Martingale property of exponential semimartingales: a note on explicit conditions and applications to financial models

TL;DR

This paper provides explicit conditions based on semimartingale characteristics to determine when exponential semimartingales are true martingales, facilitating applications in financial modeling such as Libor models.

Contribution

It introduces explicit, characteristic-based criteria for the martingale property of exponential semimartingales, aiding in the analysis of financial models.

Findings

Explicit conditions for martingale property derived

Application to well-definedness of Libor models

Enhanced understanding of measure change implications

Abstract

We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modeling in general. Especially it allows us to carefully discuss the question of well-definedness of semimartingale Libor models, whose construction crucially relies on a sequence of measure changes.