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Choosing LIBOR Market Model Time Steps Around Rate Fixings

Article Quant Q&A · Author: Hasek
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Summary

The document asks how to choose Euler simulation time steps for forward rates under the terminal measure. A step size based on the last fixing date lands exactly on that date, but may not align with earlier fixings. The question is whether to align steps to every fixing or use rate-specific step sizes, which could require a different discretization scheme.

The sole response offers informal practical guidance: because interest rates typically fix daily, it questions the value of interpolating the curve at intervals shorter than a day and suggests matching model tenors to risk measures and sensitivities. It does not derive an error estimate, compare discretization methods, or answer precisely how to handle misaligned fixing dates. Treat the recommendation as an opinion, not a general numerical rule; the document provides no simulation results or supporting analysis.

Key ideas

  • A step size based on the final fixing date may not align with earlier forward-rate fixing dates.
  • The document raises whether to align simulation steps to every fixing or use rate-specific steps.
  • The response questions the value of subdaily interpolation when rates fix daily.
  • It recommends considering whether model tenors match risk measures and sensitivities.
  • The response is informal and provides no numerical comparison of time-step methods.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model


# 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.

## Answer by BillyBobJocko2223 (score 0)

https://quant.stackexchange.com/a/73734

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.