Black–Scholes Pricing, Hedging, and Underlying Market Liquidity
Summary
The document asks whether Black–Scholes pricing remains relevant for an over-the-counter call when the option buyer cannot delta-hedge. The responses distinguish the venue where an option trades from whether its underlying asset is liquid: the accepted answer says liquidity of the underlying is the key consideration. Another answer argues that the formula can still apply without the particular trader hedging, provided the underlying follows geometric Brownian motion, and points to both no-arbitrage and equilibrium reasoning in the original theory.
These comments separate a pricing model’s assumptions from an individual trader’s ability or choice to hedge. They do not establish that every OTC option should trade at the model value, nor do they discuss model inputs, counterparty credit, transaction costs, or departures from the assumed price process. A separate, downvoted response offers personal trading observations about model values and exchange prices; those observations are not supported by systematic evidence in the document.
Key ideas
- An OTC trading venue alone does not determine whether Black–Scholes reasoning applies.
- The accepted response emphasizes liquidity in the underlying asset.
- One response states that Black–Scholes can hold without the option holder hedging if the underlying follows geometric Brownian motion.
- The document presents model assumptions and theory, but does not validate model prices against market data.
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Full text
# Black scholes OTC # Black scholes OTC Let's say you want to find the fair price of a call option. One way is to use the black scholes formula. This assumes you can delta-hedge the underlying asset and the option to eliminate risk, and hence come up with a fair price such that there are theoretically no arbitrage opportunities. However, what if you were NOT allowed to delta hedge? For example, what if the call option was bought over the counter (off exchange). Does the rationale of the black scholes option price still hold? ## Answer by Mark Joshi (score 3, accepted) https://quant.stackexchange.com/a/15431 it's the liquidity of the underlying that matters not the market in which the option was bought. ## Answer by user9403 (score 0) https://quant.stackexchange.com/a/15865 The Black Scholes formula still holds without any hedging (as long as the underlying follows a GBM) by the first fundamental theorem of asset pricing. The original paper by Black and Scholes actually made an equilibrium argument as well as a no-arbitrage argument to show that the formula is valid. ## Answer by JTHouseCat (score -2) https://quant.stackexchange.com/a/15864 I use the Black-Scholes formula here http://www.seleno.us/options.php often when I buy and sell options. Sometimes the Black-Scholes price equals the price of the option on the exchange. A lot of times when companies grant stocks options they use the Black-Scholes to report the expense of the options or determine how much the stock price might be diluted by issuing new shares and it is useful in this regard. I think if you use Black-Scholes and the price of the option is really high in comparison to Black-Scholes you shouldn't buy the option. Maybe you should sell it. I've often noticed on exchanges where the price isn't the same. Probably goes the option is getting bid up. Maybe this is an arbitrate opportunity.
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