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CMT forward formula accounting for repo

May 29th, 2023, 9:53 am

Given a bond price, we can infer its corresponding bond yield using standard formula, which depends only on the bond price. 

But how does it work for CMT forwards ? 
A CMT fixing is basically closely related to the yield of a bond that will be observed at some future date.
A CMT forward is basically the expected forward of that yield, i.e. the par rate we would agree today for receiving an instrument that pays that bond yield at that future date. 
Setting aside convexity adjustment for now, how would we compute that CMT forward taking into account bond repo ?  
To replicate this par rate, we would in principle need to replicate with bond forwards, which in turn would require us to get funding from repo, but I don't see how this would work ?
Is there any paper on the topic please ?

Thanks in advance for reading.