Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model

Sigei Sheila Chepkorir; Anthony Gichuhi Waititu; Jane Aduda Akinyi

doi:doi:10.11648/j.ijdsa.20190505.13

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Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model

Sigei Sheila Chepkorir, Anthony Gichuhi Waititu, Jane Aduda Akinyi

Published in International Journal of Data Science and Analysis (Volume 5, Issue 5)

Received: 2 October 2019 Accepted: 12 October 2019 Published: 28 October 2019

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Abstract

The Black- Scholes model is a well-known model for hedging and pricing derivative securities. However, it exhibits some systematic biases or unrealistic assumptions like the log-normality of asset returns and constant volatility. A number of studies have attempted to reduce these biases in different ways. The objective of this study is to value a European call option using a non-parametric model and a parametric model. Amongst the non-parametric approaches used to improve the accuracy of the model in this study is the Wavelet-based pricing model. This model is found as promising alternative as far as pricing of European options is concerned, due to its varied volatility of the underlying security and estimation of the risk neutral MGF. This study made an attempt to improve the accuracy of option price estimation using Wavelet method and it improves the accuracy due to its ability to estimate the risk neutral MGF. The MSE and RMSE of Wavelet model is 0.208546 and 0.456669 respectively which is much lower than that of Black-Scholes model and therefore in conclusion, Wavelet model outperforms the other model. The study was carried out using simulated stock prices of 1024 observations.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 5)
DOI	10.11648/j.ijdsa.20190505.13
Page(s)	92-98
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), 2024. Published by Science Publishing Group

Keywords

Options, Wavelet Model, Derivatives, MGF

References

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[6]	E. Haven, X. Liu, C. Ma, and L. Shen, “Revealing the implied risk-neutral MGF from options: The wavelet method,” J. Econ. Dyn. Control, vol. 33, no. 3, pp. 692–709, 2009.
[7]	E. Haven, X. Liu, and L. Shen, “De-noising option prices with the wavelet method,” Eur. J. Oper. Res., vol. 222, no. 1, pp. 104–112, 2012.
[8]	J. B. Ramsey and C. Lampart, “Decomposition of economic relationships by timescale using wavelets,” Macroecon. Dyn., vol. 2, no. 1, pp. 49–71, 1998.
[9]	R. Weron, “Heavy-tails and regime-switching in electricity prices,” Math. Methods Oper. Res., vol. 69, no. 3, pp. 457–473, 2009.
[10]	E. Capobianco, “Wavelet transforms for the statistical analysis of returns generating stochastic processes,” Int. J. Theor. Appl. Financ., vol. 4, no. 03, pp. 511–534, 2001.
[11]	E. W. Sun and T. Meinl, “A new wavelet-based denoising algorithm for high-frequency financial data mining,” Eur. J. Oper. Res., vol. 217, no. 3, pp. 589–599, 2012.
[12]	H. Asgharian, “A conditional asset-pricing model with the optimal orthogonal portfolio,” J. Bank. Financ., vol. 35, no. 5, pp. 1027–1040, 2011.
[13]	A.-M. Matache, P.-A. Nitsche, and C. Schwab, “Wavelet Galerkin pricing of American options on Lévy driven assets,” Quant. Financ., vol. 5, no. 4, pp. 403–424, 2005.
[14]	L. Ortiz-Gracia and C. W. Oosterlee, “A highly efficient Shannon wavelet inverse Fourier technique for pricing European options,” SIAM J. Sci. Comput., vol. 38, no. 1, pp. B118--B143, 2016.
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[16]	M. J. Jensen, “Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter,” J. Forecast., vol. 18, no. 1, pp. 17–32, 1999.

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Sigei Sheila Chepkorir, Anthony Gichuhi Waititu, Jane Aduda Akinyi. (2019). Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. International Journal of Data Science and Analysis, 5(5), 92-98. https://doi.org/10.11648/j.ijdsa.20190505.13

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ACS Style

Sigei Sheila Chepkorir; Anthony Gichuhi Waititu; Jane Aduda Akinyi. Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. Int. J. Data Sci. Anal. 2019, 5(5), 92-98. doi: 10.11648/j.ijdsa.20190505.13

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AMA Style

Sigei Sheila Chepkorir, Anthony Gichuhi Waititu, Jane Aduda Akinyi. Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. Int J Data Sci Anal. 2019;5(5):92-98. doi: 10.11648/j.ijdsa.20190505.13

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@article{10.11648/j.ijdsa.20190505.13,
  author = {Sigei Sheila Chepkorir and Anthony Gichuhi Waititu and Jane Aduda Akinyi},
  title = {Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {92-98},
  doi = {10.11648/j.ijdsa.20190505.13},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.13},
  abstract = {The Black- Scholes model is a well-known model for hedging and pricing derivative securities. However, it exhibits some systematic biases or unrealistic assumptions like the log-normality of asset returns and constant volatility. A number of studies have attempted to reduce these biases in different ways. The objective of this study is to value a European call option using a non-parametric model and a parametric model. Amongst the non-parametric approaches used to improve the accuracy of the model in this study is the Wavelet-based pricing model. This model is found as promising alternative as far as pricing of European options is concerned, due to its varied volatility of the underlying security and estimation of the risk neutral MGF. This study made an attempt to improve the accuracy of option price estimation using Wavelet method and it improves the accuracy due to its ability to estimate the risk neutral MGF. The MSE and RMSE of Wavelet model is 0.208546 and 0.456669 respectively which is much lower than that of Black-Scholes model and therefore in conclusion, Wavelet model outperforms the other model. The study was carried out using simulated stock prices of 1024 observations.},
 year = {2019}
}

