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

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), 2019. Published by Science Publishing Group

Keywords

Options, Wavelet Model, Derivatives, MGF

References
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[4] C. Ma, Advanced asset pricing theory, vol. 2. World Scientific, 2011.
[5] R. Garcia and R. Gençay, “Pricing and hedging derivative securities with neural networks and a homogeneity hint,” J. Econom., vol. 94, no. 1–2, pp. 93–115, 2000.
[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.
[15] V. Genon-Catalot, C. Laredo, and D. Picard, “Non-parametric estimation of the diffusion coefficient by wavelets methods,” Scand. J. Stat., pp. 317–335, 1992.
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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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    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
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    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
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    PB  - Science Publishing Group
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    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
  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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

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

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