"Black-Scholes-Artificial Neural Network": A novel option pricing model

https://doi.org/10.35912/ijfam.v5i4.1684
Published: Mar 13, 2024

Abstract:

Purpose: This study conducts a comparative study of various options pricing models and introduces a new model.

Research methodology: This paper reviews eight option pricing models, including the Black-Scholes-Merton model (BSM), Monte Carlo simulation (MC), Heston, GARCH, Lattice, Jump Diffusion models (JDM), Normal Inverse Gaussian-Cox-Ingersoll-Ross Model, and a novel model called Black-Scholes-Artificial Neural Network (BSANN). The objective is to predict the European call and put options using a payoff calculation. The underlying asset is Khodro, a famous automobile producer company in Iran, for the last year. The daily prices were also used as historical data. The primary software used for the calculations and plots was MATLAB. An Excel option pricing toolbox was used to obtain more accurate and improved results.

Results: Based on the results, it can be concluded that the proposed model, BS-ANN, provides the most accurate estimation with the lowest standard deviation.

Limitations: There are several limitations to be considered when choosing an underlying asset. An important factor is the availability of sufficient data on the number of shared transactions. Another limitation of this study is the absence of trading halts. Additionally, caution is crucial when selecting an appropriate number of estimated parameters.

Contribution: By utilizing the presented model, researchers, individuals, investors, and stock market analysts interested in trading can enhance their estimations.

Novelty: The most significant novelty of this study is the presentation of a hybrid model incorporating unique features.

Keywords:
1. Hybrid Option Pricing Models
2. Artificial neural network
3. Financial Engineering
4. Option Price Estimation
Authors:
1 . Milad Shahvaroughi Farahani
Khatam university, Tehran, Iran
https://orcid.org/0000-0002-1588-7914
2 . Shiva Babaei
Khatam university, Tehran, Iran
3 . Amirhossein Esfahani
Khatam university, Tehran, Iran
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How to Cite
Shahvaroughi Farahani, M., Babaei, S., & Esfahani, A. . (2024). "Black-Scholes-Artificial Neural Network": A novel option pricing model. International Journal of Financial, Accounting, and Management, 5(4), 475–509. https://doi.org/10.35912/ijfam.v5i4.1684
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Issue & Section
Vol. 5 No. 4 (2024): March
Articles
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

References

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    Arin, E., & Ozbayoglu, A. M. (2022). Deep learning based hybrid computational intelligence models for options pricing. Computational Economics, 59(1), 39-58.

    Bali, T. G., Hu, J., & Murray, S. (2019). Option implied volatility, skewness, and kurtosis and the cross-section of expected stock returns. Georgetown McDonough School of Business Research Paper.

    Bendob, A., & Bentouir, N. (2019). Options pricing by Monte Carlo Simulation, Binomial Tree and BMS Model: A comparative study of Nifty50 options index. Journal of Banking and Financial Economics, 1(11), 79-95.

    Bertoin, J. (1992). An extension of Pitman's theorem for spectrally positive Lévy processes. The Annals of Probability, 1464-1483.

    Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.

    Chowdhury, B., & Jeyasreedharan, N. (2019). An empirical examination of the jump and diffusion aspects of asset pricing: Japanese evidence.

    Cui, Y., del Baño Rollin, S., & Germano, G. (2017). Full and fast calibration of the Heston stochastic volatility model. European Journal of Operational Research, 263(2), 625-638.

    Dana, A. (2016). Modelling and estimation of volatility using ARCH/GARCH models in Jordan’s stock market. Asian Journal of Finance & Accounting, 8(1), 152-167.

    Das, S., Stanton, R., & Wallace, N. (2023). Algorithmic Fairness. Annual Review of Financial Economics, 15.

    Duan, J. C. (1995). The GARCH option pricing model. Mathematical finance, 5(1), 13-32.