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TY  - JOUR
T1  - Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model
AU  - Sigei Sheila Chepkorir
AU  - Anthony Gichuhi Waititu
AU  - Jane Aduda Akinyi
Y1  - 2019/10/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190505.13
DO  - 10.11648/j.ijdsa.20190505.13
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 92
EP  - 98
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190505.13
AB  - The Black- Scholes model is a well-known model for hedging and pricing derivative securities. However, it exhibits some systematic biases or unrealistic assumptions like the log-normality of asset returns and constant volatility. A number of studies have attempted to reduce these biases in different ways. The objective of this study is to value a European call option using a non-parametric model and a parametric model. Amongst the non-parametric approaches used to improve the accuracy of the model in this study is the Wavelet-based pricing model. This model is found as promising alternative as far as pricing of European options is concerned, due to its varied volatility of the underlying security and estimation of the risk neutral MGF. This study made an attempt to improve the accuracy of option price estimation using Wavelet method and it improves the accuracy due to its ability to estimate the risk neutral MGF. The MSE and RMSE of Wavelet model is 0.208546 and 0.456669 respectively which is much lower than that of Black-Scholes model and therefore in conclusion, Wavelet model outperforms the other model. The study was carried out using simulated stock prices of 1024 observations.
VL  - 5
IS  - 5
ER  -

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Author Information

Sigei Sheila Chepkorir

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Gichuhi Waititu

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Jane Aduda Akinyi

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Sigei Sheila Chepkorir, Anthony Gichuhi Waititu, Jane Aduda Akinyi. (2019). Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. International Journal of Data Science and Analysis, 5(5), 92-98. https://doi.org/10.11648/j.ijdsa.20190505.13

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ACS Style

Sigei Sheila Chepkorir; Anthony Gichuhi Waititu; Jane Aduda Akinyi. Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. Int. J. Data Sci. Anal. 2019, 5(5), 92-98. doi: 10.11648/j.ijdsa.20190505.13

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AMA Style

Sigei Sheila Chepkorir, Anthony Gichuhi Waititu, Jane Aduda Akinyi. Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model. Int J Data Sci Anal. 2019;5(5):92-98. doi: 10.11648/j.ijdsa.20190505.13

Copy | Download

@article{10.11648/j.ijdsa.20190505.13,
  author = {Sigei Sheila Chepkorir and Anthony Gichuhi Waititu and Jane Aduda Akinyi},
  title = {Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {92-98},
  doi = {10.11648/j.ijdsa.20190505.13},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.13},
  abstract = {The Black- Scholes model is a well-known model for hedging and pricing derivative securities. However, it exhibits some systematic biases or unrealistic assumptions like the log-normality of asset returns and constant volatility. A number of studies have attempted to reduce these biases in different ways. The objective of this study is to value a European call option using a non-parametric model and a parametric model. Amongst the non-parametric approaches used to improve the accuracy of the model in this study is the Wavelet-based pricing model. This model is found as promising alternative as far as pricing of European options is concerned, due to its varied volatility of the underlying security and estimation of the risk neutral MGF. This study made an attempt to improve the accuracy of option price estimation using Wavelet method and it improves the accuracy due to its ability to estimate the risk neutral MGF. The MSE and RMSE of Wavelet model is 0.208546 and 0.456669 respectively which is much lower than that of Black-Scholes model and therefore in conclusion, Wavelet model outperforms the other model. The study was carried out using simulated stock prices of 1024 observations.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Valuation of European Call Options Using Wavelet-Based Pricing Model and Black-Scholes Pricing Model
AU  - Sigei Sheila Chepkorir
AU  - Anthony Gichuhi Waititu
AU  - Jane Aduda Akinyi
Y1  - 2019/10/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190505.13
DO  - 10.11648/j.ijdsa.20190505.13
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 92
EP  - 98
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190505.13
AB  - The Black- Scholes model is a well-known model for hedging and pricing derivative securities. However, it exhibits some systematic biases or unrealistic assumptions like the log-normality of asset returns and constant volatility. A number of studies have attempted to reduce these biases in different ways. The objective of this study is to value a European call option using a non-parametric model and a parametric model. Amongst the non-parametric approaches used to improve the accuracy of the model in this study is the Wavelet-based pricing model. This model is found as promising alternative as far as pricing of European options is concerned, due to its varied volatility of the underlying security and estimation of the risk neutral MGF. This study made an attempt to improve the accuracy of option price estimation using Wavelet method and it improves the accuracy due to its ability to estimate the risk neutral MGF. The MSE and RMSE of Wavelet model is 0.208546 and 0.456669 respectively which is much lower than that of Black-Scholes model and therefore in conclusion, Wavelet model outperforms the other model. The study was carried out using simulated stock prices of 1024 observations.
VL  - 5
IS  - 5
ER  -

Copy | Download