Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model

Winnie Mbusiro Chacha; Caroline Njenga; Wilson Mahera

doi:doi:10.11648/j.ajtas.20180702.14

| Peer-Reviewed

Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model

Winnie Mbusiro Chacha, Caroline Njenga, Wilson Mahera

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 2)

Received: 1 February 2018 Accepted: 24 February 2018 Published: 22 March 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This research seeks to give insight on how advances in developed money markets can be reflected towards the establishment of derivatives markets in under developed and developing financial markets. The dynamics of the London interbank offered rate, for the developed financial market and the Kenyan interbank offered rate, for the developing financial markets, are compared. For the period between 2013-2015, both interest rates are found to have the same underlying dynamics. A European caplet is priced using the local volatility interbank offered rate model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep. Thereafter, the local volatility interbank offered rate model is formulated and used to price the European caplet for the developing markets.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 2)
DOI	10.11648/j.ajtas.20180702.14
Page(s)	80-84
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Call Option, Kenyan IBOR, LIBOR

References

[1]	Andersen, L., & Andreasen, J. (2000). Volatility skews and extensions of the libor market model. Applied Mathematical Finance, 7 (1), 1–32.
[2]	Berestycki, H., Busca, J., & Florent, I. (2002). Asymptotics and calibration of local volatility models. Quantitative finance, 2 (1), 61–69.
[3]	Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities.
[4]	Dupire, B., et al. (1994). Pricing with a smile. Risk, 7 (1), 18–20.
[5]	Henry-Labordere, P. (2009). Calibration of local stochastic volatility models to market smiles: A monte-carlo approach. Risk Magazine, September.
[6]	Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of financial studies, 6 (2), 327–343.
[7]	Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The journal of finance, 42 (2), 281–300.
[8]	Jamshidian, F. (1997). Libor and swap market models and measures. Finance and Stochastics, 1 (4), 293–330.
[9]	Sepp, A. (2002). Pricing barrier options under local volatility. Math. Comp.
[10]	Stein, E. M., & Stein, J. C. (1991). Stock price distributions with stochastic volatility: an analytic approach. Review of financial Studies, 4 (4), 727–752.
[11]	Wang, D. L, Huixia Judy “Estimation of high conditional quantiles for heavy-tailed distributions”, 2012.
[12]	Zhu, D., & Qu, D. (2016). Libor local volatility model: A new interest rate smile model. Wilmott, 2016 (82), 78–87.

Cite This Article

Plain Text BibTeX RIS

APA Style

Winnie Mbusiro Chacha, Caroline Njenga, Wilson Mahera. (2018). Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. American Journal of Theoretical and Applied Statistics, 7(2), 80-84. https://doi.org/10.11648/j.ajtas.20180702.14

Copy | Download

ACS Style

Winnie Mbusiro Chacha; Caroline Njenga; Wilson Mahera. Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. Am. J. Theor. Appl. Stat. 2018, 7(2), 80-84. doi: 10.11648/j.ajtas.20180702.14

Copy | Download

AMA Style

Winnie Mbusiro Chacha, Caroline Njenga, Wilson Mahera. Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. Am J Theor Appl Stat. 2018;7(2):80-84. doi: 10.11648/j.ajtas.20180702.14

Copy | Download

@article{10.11648/j.ajtas.20180702.14,
  author = {Winnie Mbusiro Chacha and Caroline Njenga and Wilson Mahera},
  title = {Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {2},
  pages = {80-84},
  doi = {10.11648/j.ajtas.20180702.14},
  url = {https://doi.org/10.11648/j.ajtas.20180702.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180702.14},
  abstract = {This research seeks to give insight on how advances in developed money markets can be reflected towards the establishment of derivatives markets in under developed and developing financial markets. The dynamics of the London interbank offered rate, for the developed financial market and the Kenyan interbank offered rate, for the developing financial markets, are compared. For the period between 2013-2015, both interest rates are found to have the same underlying dynamics. A European caplet is priced using the local volatility interbank offered rate model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep. Thereafter, the local volatility interbank offered rate model is formulated and used to price the European caplet for the developing markets.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model
AU  - Winnie Mbusiro Chacha
AU  - Caroline Njenga
AU  - Wilson Mahera
Y1  - 2018/03/22
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180702.14
DO  - 10.11648/j.ajtas.20180702.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 80
EP  - 84
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180702.14
AB  - This research seeks to give insight on how advances in developed money markets can be reflected towards the establishment of derivatives markets in under developed and developing financial markets. The dynamics of the London interbank offered rate, for the developed financial market and the Kenyan interbank offered rate, for the developing financial markets, are compared. For the period between 2013-2015, both interest rates are found to have the same underlying dynamics. A European caplet is priced using the local volatility interbank offered rate model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep. Thereafter, the local volatility interbank offered rate model is formulated and used to price the European caplet for the developing markets.
VL  - 7
IS  - 2
ER  -

Copy | Download

Author Information

Winnie Mbusiro Chacha

Pan African University, Institute of Basic Sciences, Nairobi, Kenya
Caroline Njenga

Pan African University, Institute of Basic Sciences, Nairobi, Kenya
Wilson Mahera

Pan African University, Institute of Basic Sciences, Nairobi, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Winnie Mbusiro Chacha, Caroline Njenga, Wilson Mahera. (2018). Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. American Journal of Theoretical and Applied Statistics, 7(2), 80-84. https://doi.org/10.11648/j.ajtas.20180702.14

Copy | Download

ACS Style

Winnie Mbusiro Chacha; Caroline Njenga; Wilson Mahera. Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. Am. J. Theor. Appl. Stat. 2018, 7(2), 80-84. doi: 10.11648/j.ajtas.20180702.14

Copy | Download

AMA Style

Winnie Mbusiro Chacha, Caroline Njenga, Wilson Mahera. Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model. Am J Theor Appl Stat. 2018;7(2):80-84. doi: 10.11648/j.ajtas.20180702.14

Copy | Download

@article{10.11648/j.ajtas.20180702.14,
  author = {Winnie Mbusiro Chacha and Caroline Njenga and Wilson Mahera},
  title = {Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {2},
  pages = {80-84},
  doi = {10.11648/j.ajtas.20180702.14},
  url = {https://doi.org/10.11648/j.ajtas.20180702.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180702.14},
  abstract = {This research seeks to give insight on how advances in developed money markets can be reflected towards the establishment of derivatives markets in under developed and developing financial markets. The dynamics of the London interbank offered rate, for the developed financial market and the Kenyan interbank offered rate, for the developing financial markets, are compared. For the period between 2013-2015, both interest rates are found to have the same underlying dynamics. A European caplet is priced using the local volatility interbank offered rate model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep. Thereafter, the local volatility interbank offered rate model is formulated and used to price the European caplet for the developing markets.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model
AU  - Winnie Mbusiro Chacha
AU  - Caroline Njenga
AU  - Wilson Mahera
Y1  - 2018/03/22
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180702.14
DO  - 10.11648/j.ajtas.20180702.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 80
EP  - 84
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180702.14
AB  - This research seeks to give insight on how advances in developed money markets can be reflected towards the establishment of derivatives markets in under developed and developing financial markets. The dynamics of the London interbank offered rate, for the developed financial market and the Kenyan interbank offered rate, for the developing financial markets, are compared. For the period between 2013-2015, both interest rates are found to have the same underlying dynamics. A European caplet is priced using the local volatility interbank offered rate model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep. Thereafter, the local volatility interbank offered rate model is formulated and used to price the European caplet for the developing markets.
VL  - 7
IS  - 2
ER  -

Copy | Download