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Limits of Put Option Models for Private Company Illiquidity Discounts

Article Quant Q&A · Author: limestreetlab
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Summary

The document challenges the use of put options to estimate illiquidity discounts for private companies. Its author argues that a put-only model truncates downside exposure while leaving upside participation, changing the investor’s payoff in a way that may not represent the underlying restriction on selling. A close match between some model estimates and observed private placements, the author contends, does not by itself establish that the option framework is logically sound.

The argument invokes put-call parity: if equivalent calls and puts are assumed available, an investor could combine them to hedge exposure, leaving only carry and trading costs. It considers a collar as a more interpretable option-based construction, but says its implied discounts remain too small to match observed conditions. The broader claim is that option pricing assumes away illiquidity when the hypothetical option writer can trade freely, while modeling illiquidity in the option price risks restating the original estimation problem. This is a critical viewpoint, not an empirical comparison or consensus conclusion.

Key ideas

  • A put-only model may cut downside risk while retaining upside, altering the payoff being valued.
  • The author argues that assuming access to both puts and calls permits a synthetic forward hedge under put-call parity.
  • A collar is proposed as a more interpretable option structure, but the author considers its discounts too low.
  • Option methods may fail to represent illiquidity if the assumed option writer can trade freely.
  • The document presents a critique rather than a systematic empirical test of competing valuation methods.

Tags

OptionsEquitiesDerivatives pricingRisk management
Full text
# Put options used in private company valuation discounts


# Put options used in private company valuation discounts












To estimate the valuation discounts in private companies, I have come across "put options", which puzzled me and as I read the cited literature, I have come to my conclusion that put options are not appropriate. What do you think?

My Thoughts I think option-theoretic approaches are inadequate and overstate the illiquidity discounts. By neglecting upside retention, a put option alone fails to represent the underlying illiquidity problem. I argue that their estimated values being close to actual private placement data is more a coincidence rather than logical necessity; in fact, given the wide range of parameters, it is natural for theoretical values to fall between 20-40% of spot. I think equation (1), the foundation of option-theoretic models, is logically flawed. By truncating downside risk but leaving upside potential intact, in the case of Chaffe, the investor’s payoff is shifted from a long 100𝛿 stock position to one of long 50𝛿 call with breakeven at spot + premium.

The put option proposition is implicitly centered on hedging opportunities. If hedging opportunities can be pursued, then illiquidity discount shall only apply to the proportion of risks that cannot be hedged. If a put option is assumed to be available, then a call option of identical terms must also be assumed available; thus, the investor can then effect a synthetic forward sale by going long put and short call. As all risks are now hedged, the illiquidity discount must only reflect the cost of carry5 and trade costs such as bid-ask spread. This must be true based on put-call parity irrespective of modelling assumptions.

The only way to arrive at interpretable illiquidity discounts with the availability of call options is then a collar position as suggested by Barenbaum and Schubert (2015). However, the resulting discounts are too low to reconcile with reality even considering an at-the-money put and a far out-of-the-money call using any realistic parameters.

Based on my definition of illiquidity discounts in terms of a constrained decision set, unless Ω is a function of either 𝛿,𝛾,𝜈, I think options simply cannot capture the nature of liquidity or liquidity risk under normal conditions, so bringing option methodologies into the mix cannot remedy illiquidity. The hypothetical option writer is where illiquidity is transformed into perfect liquidity. Pricing the option without considering illiquidity is simply assuming away the very problem; attempting to incorporate illiquidity into the pricing is circling back to the very estimation issue. In sum, I find the logic problematic and put options are not a viable option.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.