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You're missing something important. Sovereign credit ratings are very misleading when the sovereign can print its own money (like the UK). I would argue that every country is AAA in debt of its home currency, since its central bank can just print money to pay off the debts. There are examples when a sovereign chooses to default on its own currency, ...


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Per @dm63, these yield curves are basically smoothed curves that best fit the prices/yields of bonds traded in the secondary market. However, they reflect much more than market expectations. Refer to Deriving Interest Rates for details.


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Yes, yield curves are a pictorial representation of the current secondary market yields of government securities (gilts, in the UK). These market yields are determined largely by expectations about what the central bank will do to short term rates over time.


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Given the Ho-Lee interest rate model of the form \begin{align*} dr_t = \theta_t dt + \sigma dW_t, \end{align*} the price at time $t>0$ of a zero-coupon bond, with maturity $T$ and unit face, has the form \begin{align*} B(t, T) &=E\Big(e^{-\int_t^T r_s ds} \mid r_t \Big)\\ &=e^{-(T-t)r_t - \int_t^T (T-u)\theta_u du + \frac{\sigma^2}{6}(T-t)^3}. \...



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