How do you determine the volatility of an unlisted entity, and more generally, how do you forecast volatility? These are non-trivial questions. There is an interesting discussion on Stackexchange:
Here is a question I had for a long time but I never asked. Let’s take an easy example, AirBnb will likely have an IPO soon, the stock will be quoted on the market. Let’s say I would like to price an option on this stock, how would I proceed?
For sure I could sell some with a premium equal to the spot, and wait for the secondary market to adjust, and then extract the IV to do a better pricing, but I would still need to find people to buy at that price.
So in practice how does it work, there is no underlying historical data, nor implied volatility available. Read more
The following could be a solution
With completely no historical stock price, the best I can think of is to find several companies in the same business (e.g. BOOKING for AIRBNB) and look at the range of their vols. Then estimate which percentile it will be in this range according to the size of the company. This is very very raw estimate. Once the stock starts trading then you can adjust.
More discussion on volatility trading can be found in Colin Bennett’s book Trading Volatility: Trading Volatility, Correlation, Term Structure and Skew