<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects of such unexpected occurrences in real life. A good risk manager needs to have a better model that considers possibility of unexpected occurrences. In this paper, we discuss step by step extension of Vasicek model to both jump model and jumpdiffusion model using Itô’s formula as the major tool. We also derive the greeks ‘delta’ and ‘vega’ that measure sensitivity of the interest rate with respect to both changes in its initial interest rate and volatility in an interbank rate.</p>
</abstract>

Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects of such unexpected occurrences in real life. A good risk manager needs to have a better model that considers possibility of unexpected occurrences. In this paper, we discuss step by step extension of Vasicek model to both jump model and jumpdiffusion model using Itô’s formula as the major tool. We also derive the greeks ‘delta’ and ‘vega’ that measure sensitivity of the interest rate with respect to both changes in its initial interest rate and volatility in an interbank rate.

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Department of Mathematics, Faculty of Science

Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences

Department of Mathematics, Faculty of Physical Sciences

Annals of Science and Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities"}

Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects...

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Publié en ligne: 01 juil. 2021

Pages: 9 - 15

Reçu: 23 déc. 2020

Accepté: 15 avr. 2021

DOI: https://doi.org/10.2478/ast-2021-0002

Mots clés
Interest Rate, Vasicek model, Compound Poisson process, Jump-diffusion process, Itô formula

© 2021 Adaobi M. Udoye et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Publié en ligne: 01 juil. 2021

Pages: 9 - 15

Reçu: 23 déc. 2020

Accepté: 15 avr. 2021

DOI: https://doi.org/10.2478/ast-2021-0002

Mots clésInterest Rate, Vasicek model, Compound Poisson process, Jump-diffusion process, Itô formula

© 2021 Adaobi M. Udoye et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Interest Rate, Vasicek model, Compound Poisson process, Jump-diffusion process, Itô formula