I need to price bonds with CMS-linked coupons. In order to determine the convexity adjustment to apply to the forward rates, I would use the formula that appears in Hull's Futures, Options and other derivatives:

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The bonds are denominated in EUR whose curve presents negative interest rates. I understand Hull's adjustment implies a log-normal process of the interest rate so that the above formula should not be used (swaption vols are not available anyway). Is there an equivalent formula to be used assuming normal process?

I've been reading some papers like "Convexity Adjustments Made Easy -A Review of Convexity Adjustment Methodologies and Formulae in Interest Rate Markets" by Nicholas Burgess but I find hard to understand and apply in practice, specially because I don't see the relation between the lognomal adjustment there and Hull's: enter image description here

Your help is really appreciated.


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