Why Options Traders Quote Implied Volatility Instead of Price

Summary

The document describes implied volatility as a way to represent option prices on a more interpretable and comparable scale. A pricing model maps a market option price to the volatility input that would reproduce that price, allowing traders to discuss an option in volatility terms and compare points across strikes and maturities.

It gives two practical reasons for modeling and calibration on an implied volatility surface: the surface is easier to interpret, and its values are more numerically manageable for optimization than option prices that can vary greatly in scale. It also notes that extrapolation at low or high strikes may be specified through parametric price functions. The price surface remains useful: its second derivative with respect to strike is related to the discounted implied density of the underlying. The explanation is conceptual and does not address model assumptions or calibration procedures in detail.

Key ideas

• Implied volatility transforms an option price into the volatility input that reproduces that price under a pricing model.
• A volatility surface can be easier to interpret and calibrate than prices whose magnitudes vary across strikes and maturities.
• Price-based parameterizations may still be used to describe extrapolation beyond observed strikes.
• The second strike derivative of option prices is related to the discounted implied density of the underlying.

Tags

# Implied volatility as price transform


# Implied volatility as price transform












- Implied volatility

The way I understand it, traders often think of implied volatility as a transformed price. So in a way, the Black Scholes model is considered a 'model-free' blackbox that takes a market price and returns an 'implied volatility'. A trader might very well say 'I bought AstraZeneca at 20 vol'. Why is that they prefer implied vol as a price?

- Implied vol surface

When you devise a new stochastic volatility model, you want it to match the empirical volatility surface as closely as possible (thereby matching the price surface as closely as possible because there is this one to one relationship between implied volatility and price). Why do quants prefer the implied vol surface instead of bespoke price surface?

Thanks!

## Answer by Antoine Conze (score 2, accepted)

https://quant.stackexchange.com/a/21927

It is difficult to gain intuition by just looking at the price surface, and it is also easier to calibrate models on the volatility surface rather than on the price surface because with the later you are dealing with numbers of very different sizes (depending on the moneyness and maturity) which is not good for minimization algorithms. However low and high strikes extrapolation of the volatility surface are often specified in terms of parametric functions for the price.

A useful quantity directly related to the price surface is its second derivative w.r.t strike because it gives you the (discounted) implied density of the underlying asset.

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.