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Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty) at any time.

If its helpful, assume the loan asset has liquid secondary market and mature futures market with a known term structure basis.

How would one calculate the duration and convexity of a loan with these attributes? How would one think about hedging these risks when considering a loan book made up of these loans?

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Your loan seems to be one that would be either called by the bank or closed by the borrower as soon as the coupon rate moves below or above the prevailing market rate, so for the loan to be outstanding there needs to be some transaction cost or friction to keep it around. For that reason it is most similar to US mortgages which can be prepaid, but where some borrowers do not for various reasons.

If this sounds like a reasonable explanation then you would need to develop a model of when the bank would call the loan and when the borrower would close the loan, and then use a simulation to model to calculate its values in different scenarios. From there you can derive the effective duration and convexity based on the price change relative to interest rate changes.

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  • $\begingroup$ Yes so in the absence of such frictions, duration and convexity are zero. $\endgroup$
    – dm63
    Oct 21, 2021 at 17:40

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