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For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing how the same analysis can be applied to value interest rate options. Does the concept of replication apply to interest rate derivatives? If so, what would a replicating portfolio look like?

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It's made of interest rate instruments, of course, one per dimension of your SDE. Money market accounts, swaps and zero coupon bonds are common choices. –  Brian B Dec 13 '12 at 1:44
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