    El Fallahi, F., Ibenrissoul, A., & Adil, E. (2022). Does Innovation Play a Role in the Relationship Between Corporate Social and Financial Performance? A Systematic Literature Review. International Journal of Financial, Accounting, and Management, 4(3), 315-334.

    Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.

    Gen, M., & Lin, L. (2023). Genetic algorithms and their applications. In Springer handbook of engineering statistics (pp. 635-674): Springer.

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    Guo, Z. (2022). Derivatives and Personal Finance: Structured Financial Products. Frontiers in Business, Economics and Management, 5(2), 188-191.

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    He, T. (2019). Nonparametric predictive inference for option pricing based on the binomial tree model. Durham University.

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    Jayaraman, S. K. (2022). Derivatives Pricing with Fractional Discrete-time Models.

    Jiang, G. J., & Pan, G. (2022). Speculation or hedging?—Options trading prior to FOMC announcements. Journal of Futures Markets, 42(2), 212-230.

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    Lin, L., Li, Y., Gao, R., & Wu, J. (2021). The numerical simulation of Quanto option prices using Bayesian statistical methods. Physica A: Statistical Mechanics and its Applications, 567, 125629.

    Liu, Z., & Huang, S. (2019). Research on Pricing of Carbon Options Based on GARCH and BS Model. Journal of Applied Science and Engineering Innovation, 6(3), 109-116.

    Liviani, R., & Rachman, Y. T. (2021). The influence of leverage, sales growth, and dividend policy on company value. International Journal of Financial, Accounting, and Management, 3(2), 165-178.

    Mayes, C.-L., & Govender, K. K. (2019). Exploring uplift modelling in direct marketing. International Journal of Financial, Accounting, and Management, 1(2), 69-79.

    Parameswaran, S. K. (2022). Fundamentals of Financial Instruments: An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives: John Wiley & Sons.

    Pucci di Benisichi, B. (2019). A Monte Carlo simulation: comparison of option pricing models.

    Qin, S. J., & Chiang, L. H. (2019). Advances and opportunities in machine learning for process data analytics. Computers & Chemical Engineering, 126, 465-473.

    Rebentrost, P., Gupt, B., & Bromley, T. R. (2018). Quantum computational finance: Monte Carlo pricing of financial derivatives. Physical Review A, 98(2), 022321.

    Roy, S. K. (2023). Impact of SMS advertising on purchase intention for young consumers. International Journal of Financial, Accounting, and Management, 4(4), 427-447.

    Shahvaroughi Farahani, M., & Razavi Hajiagha, S. H. (2021). Forecasting stock price using integrated artificial neural network and metaheuristic algorithms compared to time series models. Soft computing, 25(13), 8483-8513.

    Simiyu, H. M., Waititu, A. G., & Akinyi, J. A. (2019). Comparative analysis of the artificial neural networks options pricing model under constant and time-variant volatilities. J Math Stat, 15(1), 158-175.

    Smith, J. S. (2019). International trade promotion methods for SMEs in low and lower-middle-income economies. International Journal of Financial, Accounting, and Management, 1(3), 131-145.

    Taheri, S., & Aliakbary, S. (2022). Research trend prediction in computer science publications: a deep neural network approach. Scientometrics, 127(2), 849-869.

    Trinh, Y. T., & Hanzon, B. (2022). Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method. arXiv preprint arXiv:2202.00785.

    Tudor, A. (2022). Comparison between traditional and modern option pricing models. University of Twente.

    Veganzones, D., & Severin, E. (2021). Corporate failure prediction models in the twenty-first century: a review. European Business Review, 33(2), 204-226.

    Velasquez, R. (2020). Option Pricing on Levy Based Markets.

    Wang, T., Cheng, S., Yin, F., & Yu, M. (2022). Overnight volatility, realized volatility, and option pricing. Journal of Futures Markets, 42(7), 1264-1283.

    Wani, A. S. (2022). The genesis of Islamic finance system: Exploring the mainsprings and emerging markets. International Journal of Financial, Accounting, and Management, 4(1), 31-47.

