# How to estimate the price of a European call when the underlying is not tradable?

Assume you have a vanilla call on an underlying $S$ with strike price $K$ and expiry at time $T$.

Let's say that $S$ follows a GBM with volatility $\sigma$.

In general, one would use the Black-Scholes formula to price this option, but this relies on many assumptions and in particular that one can buy/sell the stock in continuous time.

What if we cannot trade the stock (for example, we're not allowed to). What are the different ways of valuing this options?

The only way I see is to estimate your own utility function given an expected payoff and a volatility, which is really hard, but I wanted to know if there was any other well-known approach?

• If the asset is non-tradable, isn't this worthless? So the price of the option should be zero? Dec 1, 2015 at 7:24
• @StudentT I've heard this argument, but let's say the payoff is cash-settled, then it clearly has a value right?
– SRKX
Dec 1, 2015 at 7:49
• Is there a liquid market for these options? You could calibrate your favorite option model to this market.
– Olaf
Dec 1, 2015 at 12:03
• @Olaf I see your point. I'm trying to consider a case where the options are not traded either.
– SRKX
Dec 2, 2015 at 1:34
• Did you have a look at weather derivatives?
– Olaf
Dec 2, 2015 at 9:32

1 - Try real options valuation methods if underlying is not tradable, and use the volatility of a proxy / peer or comparable asset as an estimate. None of the approaches would be perfect with unlisted stocks (in general), so you'll surely end up in using own judgement to gauge the fair value of the option under study.

• @SRKX: could you be a bit more specific in providing us with the nature of the non-tradable asset, since there exists a profusion of alternative asset classes (non-traded)? and the methods could be more or less suited depending on type you're dealing with. Dec 1, 2015 at 7:37
• @StudentT: The option price should not be 0 in any case (just because underlying is non-traded). Dec 1, 2015 at 7:38