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What are the standard methods to price american call/put options on illiquid underlyings?

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With whom would you trade an option for an unlisted company? The options exchange chooses who to list (and do so to maximize the exchange's profit), but the SEC gives minimum listing requirements to protect investors: 1. underlying must be listed (i.e., publicly traded) 2. >7E6 shares of "float" (i.e., shares available for trade / not controlled by insiders) 3. >2E3 shareholders 4. cumulative trading volume >2.4E6 over the last year 5. daily close share price >$7.50 for three months. Is there some other venue? –  Richard Herron Mar 1 '11 at 20:54
    
Are you referring to employee stock options? As @richard points-out, unlisted underlyings cannot have listed options. –  chrisaycock Mar 2 '11 at 0:58
    
@ chrisaycock: yes; @ richardh: my question is theoretical, I have changed the wording –  RockScience Mar 2 '11 at 2:44
    
Ah, makes sense. You don't need to underlying price to price the option, just the vol. If you don't trust the vol for the stock (or don't have it) I think I would look at the vol for similar firms (industry, leverage, market-to-book, etc) that do have enough volume. When getting vol for these firms keep in mind that their price will have a liquidity premium relative to your unlisted/low volume stock. –  Richard Herron Mar 2 '11 at 14:20
    
Maybe double check this with a Monte Carlo simulation with a variety of parameters? If there are employee stock options, I assume they have some long vesting period (5-10 years?). You don't need the underlying price to Black-Scholes, but if the t=0 price is "wrong", then I'm not sure how that affects the assumptions. –  Richard Herron Mar 2 '11 at 14:25
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2 Answers

up vote 4 down vote accepted

For a non-listed company you usually have a poor idea of the share value. If you do not know the underlying price it is impossible to accurately estimate the option price.

So, for cases like this, people typically analyze the options on a risk/reward basis, using similar scenario analyses to those used to analyze the cashflows, assets and other components of the firm valuation.

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what about a stock which is listed but not liquid? –  RockScience Mar 2 '11 at 2:44
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To be honest, you see "sophisticated" market players using the scenario approach even with options on liquid underlyings.How can that possibly be right? Well, consider that these are typically people who take positions in equity, which is entirely contrary to the assumption in contingent claims theory that equity is fairly priced. If they feel the equity is priced inefficiently, then why not the options as well? So, the answer to your question is still: scenario analysis. –  Brian B Mar 2 '11 at 13:45
    
seams fair, thanks for your input –  RockScience Mar 3 '11 at 2:09
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Here are some practical application for trading illiquid names:

For pricing/forecasting: You still still calculate fair volatility using stock print data. In an illiquid stock and there's a large open interest in the market where professional traders are long, vol might diminish since when stock goes up(down), all the vol traders would be selling(buying) stock to gamma scalp and thus diminish vol.

For quoting: You quote width for options should be correlated with the average width of the stock market. For example: for a 50d call, you would quote 0.3 - 0.32 when stock is: 1.00 - 1.01. In the case where market is wider for stock say 1.00 - 1.05 you should only be willing to quote 0.3 - 0.34. This is because in the first case, when someone lifts your .32 offer, you can buy 1.01 to hedge but in the latter case, you can only buy 1.05.

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