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Instrument 2 looks to me like the standard regular definition of a 3x6 FRA. This is a relatively liquid instrument, so that forward rate r2 is just the price of the FRA and is available on Bloomberg, etc. If you have a yield curve model and associated suite of functions there will certainly be a function to return that forward rate, because it's vanilla. ...


This is actually only true when the yield curve is upward sloping. Intuitively, zero rates are average forward rates; e.g., the 10-year zero coupon yield is the geometric average of the 0y forward 1y rate, 1y forward 1y rate, 2y forward 1 year rate, ..., and 9y forward 1y rate: $$ (1 + y_{10})^{10} = (1 + f_{0,1})(1 + f_{1,2})\ldots(1 + f_{9,10}). $$ So ...

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