Approaches to Arbitrage-Free Implied Volatility and Local Volatility Calibration

Summary

The discussion concerns calibrating a Dupire local volatility model and asks whether the Andreasen and Huge interpolation method is robust and widely used. The response frames the choice of method around the source of concern, especially how implied volatility data are interpolated before deriving a local volatility surface.

It points to several approaches: smoothing implied volatilities while enforcing arbitrage constraints, arbitrage-free interpolation of volatility, and interpolation of call prices. It also mentions finite-difference schemes designed to recover vanilla option prices exactly, along with further work by other researchers. These references illustrate a range of relevant methods, but the response does not compare their performance, specify implementation details, or establish that one method is universally preferred. Selection therefore depends on the calibration requirements and the issues the practitioner wants to address.

Key ideas

• Dupire local volatility calibration depends on how the implied volatility or option price surface is interpolated.
• Arbitrage-free smoothing and interpolation are established approaches for constructing usable surfaces.
• Interpolation can be performed on implied volatilities or on call option prices.
• Finite-difference schemes with exact recovery of vanilla prices are another approach to consider.
• The response offers references but no empirical comparison or universal recommendation.

Tags

# Dupire's calibration


# Dupire's calibration












I'm trying to implement a method for calibrating the local volatility model (Dupire's one). I'm working on the paper from Andreasen and Huge : Volatility interpolation (SSRN). Is this considered to be a robust and commonly used algorithm for calibrating the local volatility or is there any other paper which might be better and commonly used ?

Thank you.

## Answer by KT8 (score 2)

https://quant.stackexchange.com/a/78440

There have been advances in that regard, but which papers are relevant really depends on what is it thay you may worry about.

For example, to compute a local volatility surface, you need to interpolate implied volatilities. Different approaches have been followed, the main ideas coming from the following two papers: M. Fengler - Arbitrage-Free Smoothing of the Implied Volatility Surface (2005) where the points in the implied volatility surface are adjusted to avoid arbitrage, and N. Kahale - An Arbitrage-free Interpolation of Volatilities (2003). These are a bit older than the one you mentioned, but triggered the following: C. Bender and M. Thiel - Arbitrage-free Interpolation of Call Option Prices (2019)

Another interesting paper is P. Austing Finite Difference Schemes with Exact Recovery of Vanilla Option Prices (2019).

Moreover, Labordere and Conze have been working on the topic. The paper actually granted Labordere another quant of the year award by Risk.net.

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