Why OTC Vanilla Options Are Quoted by Delta and Implied Volatility

Summary

The document explains why over-the-counter vanilla options are commonly quoted using delta and implied volatility rather than option premium. Delta identifies an option in a way that supports communication across counterparties: a 25-delta call can be discussed without fixing a spot-dependent strike before a trade is close to execution. This can simplify quoting when options are hedged promptly.

Implied volatility provides a comparable measure of option pricing across strikes because it separates the volatility component from intrinsic value embedded in an in-the-money premium. It also makes patterns such as volatility smiles and smirks easier to observe and use when fitting pricing models. The explanation assumes a one-to-one mapping between strike and delta, and between premium and volatility under the relevant pricing setup; it gives conceptual reasons for quote conventions rather than empirical comparisons or a detailed account of model, market, or convention differences.

Key ideas

• Delta-based quotes let traders request an option by a spot-independent exposure before finalizing its strike.
• Implied volatility supports comparison of relative option pricing across strikes.
• Volatility quotes make smile and smirk patterns more visible for model fitting.
• The document offers conceptual motivations rather than evidence comparing quote conventions.

Tags

# Why are vanilla OTC options are quoted in delta and vol?


# Why are vanilla OTC options are quoted in delta and vol?












Why do we quote options in delta bid-ask & volatility bid-ask & why not it is quoted in terms of option premium?

## Answer by Igor Pozdeev (score 3)

https://quant.stackexchange.com/a/39831

Both the delta and volatility are a one-to-one mapping from the strike and premium respectively, so it does not harm to quote the latter in terms of the former. Now, does it any good? As options are often delta-hedged immediately, quotation in terms of delta allows to do so easily, cf. Wystup (link):

> This allows market participants to ask various partners for quotes on a 25-Delta call, which is spot independent. The actual strike will be set depending on the spot if the trade is close to being finalized.

Quotation in terms of volatility allows to compare how over- or underpriced options on different strikes are, as it makes the in-the-money part of the premium be accounted for.

Fitting option pricing models to the volatilities makes more sense as well, as several stylized facts (e.g. smile, smirk etc) are only pronounced in this representation.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.