    Yeh, I.-C., & Lien, C.-H. (2020). Evaluating real estate development project with Monte Carlo based binomial options pricing model. Applied Economics Letters, 27(4), 307-324.

  1. Almeida, C., Fan, J., Freire, G., & Tang, F. (2023). Can a machine correct option pricing models? Journal of Business & Economic Statistics, 41(3), 995-1009.
  2. Arin, E., & Ozbayoglu, A. M. (2022). Deep learning based hybrid computational intelligence models for options pricing. Computational Economics, 59(1), 39-58.
  3. Bali, T. G., Hu, J., & Murray, S. (2019). Option implied volatility, skewness, and kurtosis and the cross-section of expected stock returns. Georgetown McDonough School of Business Research Paper.
  4. Bendob, A., & Bentouir, N. (2019). Options pricing by Monte Carlo Simulation, Binomial Tree and BMS Model: A comparative study of Nifty50 options index. Journal of Banking and Financial Economics, 1(11), 79-95.
  5. Bertoin, J. (1992). An extension of Pitman's theorem for spectrally positive Lévy processes. The Annals of Probability, 1464-1483.
  6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.
  7. Chowdhury, B., & Jeyasreedharan, N. (2019). An empirical examination of the jump and diffusion aspects of asset pricing: Japanese evidence.
  8. Cui, Y., del Baño Rollin, S., & Germano, G. (2017). Full and fast calibration of the Heston stochastic volatility model. European Journal of Operational Research, 263(2), 625-638.
  9. Dana, A. (2016). Modelling and estimation of volatility using ARCH/GARCH models in Jordan’s stock market. Asian Journal of Finance & Accounting, 8(1), 152-167.
  10. Das, S., Stanton, R., & Wallace, N. (2023). Algorithmic Fairness. Annual Review of Financial Economics, 15.
  11. Duan, J. C. (1995). The GARCH option pricing model. Mathematical finance, 5(1), 13-32.
  12. El Fallahi, F., Ibenrissoul, A., & Adil, E. (2022). Does Innovation Play a Role in the Relationship Between Corporate Social and Financial Performance? A Systematic Literature Review. International Journal of Financial, Accounting, and Management, 4(3), 315-334.
  13. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.
  14. Gen, M., & Lin, L. (2023). Genetic algorithms and their applications. In Springer handbook of engineering statistics (pp. 635-674): Springer.
  15. Guides, T. S. (2018). Call Option vs Put Option – Introduction to Options Trading. from https://tradingstrategyguides.com/call-option-vs-put-option/
  16. Guo, Z. (2022). Derivatives and Personal Finance: Structured Financial Products. Frontiers in Business, Economics and Management, 5(2), 188-191.
  17. Hamid, A. A., & Razak, A. (2023). Determinants of bond rating and its implications to corporate bond yield.
  18. He, T. (2019). Nonparametric predictive inference for option pricing based on the binomial tree model. Durham University.
  19. He, T., Coolen, F. P., & Coolen-Maturi, T. (2021). Nonparametric predictive inference for American option pricing based on the binomial tree model. Communications in Statistics-Theory and Methods, 50(20), 4657-4684.
  20. Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2), 327-343.
  21. Jang, J. H., Yoon, J., Kim, J., Gu, J., & Kim, H. Y. (2021). DeepOption: A novel option pricing framework based on deep learning with fused distilled data from multiple parametric methods. Information Fusion, 70, 43-59.
  22. Jansen, M., Nguyen, H., & Shams, A. (2020). Human vs. machine: Underwriting decisions in finance: Ohio State University, Fisher College of Business, Charles A. Dice Center ….
  23. Jayaraman, S. K. (2022). Derivatives Pricing with Fractional Discrete-time Models.
  24. Jiang, G. J., & Pan, G. (2022). Speculation or hedging?—Options trading prior to FOMC announcements. Journal of Futures Markets, 42(2), 212-230.
  25. Karagozoglu, A. K. (2022). Option Pricing Models: From Black-Scholes-Merton to Present. The Journal of Derivatives.
