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Based on this article: https://en.wikipedia.org/wiki/Forward_rate

If we were to calculate forward rate on libor 3M at times T1,T2 (ie, forward rate at T1, going forward T2), does that value change if we compute it today vs tomorrow, assuming T1 and T2 does not change.

My guess that it does, because our calculation of spot rate at T1 would change from day to day, as market conditions change, right?

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    $\begingroup$ Yes it would change, but that is a general characterization. The product you are pricing might only re-price every 30 days or every quarter. For example, in the syndicated loan market (often pricing off LIBOR), the loans will usually recalculate the last business day of each month. That ultimately changes the interest payments (cash flows) of the loan. So yes, the forward rate would "change", but what are you asking in regards to? Just intuition? $\endgroup$ – HK47 Jun 25 '18 at 14:47
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The IBOR forecast curve is the market's expectation of the evolution of IBOR fixings. If today is 1-Jan-2018 and you have a curve that prices 27-April-2018 for 3M as 1% then if the market evolves as predicted and there is no (exogenous supply/demand) market movement between today and tomorrow then on the 2-Jan-2018 the 3M rate priced to start at 27-April-2018 is the same as it was yesterday, i.e. 1%. This is precisely what you will observe on futures markets, since the futures contract settle to fixed dates (IMM dates). Any fluctuation in those rates is market movement, i.e. change in expectations.

However if your dates are generic maturities, i.e. start-3M-end-3M, then the rates will change since a forward rate that is priced as 3M3M from 1-Jan-2018 has dates 1-April-2018 to 1-Jul-28, whereas a 3M3M priced from 2-Jan-2018 has dates 2-April-18 to 2-Jul-18, and therefore it does not represent the same price as yesterday.

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