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Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps parameter in the Monte Carlo simulation which calculates the time step as $$dt = \frac{T_{N-1}}{\mbox{num of steps}}$$ The fixing time $T_{N-1}$ of a terminal rate is always divisible by $dt$ by construction, so there are always integer number of time steps required to reach $T_{N-1}$. However we cannot be sure about the same property for all the non-terminal rates with fixing times $T_1, \ldots, T_{N-2}$ since it may happen that $T_j$ is not divisible by $dt$ for some $j$ and so the simulation of $F_j$ spanning $[T_{j-1}, T_j)$ will stop at some $t_j$ such that $t_j < T_{j-1} < t_j + dt$ while the real fixing of this rate should have happen at $T_{j-1}$.

Is it bad? Should one always choose a time step $dt$ such that all fixings $T_{1}, \ldots, T_{j-1}$ are divisible by $dt$? Should one employ different time steps $dt_i = \frac{T_{i-1}}{\mbox{num of steps}}$ for different rates? The later seems to require an introduction of a different discretization scheme.

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  • $\begingroup$ Hi, could this be a "duplicate" of quant.stackexchange.com/questions/65823/… ? Technically, you could always interpolate missing fixings from neighbouring fixings. I cannot comment on possible model errors, though, sorry. $\endgroup$ Nov 8, 2022 at 22:56

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Well, just my opinion- I would say look at the weather through the window instead of trying to model meteological events ;) most interest rates are being fixed once a day on a Act/ 365 dcc . Why would you want to interpolate your IR curve in shorter dt than daily ? ; I gues it is more important to have your tenors matching your riks measures and your sensis - 1y 2y , ... until 30y to 50y LCH papers are good on this

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