JUMP-DIFFUSION PROCESS OF INTEREST
RATES AND THE MALLIAVIN CALCULUS
A.M. Udoye1, C.P. Ogbogbo2, L.S. Akinola3
1,3 Department of Mathematics
Federal University Oye-Ekiti
Ekiti - P.M.B. 373, NIGERIA
2 Department of Mathematics
University of Ghana, Legon
Accra - P.O. Box LG 62, GHANA

Abstract

In this paper, we employ the existing Hull-White short rate model to derive an interest rate model driven by jump-diffusion process. Interest rates experience both positive and negative jumps at some intervals as a result of several factors which include natural disasters and presence of pandemics such as corona virus. Much has been done in the modelling of interest rates driven by Brownian motion process whereas little emphasis are laid on jumps inherent in the interest rates. For efficient modelling and pricing of financial derivatives, there is need to consider the aspect of jumps. Hence, this paper bridges the gap by focusing on an improved model. Sensitivities namely `delta', `vega', `Theta' and `Gamma' of the new model are also derived using Malliavin calculus.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 1
Year: 2021

DOI: 10.12732/ijam.v34i1.10

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