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8

Practically, few things in real life have convenient closed-form calculations. Instead, you price some exotic, then you bump the various inputs, one or several at a time, up and down, by various small amounts, and re-price. There are seldom any short-cuts. (Autodiff can sometimes be a shortcut.) This Wikipedia article actually has a good list of commonly ...


5

If the question is how one defines Greeks for interest rate options, then it is a relatively straightforward extension of the concept from the basic idea for say equity options. They are defined as sensitivities to the inputs that go into pricing an option. Any half-decent interest rate derivatives book (search for interest rate modelling on Amazon, say) ...


3

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 ...


2

The procedure you have specified in your last paragraph is the only reasonable way to do it. Clearly the cap volatility is some sort of weighted average of the constituent caplet volatilities, but the weighting is complex , having strike dependence as well as maturity dependence.


2

I think it is necessary to be more precise on the terminology here, so my answer will be a bit longer. Firstly, we need to distinguish the FRA, the FRA option and the caplet/floorlet. A FRA basically locks in a future LIBOR fixing for you, e.g., the 1x7 FRA strike allows you to lock in the 6m LIBOR that will fix in 1m from now. Note that it is a linear ...


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