Pricing Bespoke Options with Hedgable and Unhedgeable Risk

Summary

The document considers how two parties might price an over-the-counter option when there is no active market to reveal an implied volatility. It distinguishes factors that can be hedged from those that cannot: market prices can inform assumptions for hedgeable risks, while conservative real-world estimates may be appropriate for risks that remain exposed. The example contrasts an option priced at a lower volatility with a highly uncertain range of possible realized volatility, illustrating how a buyer with a need for liquidity might still value the contract.

The answer also points to indifference pricing and certainty-equivalent pricing as theoretical approaches for bespoke trades. No derivation, calibration procedure, or empirical evidence is provided, so the document offers a conceptual framework rather than a practical pricing model. Any price would depend on the parties’ exposures, risk preferences, and ability to hedge.

Key ideas

• Without a liquid market, bespoke option prices cannot be read from an observed implied volatility.
• Use market-based assumptions for risks that can be hedged and conservative estimates for risks that cannot.
• A buyer’s liquidity needs may affect the value of an option on an illiquid asset.
• Indifference pricing and certainty-equivalent pricing are possible theoretical frameworks.

Tags

# How is anything bespoke priced and traded?


# How is anything bespoke priced and traded?












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.

## Answer by Misha Fomytskyi (score 1)

https://quant.stackexchange.com/a/85831

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.

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