How to make Dupire's local volatility work with jumps

TL;DR

This paper explains why Dupire's local volatility model can be adapted to work with jump processes by proposing a regularization method for option data, bridging the gap between theory and practical application.

Contribution

It introduces a regularization procedure for option data that enables Dupire's local volatility model to accurately reflect jump processes.

Findings

Regularization improves local volatility modeling with jumps

Dupire's formula can be adapted for non-diffusion processes

Practical preconditioning aligns theory with market data

Abstract

There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire's local vol diffusion process recreates the correct option prices, even in manifest presence of jumps.