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You're pretty much correct, so these are mostly confirmations: Yes, the "3-month" USD LIBOR rate is really a 2 business day forward 3-month LIBOR rate (assuming the anchor date of your yield curve, the date on which the discount factor is 1, is "today"). USD swaps observe both New York and London holidays. If the maturity date is a bad day, it is adjusted ...


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"Calibrating the model to them via regression"... Vasicek has just three parameters: $\sigma$ (vol), $r_L$ (long rate) and $a$ (mean reversion) and a time-dependent short rate $r_0$. Can you specify what you are thinking of in terms of a regression model to estimate these? Obviously $r_0$ will not be a stable parameter. If you want to estimate $\sigma$, ...


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In practice, you can calibrate to either 1 month libor or 3 month libor, but not both. That's because there's a basis swap between 1 month libor and 3 month libor that can't be explained by your model.



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