Interest rate cap vs. put option on fixed-income price

FrankCFA

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Can we say a long cap is equivalent to a portfolio of long put optionson fixed-income security price?
 
we are capping icnrease of interest rates which means that when interest rate rises we will face the heat, to get a hedge we can either get put on bond so that we dont go beyond a price level for our bonds,
which means both of them shoudl mean the same thing.
 
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