In historical simulation VaR, if we have stale data for some of our risk factors, which means daily returns on a particular risk factor is 0 on multiple occasions. Is there any way to solve this other than changing the data source to get more updated data.
In historical VaR,for time t=0,1,2, if t=1 is a holiday then the pnl of the portfolio at EOD t=1 will be 0 as there was no change between t=0 and t=1. Should we consider this 0 pnl in VaR calculation or directly compute pnl based on t=2 and t=0?
It depends what kind of parameter it is. Is it observable and liquid or not ? There could be true gaps in the data. If you have a gap in your data while the parameters moved in a linear manner in real life, you might overestimate your VaR. While conversly if you adjust your data in a linear way while there was an actual gap you might underestimate it.
By convention you should exclude holidays from your calculation, if you're computing a 1 day var, it's for a trading day.