Determining the implied volatility in the Dupire equation for vanilla European call options

TL;DR

This paper proves Lipschitz stability for the inverse problem of determining implied volatility from vanilla European call option prices across different strikes, enhancing understanding of the model's robustness.

Contribution

It establishes Lipschitz stability in the inverse problem of recovering implied volatility from market data, a novel theoretical result.

Findings

Lipschitz stability proven for the inverse problem

Implied volatility can be stably recovered from option prices

Enhances theoretical understanding of the Dupire equation

Abstract

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a collection of quoted option prices with different strikes.