The last two years I spent at Goldman in risk management I was involved in developing methodologies to mark illiquid derivatives held by a variety of trading desks. The approach we took for illiquids was to simulate, under a broad variety of scenarios, both underlier behaviour and a trader’s hedging strategy, even if it isn’t optimal, and then to create distributions of the resultant profit or loss of the entire portfolio. These distributions and their standard deviation or tail loss were then used to determine a realistic adjustment to the trading desk’s conventional marks that could be withheld until the trade was unwound and their realised profit or loss determined.
Here’s a link to the Risk paper that described it. Maybe it’s a complicated but reasonable way to estimate prices and their uncertainty when markets disappear.