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The derivative of the bond prices is very sensitive to the interpolation mode. actually, if you use a linear interpolation mode, you will have some cases for which the right derivative is different from the left derivative at a given point.


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You can check out here a blog post on simulating the yield term structure for the HullWhite model. The basic idea is that once you have the paths for the short rate, you can simply integrate (approximately) the short rate throughout each path to obtain the discount factors. The average of the simulations should match the initial term structure. Here is an ...


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You are obviously using a local-optimizer ( here Nelder-Mead method). One should expect different results for different initial guesses as it will get stuck to a local minima ( or just a "solution" for Nelder-Mead, as it is a heuristic optimizer). In practice, play around and collect the different solutions and their errors, the smaller the error , the ...


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