How is anything bespoke priced and traded?

External question — Quantitative Finance Stack Exchange Author: CarefulBro45 Original post: https://quant.stackexchange.com/questions/85824 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Over the counter, how would you price a put option, say? We know the formula, but the formula requires a risk-neutral volatility, decided by a market that doesn't exist. If two fellas, A and B, want to trade this option, how do they agree on a price?? We can come up with all kinds of fancy vol models, but ultimately they depend on parameters that we need to calibrate to a market that isn't there. WE are the market.

External answer — Quantitative Finance Stack Exchange Author: Misha Fomytskyi Original post: https://quant.stackexchange.com/a/85831 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. In practice, you use the market price (Q-measure) for the factors you can hedge and very conservative (P-measure) estimates for the factors you cannot. You buy at 40 vol an option on an illiquid underlier that realizes between 50 and 100. For someone who cannot sell the asset but needs cash that may be a good deal as well. In theory you can look at indifference pricing and certainty equivalent pricing.