Extension of Short Rate Model Under a Lévy Process

Abstract

A lot of abnormalities occur in real-life scenarios, thus leading to some difficulties in modelling such scenarios without a deeper understanding of certain aspects of Lévy processes. In this paper, the short rate model of Hull-White (1990) is extended to a model for capturing possibilities of jumps in real-life situations using a class of Lévy processes called a variance gamma process. Mathematics Subject Classification (2020). 91G30, 62P05 Keywords: Lévy processes, Brownian motion, Hull-White model, Variance gamma process

Generalization of a Variance-Gamma-Driven Interest Rate Derivative

“…Moreover, Fischer [5] discussed update on distribution theory of the process. This work generalizes the work of Udoye and Ekhaguere [13] who derived an extended Vasicek model under a VG process and used the derived expression to obtain an interest rate derivative driven by the VG process.…”

“…The Lévy processes have contributed to better modelling of phenomenon in different fields (Wei [17], Udoye & Ekhaguere [13], Udoye et al [14]). A variance gamma (VG) process is a type of Lévy process that was launched by Madan and Seneta [7] in order to take care of unexpected occurrences which can lead to inadequate modelling of a given phenomenon.…”