Skip to content
All library documents

Libraries for Building Local Volatility Surfaces from Option Quotes

Article Quant Q&A · Author: Contango
Read the original

Summary

The document surveys tools and references for constructing an options volatility surface from strike prices and bid–ask quotes. It mentions QuantLib, NAG, Intermark toolkits, an empirical study with source code, OpenGamma Strata, and research on consistent FX option pricing. The discussion distinguishes implied volatility surface construction from deriving a local volatility model, though it does not explain the numerical methods behind either task.

The replies add that one contributor chose to write a library independently, while another points to a local volatility model and its mathematical basis in OpenGamma’s analytics materials. A further reply recommends a paper presenting a closed-form local volatility function as a way to visualize the result. The document offers leads rather than a comparative evaluation: it gives no implementation details, tests, or criteria for selecting a library, and the references may require checking for current availability and capabilities.

Key ideas

  • Several libraries and research references are suggested for constructing option volatility surfaces.
  • The thread distinguishes implied volatility surfaces from local volatility models.
  • OpenGamma Analytics is identified as including a local volatility model and supporting mathematical material.
  • A closed-form treatment is suggested for visualizing the local volatility function.
  • The discussion does not benchmark tools or explain how to build a surface from bid–ask quotes.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Recommendation for a library to calculate the local volatility surface?


# Recommendation for a library to calculate the local volatility surface?












I'd like a library to calculate the options local volatility surface, i.e. the options implied volatility surface for a collection of strikes and their bid/ask prices.

Here are the libraries I've looked at:

- QuantLib (Quote: "from memory, the function qlBlackVol will interpolate vols making sure that the surface is arbitrage free" (see forum post).

- NAG (see "Using the NAG Toolbox for MATLAB in Mathematical finance").

- Intermark Tookits.

- Modelling the implied volatility surface: an empirical study for FTSE options (contains source code).

- Consistent Pricing of FX Options (doesn't calculate a surface, but interesting nevertheless).

- Strata from OpenGamma (apparently, the source contains Java calls to calculate the local volatility surface).

Do you know of any other libraries?

## Answer by Contango (score 0, accepted)

https://quant.stackexchange.com/a/1267

I ended up writing my own library - not easy, but doable.

## Answer by Kirk Wylie (score 4)

https://quant.stackexchange.com/a/3838

The OpenGamma Analytics Library definitely does have a Local Volatility model available. In addition, in our Quantitative Papers page there's a link to the full mathematics and basis for our Local Volatility implementation.

I'd be interested to know why you decided to write your own rather than using one of the above.

## Answer by Steve Lihn (score 2)

https://quant.stackexchange.com/a/32191

You may be interested in the closed form solution of local volatility function, a paper I just finished. This can help you visualize what it looks like.

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.