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The most common approach is to multiply by sqrt of 250. This is the standard. Although very basic. A much better solution is to make your monte carlo simulation on a 1 year time period using scaled parameters over 1 year.

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It depends on the method by which you calculate VaR. Some models (t-distributuion, normal) lead to a form of VaR such that it is just scaled volatility: $$VaR = c \sigma$$ with some proper $c$ (e.g. $q_{\alpha}$ in the case of normal, bit more complicated for the t-distribution). Then as $\sigma$ scales with square-root-of-time so does VaR. If VaR is ...

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The most commonly used approach is multiplication by the square-root of T, 19.1 in this case. This assumes no autocorrelation, however (Markov process). Interest rates tend to show a mean reversion, so the number would be smaller than 19.1. Other cases could show the oppoite effect if there are positive feedbacks. In both of these cases, a simple time ...

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The standard approach is to multiply by the square root of the number of trading days in a year. If you assume there are 250 trading days in the year, you multiply by $\sqrt{250}$. Investopedia is one source explaining this approach.

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You don't really have a multivariate case: we can only define VaR (in its usual sense) for a one-dimensional output. Recall that $$\operatorname{VaR}_\alpha(X) = \inf\{v:F_X(v)\geq \alpha\}$$ and since in your case $X = X_1+X_2$ you just need to compute $F_X$ in terms of $X_1$ and $X_2$. For the notation of partial derivatives, I denote the generic ...

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