Inferring an Option Liquidity Parameter from Bid–Ask Quotes

Summary

The document introduces an approach for inferring a liquidity parameter from market bid and ask prices for a European call. The parameter, denoted by λ, represents a symmetric distortion around the option’s mid price. Rather than deriving liquidity from the underlying alone, the method fits the parameter so that model expectations for the option payoff reproduce the observed ask and bid under the distorted pricing measure.

The supplied definition gives paired pricing relationships: the ask corresponds to the negative expected negative payoff, while the bid corresponds to the expected positive payoff, with discounting to present value. This frames implied liquidity as a quantity calibrated to the quoted spread. The excerpt does not provide the full stochastic liquidity model, numerical solution procedure, or details for extending the fit across strikes and maturities. It therefore establishes the parameter’s interpretation and quote-matching definition, but not a complete implementation recipe.

Key ideas

• Implied liquidity is defined as a parameter fitted to an option’s bid–ask spread.
• The stated distortion is symmetric around the option’s mid price.
• Bid and ask are matched to separate distorted expectations of the call payoff.
• The excerpt defines the concept for European calls but omits calibration and implementation details.

Tags

# How do you calculate the implied liquidity of an option?


# How do you calculate the implied liquidity of an option?












How does one calculate the implied liquidity of a specific option contract given a set of vanilla puts and calls with various strikes and maturities on a single underlying?

## Answer by phil (score 7)

https://quant.stackexchange.com/a/589

From Implied Liquidity : Towards stochastic liquidity modeling and liquidity trading

> We will call the parameter, fitting the bid-ask spread (under a symmetric distortion) around the mid price, the implied liquidity parameter. Hence for the European Call option (strike K and maturity T ) with given market bid (b) and ask (a) prices, the implied liquidity parameter is the specific λ > 0, such that: a = − exp(−rT )Eλ [−(ST − K )+ ] and b = exp(−rT )Eλ [(ST − K )+ ]

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