Scaling Vasicek Parameters for Daily Simulation

Summary

The document considers whether a Vasicek process estimated from monthly data can be simulated with a daily time step. Its response emphasizes matching parameter units to the simulation frequency: estimates based on monthly observations should first be converted to annual units, with volatility scaled by the square root of the number of months in a year. The resulting model can then be simulated with a daily increment of one trading day expressed as a fraction of a year.

This is a brief guidance note on frequency conversion, not a full derivation of the Vasicek discretization or a worked simulation. It assumes a 252-trading-day convention and gives no discussion of calendar-time versus trading-time choices, estimation uncertainty, or checks that the continuous-time model fits the data. Readers should therefore treat the scaling recipe as the response’s stated approach, rather than a comprehensive treatment of parameter conversion for every stochastic process.

Key ideas

• Parameters estimated from monthly observations are expressed at a monthly frequency.
• The response converts monthly estimates to annual units before daily simulation.
• It scales volatility by the square root of the number of months in a year.
• The daily time step is set as one trading day over 252 trading days.
• The note does not derive the discretization or discuss model fit and estimation uncertainty.

Tags

# simulation and timestep


# simulation and timestep












Suppose I have a stochastic process i.e. a Vasicek process with parameteres estimated with monthly (RW measure) data and want simulate the process using a daily timestep. Is this a good practice?

## Answer by Egodym (score 1)

https://quant.stackexchange.com/a/21729

By estimating the model parameters using monthly data, you will get monthly estimates. Thus, you will need to multiply them by $12$ (or by $\sqrt{12}$ for the volatility) in order to get annual estimates. Once you have done this, you can simulate the model using the timestep $\Delta t=\frac{1}{252}$.

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