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Bootstrapping is primarily a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. deposits, forwards/futures, bonds, swaps etc. The term convers also any recursive procedure of the same kind, for instance default probability curve bootstrapping, caplet volatility bootstrapping.

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LIBOR Curve bootstrapping and compounding

It all depends on how you want to represent your yield curve internally. If you choose to use compounded rates as internal yield curve then yes you would need to convert. All you care about in curve …
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How to do simultaneous dual curve bootstrapping?

It's done in 2 steps: 1) First you bootstrap OIS curve independently from Libor curve, get OIS discount factors 2) Then use these to bootstrap Libor curve (using OIS discount factors instead of Lib …
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