Valuing European Calls on Nontradable Underlyings
Summary
The document considers valuing a European call when its underlying asset cannot be traded, so the continuous-trading replication assumptions behind Black–Scholes are unavailable. Suggested inputs and approaches include estimating the underlying’s value from a discounted cash flow or comparable-company analysis, and estimating volatility from peers or proxy assets. For a prospective IPO, broker estimates are mentioned as another possible source for a share-price estimate.
The response also suggests real-options valuation and numerical methods such as trinomial trees, with estimated value and volatility used to model possible payoffs and discount them. These are practical approximations rather than a uniquely justified market price: an illiquid or unlisted underlying lacks direct market prices for calibration, and peer volatility or valuation estimates may not capture its specific risks. The document offers no worked example or comparison of accuracy, and emphasizes that judgment remains necessary.
Key ideas
- A nontradable underlying prevents direct replication through continuous trading.
- Real-options methods and proxy volatility are suggested for valuing the option.
- Company valuation methods can provide an estimated underlying price for a pricing model.
- Tree methods can model payoffs, but estimates and judgment remain central.
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Full text
# How to estimate the price of a European call when the underlying is not tradable? # 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? ## Answer by owner (score 2) https://quant.stackexchange.com/a/22018 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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