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I'm not sure I agree with that being a very difficult task... The black formula for a caplet (using notation from Hull's book) is given by: $caplet = L \delta_k P(0, t_{k+1}) [F_k N(d_1) - R_kN(d_2)]$ where: $d_1 = \frac{ln(F_k/R_k) + \sigma_k^2t_k/2}{\sigma_k\sqrt{t_k}}$ and $d_2 = d_1 - \sigma_K \sqrt{t_k}$ The delta will just be the first derivative of ...

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