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Note that you can also use trees instead of running monte carlo (if a closed form solution is not avaliable) As far as I know it is even an industry standard to work with the Hull-White tree instead of monte-carlo. For mote informiation you can have a look at the paper: USING HULL-WHITE INTEREST-RATE TREES


Once the single-factor Hull-White model is calibrated, you can compute zero-coupon bond prices in closed form (i.e., without running simulations). See http://en.wikipedia.org/wiki/Hull%E2%80%93White_model#Analysis_of_the_one-factor_model .

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