Dynamic Term Structure Modelling with Default and Mortality Risk: New Results on Existence and Monotonicity

TL;DR

This paper develops a comprehensive framework for dynamic term structure models incorporating default and mortality risks, establishing conditions for their existence, no-arbitrage, and monotonicity, with practical examples.

Contribution

It introduces a general model with infinitely many Brownian motions and random measures, extending existing models and providing new conditions for monotonicity and no-arbitrage.

Findings

Derived drift conditions equivalent to no arbitrage

Proved existence of models under general conditions

Identified conditions ensuring model monotonicity

Abstract

This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. Then we derive drift conditions which are equivalent to no asymptotic free lunch on the considered market. Existence results are also given. In practice, models possessing a certain monotonicity are favorable and we study general conditions which guarantee this. The setup is illustrated with some examples.