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I think that you are confusing instantenous sport rate $r(t)$ with continously compounded spot interest rate $R(t,T)$. The instantenous sport rate $r(t)$ is just a rate over infinitesimal interval $dt$ and this rate is not observable, because the shortest rate traded is overnight rate i.e. 1 day rate. The continuously-compounded spot interest rate $R(t,T)$ ...

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Spot rates cannot be directly observed --- Wikipedia The way I understood this (in a more basic context) is simply that if the 1-year forward rates during year 1,2,3 are $i_1,i_2,i_3$, a bond coupon payment is to be made at the end of year 3, and the spot rate for that payment is $i$ then $$(1+i_1)(1+i_2)(1+i_3)=(1+i)^3$$ so that we can calculate $i$, but ...

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This seems to be solved direct application of differentiation under Integral Sign, Leibniz rule since $h(s,t)$ is a well-behaving deterministic function: \begin{equation} dX(t)=\int_{0}^{f(t)}\frac{\partial h(s,t)}{\partial t}dW(t)+\frac{\partial f(t)}{\partial t}h(t,t)dW(t). \end{equation} Here $f(t)=t$ therefore we have, \begin{equation} dX(t)=\int_{0}^{t}\...

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You can go short eurodollar futures. The contact months go out for years and is tied to LIBOR rates, which are tied to fed funds

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It really depends for what purpose you are using the model. Let’s say you are using it for valuation of some instrument. If you want the fair market value, then a) is irrelevant and you would instead calibrate to the current term structure. For hedging , one usually means hedging the market value so again b) is appropriate. The only reason to use a) is to ...

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Hull used a single Brownian driver. He did add, a few pages down, equation (31.15) (in my 7th edition) with $p$ independent Brownian drivers: $$\frac{dF_k(t)}{F_k(t)} = \sum_{i=m(t)}^k \frac{\delta_iF_i(t) \sum_{q=1}^p\zeta_{i,q}(t)\zeta_{k,q}(t)}{1+\delta_iF_i(t)} dt +\sum_{q=1}^p \zeta_{k,q}(t) dz_q$$ with $\zeta_{k,q}(t)$ the component of the ...

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