# Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model

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.

• 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. Commented Nov 8, 2022 at 22:56