For callable bonds we can use the effective duration to approximate the modified duration, since the future interest rates will affect the expected cash flows. For convertible bonds the underlying of the embedded option does not depend of the interest rate levels but the underlying also affects the (possible early) redemption.

You can run simulations starting with a slightly lower and slightly higher rate. Then calculate the difference of present value of expected payoff.

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    thank you for your answer. But how would you proceed if you wanted to do it analytically? – Xavi Hernandez Sep 19 at 8:22

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