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So this the question and the answer to the first one states that only the 5 year swap rate will be adjusted for convexity and the answer to the second one states that neither of the rates will be adjusted for convexity.

My question is why? Why won't both the rates (ie the the sofr and treasury rate) go under the adjustment as well?

I've cracked my head on this question and I still can't figure it out so any help would be highly appreciated!

Source : Options, Futures, and other Derivatives : Hull, John C

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The first question relates a 5y tenor security paid quarterly while the second is a (spread of) quarterly securities paid quarterly - fixed in advance, paid in arrears. Timing/convexity adjustments are necessary when there is a differential between the fixing/payment period tenors or if the fixing is at any time other than advanced during the period. E.g. 3m compounded SOFR rate (fixed in adv) paid in arrears quarterly wouldn't require an adj, while paid semi-annually it would. Similarly if the 5y swap rate is paid in any way other than as a 5y set of fixed/float cashflows (i.e. a vanilla swap), it would have convexity. All of this has to do with messing around with the discount factors used to value your security free of arbitrage, and these guys don't react well to moving fixing or payment times around because they're a non-linear function of rates.

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I think you've missed the fact that the first question deals with a spread option and the second one with a linear derivative.

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