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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?

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

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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.

Here is an interesting link.

2 - Alternatively, I would have valued this company using DCF methods to get an expected firm value, then expected price. Once expected S is known, use volatility of the firm peers, then plug those info to the BS formula. Otherwise in case of IPO, use estimated share price from brokers, as it might be quicker than valuing the firm by your own

3 - Finally (might be least favourable), use numerical methods (like trinomial trees, etc.) if you're stuck with the maths as you seem to have mentioned in the initial post. Although you're dealing European options, as long as nodes get bigger prices from tree and BS methods do converge (undeniable fact). Once again: use estimated share price (from brokers in case of IPOs or use own company valuation via DCF methods, Multiples...) and volatility (from peers / industry..) to work out the payoffs up to the end, before discounting them back.

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  • $\begingroup$ Well a real option would be valued assuming you delta hedge in most cases, I'm looking to see which other methods are available. $\endgroup$
    – SRKX
    Dec 1, 2015 at 7:05
  • $\begingroup$ @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. $\endgroup$
    – owner
    Dec 1, 2015 at 7:37
  • $\begingroup$ @StudentT: The option price should not be 0 in any case (just because underlying is non-traded). $\endgroup$
    – owner
    Dec 1, 2015 at 7:38
  • $\begingroup$ @owner example is a call on a company not publicly traded, which might become tradable in the future $\endgroup$
    – SRKX
    Dec 1, 2015 at 7:39

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