Extension of Short Rate Model Under a Lévy Process

Main Article Content

Dr A. M. Udoye


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


Download data is not yet available.


Metrics Loading ...

Article Details

How to Cite
Udoye, D. A. M. (2023). Extension of Short Rate Model Under a Lévy Process. Fountain Journal of Natural and Applied Sciences, 12(2). https://doi.org/10.53704/fujnas.v12i2.464


Chan, K. C., Karolyi, G. A., Longstaff, F. A. & Sanders, A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. The Journal of Finance, 47(3), 1209-1227.

Hirsa, A. & Madan, D. B. (2004). Pricing American options under variance gamma. Journal of Computational Finance 7(2), 63-80.

Hull, J. & White, A. (1990). Pricing interest rate derivative securities. Review of Financial Studies 3, 573-592.

Klingler, S., Kim, Y. S., Rachev, S. T. & Fabozzi, F. J. (2013). Option pricing with time-changed Lévy Processes. Applied Financial Economics 23(15), 1231-1238.

Kyprianou, A. E. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer-Verlag Berlin Heidelberg.

Lang, S., Signer, R. & Spremann, K. (2018). The choice of interest rate models and its effect on bank capital requirements regulation and financial stability. International Journal of Economics and Finance 10(1), 74-92.

Ma, C. (2003). Term structure of interest rates in the presence of Lévy jumps: The HJM approach. Annals of Economics & Finance 4, 401-426.

Madan, D.B., Carr, P. & Chang, E.C. (1998). The variance gamma process and option pricing. European Finance Review 2: 79-105

Madan, D.B. & Seneta, E. (1990). The variance gamma model for share market returns. The Journal of Business 63(4), 511-524

Papapantoleon, A. (2008). An Introduction to Lévy Processes with Applications in Finance.

Park, K. & Kim, S. (2015). On Interest Rate Option Pricing with Jump Processes. International Journal of Engineering & Applied Sciences (IJEAS) 2(7), 64-67.

Park, K., Kim, S. & Shaw, W.T. (2014). Estimation and simulation of bond option pricing on the arbitrage-free model with jump. Journal of Applied & Computational Mathematics 3(2), 1-4.

Rachev, S. T., Menn, C. & Fabozzi, F. J. (2005). Fat-tailed and skewed asset return distributions: Implications for risk management, Portfolio Selection and Option Pricing. John Wiley & Sons.

Rhee, J.H. & Kim, Y.T. (2004). The market price of risk on the Lévy Interest Rate Model. Journal of Economic Research 9, 1-28.

Salem, M. B., Fouladirad, M. & Deloux, E. (2020). Variance gamma process for predictive maintenance of mechanical systems, Cogr`es Lambda Mu 22 “Les risque au cœur des transitions.” -22e Congr`e de Maˆ?trise des Risques, Oct 2020, Le Havres, France. hal-03295749v2.

Swishchuk, A. (2008). Multi-Factor Lévy Models for pricing financial and energy derivatives. Canadian Applied Mathematics Quarterly 17(44), 777-806.

Udoye, A. M. & Akinola, L. S. (2023). Special greeks of a variance-gamma driven Vasicek model. Scientific African, 19, e01466.

Udoye, A. M., Akinola, L. S., Annorzie, M. N. & Yakubu, Y. (2022). Sensitivity analysis of variance gamma parameters for interest rate derivatives. IAENG International Journal of Applied Mathematics, 52(2), 492-499.

Udoye, A. M. & G. O. S. Ekhaguere (2022). Sensitivity analysis of a class of interest rate derivatives in a variance gamma Lévy market. Palestine Journal of Mathematics. 11(2), 159-176.

Udoye, A. M., C.P. Ogbogbo & L.S. Akinola (2021). Jump-diffusion process of interest Rates and the Malliavin calculus. International Journal of Applied Mathematics34(1),183-202. http://dx.doi.org/10.12732/ijam.v34i1.10.

Yang, H. & Zhang, L. (2001). Spectrally negative Lévy processes with applications in risk theory. Advanced Applied Probability 33, 281-291