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!

  • What do you want to compute exactly? Is it a daily (annual?) VaR? What question are you trying to answer: how much can you lose in a day (in a year?) with a given confidence level? – byouness May 14 at 17:36
  • Annual VaR. Then I'd like to compare it to Parametric VaR. – AK88 May 14 at 19:49

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