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Hi Ro

During a paired trade, we never exit only one leg of the trade. This would lose the mutual cancellation effect on systemic risk and suffer more losses. I would not recommend applying a Risk Management Model with that, maybe you could apply one that measures the PnL of the pair with a stop-loss that liquidate both legs.

You're assuming these correlations will last from the period that you feed data into the copula model to the period you trade them, as well as constant correlation within the whole period, which are both not always the case! The breakdown of the correlation will cause your paired trade “unhedged”. 

A copula is just a tool to fit and predict a higher-dimension distribution between multiple distributions. Although you could reduce the risk of the whole portfolio by weight optimization with a better-estimated distribution, its context is not really a good idea for paired trading, but more on hedging by options/uncorrelated stocks. For pair trading, cointegration or machine learning might be a better idea. We also have a basic example in here.

Best
Louis

I am not very familiar with pairs trading with copulas (as opposed to classical cointegration methods), but for pairs trading before you can realize a large profitable movement towards the mean there by definition has to be a period of mispricing. Instead of focusing on the exit, I would actually suggest the opposite and focus on the entry logic (i.e. enter positions only when you think the “mispricing has peaked”).

Also seconding Louis' answer - entering/exiting individual positions in this context doesn't really make any sense. You should treat the pair as a single asset, and enter/exit the pair simultaneously.