/27626/carr-madan-formula and here : https://quant.stackexchange.com/questions/26126/carr-madan-european-contingent-claim-payoff-decomposition-formula-application – DeepInTheQF Sep 28 '20 at 19:04
  • Thanks a lot for your responses. I suppose this approach can't be used to replicate American payoffs/exotics. What can we use then? – Metrician Sep 29 '20 at 10:41
  • Not ot my knowledge. This approach is for European payoffs. – nbbo2 Sep 30 '20 at 11:39

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