  26. Kase, M. S., & Laka, E. I. (2019). Influence analysis of capital shopping and local own-source revenue on non-food shopping. International Journal of Financial, Accounting, and Management, 1(3), 147-154.
  27. Kovachev, Y. (2014). Calibration of stochastic volatility models: Uppsala Universitet.
  28. Li, W. (2022). Application of Machine Learning in Option Pricing: A Review. Paper presented at the 2022 7th International Conference on Social Sciences and Economic Development (ICSSED 2022).
  29. Lin, L., Li, Y., Gao, R., & Wu, J. (2021). The numerical simulation of Quanto option prices using Bayesian statistical methods. Physica A: Statistical Mechanics and its Applications, 567, 125629.
  30. Liu, Z., & Huang, S. (2019). Research on Pricing of Carbon Options Based on GARCH and BS Model. Journal of Applied Science and Engineering Innovation, 6(3), 109-116.
  31. Liviani, R., & Rachman, Y. T. (2021). The influence of leverage, sales growth, and dividend policy on company value. International Journal of Financial, Accounting, and Management, 3(2), 165-178.
  32. Mayes, C.-L., & Govender, K. K. (2019). Exploring uplift modelling in direct marketing. International Journal of Financial, Accounting, and Management, 1(2), 69-79.
  33. Parameswaran, S. K. (2022). Fundamentals of Financial Instruments: An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives: John Wiley & Sons.
  34. Pucci di Benisichi, B. (2019). A Monte Carlo simulation: comparison of option pricing models.
  35. Qin, S. J., & Chiang, L. H. (2019). Advances and opportunities in machine learning for process data analytics. Computers & Chemical Engineering, 126, 465-473.
  36. Rebentrost, P., Gupt, B., & Bromley, T. R. (2018). Quantum computational finance: Monte Carlo pricing of financial derivatives. Physical Review A, 98(2), 022321.
  37. Roy, S. K. (2023). Impact of SMS advertising on purchase intention for young consumers. International Journal of Financial, Accounting, and Management, 4(4), 427-447.
  38. Shahvaroughi Farahani, M., & Razavi Hajiagha, S. H. (2021). Forecasting stock price using integrated artificial neural network and metaheuristic algorithms compared to time series models. Soft computing, 25(13), 8483-8513.
  39. Simiyu, H. M., Waititu, A. G., & Akinyi, J. A. (2019). Comparative analysis of the artificial neural networks options pricing model under constant and time-variant volatilities. J Math Stat, 15(1), 158-175.
  40. Smith, J. S. (2019). International trade promotion methods for SMEs in low and lower-middle-income economies. International Journal of Financial, Accounting, and Management, 1(3), 131-145.
  41. Taheri, S., & Aliakbary, S. (2022). Research trend prediction in computer science publications: a deep neural network approach. Scientometrics, 127(2), 849-869.
  42. Trinh, Y. T., & Hanzon, B. (2022). Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method. arXiv preprint arXiv:2202.00785.
  43. Tudor, A. (2022). Comparison between traditional and modern option pricing models. University of Twente.
  44. Veganzones, D., & Severin, E. (2021). Corporate failure prediction models in the twenty-first century: a review. European Business Review, 33(2), 204-226.
  45. Velasquez, R. (2020). Option Pricing on Levy Based Markets.
  46. Wang, T., Cheng, S., Yin, F., & Yu, M. (2022). Overnight volatility, realized volatility, and option pricing. Journal of Futures Markets, 42(7), 1264-1283.
  47. Wani, A. S. (2022). The genesis of Islamic finance system: Exploring the mainsprings and emerging markets. International Journal of Financial, Accounting, and Management, 4(1), 31-47.
  48. Yeh, I.-C., & Lien, C.-H. (2020). Evaluating real estate development project with Monte Carlo based binomial options pricing model. Applied Economics Letters, 27(4), 307-324.