Moment Explosion in the LIBOR Market Model

TL;DR

This paper investigates the tail behavior of forward interest rates in the LIBOR market model, revealing that their distributions exhibit approximately log-normal tails under different forward measures, which has implications for risk assessment.

Contribution

It demonstrates that forward interest rates in the LIBOR model have approximately log-normal tails under various measures, extending understanding of their distributional properties.

Findings

Forward rates have approximately log-normal tails under different measures

Tail behavior impacts risk management in LIBOR models

Distributional properties vary across measures

Abstract

In the LIBOR market model, forward interest rates are log-normal under their respective forward measures. This note shows that their distributions under the other forward measures of the tenor structure have approximately log-normal tails.