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A lot of research has been done in the direction of replication techniques, and most of them consider the max function. I was wondering if we have an interest rate benchmark $R$, a cap $C$, a floor $F$, and a strike $K$, if we can replicate the payoff

$$\max(C,\min(K-R,F))$$

in terms of caplets, floorlets, and also forward prices.

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  • $\begingroup$ You can replicate any payoff at maturity by a portfolio of calls and puts. This is because together across strikes they give you the risk neutral density. Any payoff can be valued then by an expectation w.r.t this density. $\endgroup$
    – Arshdeep
    Jul 10, 2023 at 15:09

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