Liquidity-free implied volatilities: an approach using conic finance

TL;DR

This paper introduces a novel method using conic finance to derive risk-neutral implied volatilities directly from bid and ask prices of European options, eliminating the need for mid-price data and enabling liquidity measurement.

Contribution

It presents a unique approach to extract implied volatilities and liquidity from bid-ask quotes without restrictive assumptions, expanding the tools for market analysis.

Findings

Successfully derives implied volatilities from bid-ask quotes

Provides a method to estimate market liquidity

Applicable to other implied parameters from bid-ask data

Abstract

We consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the implied liquidity of the market. The idea outlined in this paper can be applied to calculate other implied parameters from bid and ask security prices as soon as their theoretical risk-neutral counterparts are strictly increasing with respect to the former.