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I am aware that under the dual curve method for pricing standard collateralized fixed floating interest rate swaps, that first a discounting curve should be constructed e.g. OIS Discounting curve, as well as a separate forecasting curve that is used to forecast the cash flows e.g. 6m LIBOR.

And as far as I understand the existing swaps that are used to bootstrap the forecasting curve are themselves collateralized, will those rates be the same implied rates as if we were to bootstrap the curve using uncollateralized instruments

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  • $\begingroup$ Sorry edited question for more clarity hopefully. Basically just wondering if using collateralized va non collateralized instruments will yield the same implied rates when bootstrapping the forecasting curve $\endgroup$ – Skrrrrrtttt Mar 8 at 1:59
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    $\begingroup$ You will never bootstrap a curve using uncollateralized instruments. Everyone uses the liquid interbank (collateralized) market to bootstrap. $\endgroup$ – dm63 Mar 8 at 3:28
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The price of something under OIS discounting is (supposed to be) the expectation of its value under a particular measure, which specifies the measure and the interest rate of the collateral account etc.

So given the price of a set of ATM Libor IRS and their relevant discount curve, the immediate thing to do is to infer the markets' expectation of forward Libor, under that measure. So we're still looking at that rate e.g. as a FRA with the same collateralisation as the swap.

To see the rate priced without collateralisation, we have to somehow account for the change to that measure. The theoretical approach is a change of measure, which accounts for the differences between the distributions of future paths built into the measures by the market etc.

In reality people seem to usually essentially treat the expectations derived under a given measure as though they didn't need adjusting because the change of discount curve makes more difference to the final price.

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  • $\begingroup$ Thanks for the answer. So the implied rates from the collateralized swaps would be used to forecast the cash flows for any new swaps that are being priced? $\endgroup$ – Skrrrrrtttt Mar 8 at 16:21

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