On continuity properties for option prices in exponential L\'evy models

TL;DR

This paper investigates the convergence of option prices in exponential Lévy models, providing conditions for convergence and analyzing behavior in cases where convergence does not occur, with applications to entropy and Hellinger measure minimization.

Contribution

It establishes new conditions for option price convergence in exponential Lévy models and explores the effects of different martingale measure choices.

Findings

Convergence conditions for option prices are identified.

Behavior of prices without convergence is analyzed.

Special cases include entropy and Hellinger measure minimization.

Abstract

For a converging sequence of exponential L\'evy models, we give conditions under which the associated sequence of option prices converges. We also study the behaviour of the prices when no such convergence holds. We then consider two special cases, first when the martingale measure is chosen by minimisation of entropy and then when it minimises Hellinger integrals.