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!

  • $\begingroup$ 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? $\endgroup$ – byouness May 14 '18 at 17:36
  • $\begingroup$ Annual VaR. Then I'd like to compare it to Parametric VaR. $\endgroup$ – AK88 May 14 '18 at 19:49

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.