Choosing Daily or Annual Parameters for Monte Carlo VaR

Summary

The document asks how to simulate annual value at risk from a security’s initial price, annualized return, and volatility under a geometric Brownian motion model. It compares simulating a one-year horizon directly with annualized inputs against simulating daily steps using daily-scaled parameters and then annualizing the result.

The post frames this as a choice of time units and asks about the consequences of mixing daily and annual quantities. It does not include an answer, simulation results, or a preferred procedure, so it offers no evidence to settle the comparison. Any implementation must align the horizon, drift, and volatility units consistently; annualizing a daily percentile is not automatically equivalent to directly simulating the annual horizon, particularly when the return definition or model assumptions differ.

Key ideas

• The simulation equation combines drift and volatility with a time horizon expressed in matching units.
• The question contrasts direct annual-horizon simulation with daily simulation followed by annualization.
• The document supplies no answer or empirical comparison between the proposed approaches.
• Consistent time units and return definitions are essential when simulating VaR.

Tags

# Monte Carlo simulation based VaR: daily vs annual parameters


# Monte Carlo simulation based VaR: daily vs annual parameters












I am given the initial price, annualized return, and volatility of a security. I am trying to calculate annualized VaR using Monte Carlo simulation approach. To do this I will use the following equation:

$$ S_t = S_0 \exp\left(\left(\mu-\frac{\sigma^2}{2}\right)T + \sigma\sqrt{T}\epsilon_i\right)$$

Do I have to convert the annualized return and volatility to daily and then proceed with generating $N$ number of simulations (taking $T=1$), find the daily returns, sort them, take 95/99 percentile, and then annualize it?

Or can I proceed with annualized parameters and taking $T=252$, generate simulations, take the returns, sort them, and then just read off 95/99 percentile?

Which one is the correct approach? What are the reasons for choosing it and what are the possible negative consequences of selecting the wrong method?

Thank you for your input!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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