| تعداد نشریات | 63 |
| تعداد شمارهها | 2,257 |
| تعداد مقالات | 18,555 |
| تعداد مشاهده مقاله | 57,400,884 |
| تعداد دریافت فایل اصل مقاله | 29,417,372 |
European option pricing underlying two assets using PINN | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 4، شماره 2، اسفند 2024، صفحه 17-31 اصل مقاله (589.31 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.79962.1135 | ||
| نویسندگان | ||
| Kimiya Tavakoli1؛ Abdolsadeh Neisy* 2؛ Alireza Zamanpour3 | ||
| 1Department of Mathematics, Allameh Tabataba’i University (ATU), Tehran, Iran. | ||
| 2Department of Mathematics, Allameh Tabataba’i University (ATU), Tehran, Iran | ||
| 3Department of financial engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran | ||
| چکیده | ||
| Modeling and pricing European options are crucial tasks for financial companies seeking to determine the fair value of these instruments. Conventional methods, such as using Black-Scholes partial differential equations (PDEs), face challenges due to the high complexity involved and lack of data. To address these challenges, PINNs have recently emerged as a promising approach to solving the Black-Scholes PDEs for European options. In this paper, we tackle the two-dimensional Black-Scholes model to determine the price of a European exchange option. We employ a kind of ANNs (PINN) that is specifically designed to learn the option’s value by minimizing an appropriately defined loss function. The data for our study were generated through simulations conducted in Python. Our results demonstrate the efficacy of the PINN approach by comparing the computed fair value of a European exchange option with the traditional solutions. The findings underscore the potential of PINNs in providing accurate and efficient pricing for complex financial derivatives. | ||
| کلیدواژهها | ||
| Physics-informed Neural Networks؛ Two-dimensional Black-Scholes Model؛ Loss Function؛ Activation Function؛ ANN | ||
| مراجع | ||
|
[1] Azizi, E., Neisy, A., 2018, A New Approach in Geometric Brownian Motion Model, Fuzzy Information and Engineering and Decision, Advances in Intelligent Systems and Computing Springer International Publishing AG, 646, 334-350. [2] Amilon, H., 2003, A Neural Network Versus BlackScholes: A Comparison of Pricing and Hedging Performances, J. Forecast, 22, 317335. [3] Bjork, T, 2009, Arbitrage Theory in Continuous Time, Oxford University Press , 546 pp. [4] Chen, Y., 2017, Numerical Methods for Pricing Multi-Asset Options, Department of Computer Science, University of Toronto, 85. [5] Duffy, J., 2022, Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach, Wiley, 544 pp. [6] Esfahani, M. K., Neisy, A., De Marchi, S., 2021, An RBF approach for oil futures pricing under the jump-diffusion model, Journal of Mathematical Modeling, 9, 81-92. [7] Glasserman, P., 2004, Monte Carlo Methods in Financial Engineering, Springer Science and Business Media, 596 pp. [8] Grohs, P., Hornung, F., Jentzen, A., Wurstemberger, P.V., 2023, A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations, Memoirs of the American Mathematical Society, 47-109. [9] Hagan, M., Demuth, H., Beale, M., De Jes´us, O., 1996, Neural Network Design, PWS Pub, 744 pp. [10] Han, J., Jentzenb, A., E, W., 2018, Solving high-dimensional partial differential equations using deep learning, Proc. Natl. Acad. Sci. USA, 34, 85058510. [11] Hull, J., 2000, Options, Futures Other Derivatives, Volume 1, Prentice Hall, 698 pp. [12] Kohler, M., Krzyzak, A., Todorovic, N., 2010, Pricing of highdimensional American options by neural networks, Math. Financ, 20, 383410. [13] Kollmannsberger, S., Angella, D., Jokeit, M., Herrmann, L., 2021, Deep Learning in Computational Mechanics, Springer, 108 pp. [14] Liu, S., Oosterlee, C.W., Bothe, S.M., 2019, Pricing options and computing implied volatilities using neural networks, Risks, 7, 16. [15] Margrabe, W, 1978, The value of an option to exchange one asset for another, J. Financ, 33, 177186. [16] Neisy, A., Salmani Gharaei, K., 2017, Financial Engineering and Markets Modeling: A MATLAB-based Approach, Allameh Tabatabaei University , 323 pp. [17] Neisy, A., De Marchi, S., Jalili, R., 2018, A Radial Basis Function Method for Solving Bond Pricing Model, Dolomites Research Week on Approximation (DRWA18), Alba di Canazei. [18] Oksendal, B., 2003, Stochastic Differential Equations: An Introduction with Applications, Springer, 406 pp. [19] Pasquale, A. Cuomo, S. Mariapia, R., 2024, A physicsinformed deep learning approach for solving strongly degenerate parabolic problems, Engineering with Computers Springer. [20] Pettersson, U., Larsson, E., Marcusson, G., 2008, Improved radial basis function methods for multi-dimensional option pricing, Computational and Applied Mathematics, 222, 8293. [21] Raissi, M., Karniadakis, G.E., Perdikaris, P., 2017, Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations, arXiv, arXiv:1711.10561v1.. [22] Salvador, B., Oosterlee, C.W.,Van der Meer, R., 2021, Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks, Mathematics MDPI, 9,1-20. [23] Sirignano, J., Spiliopoulos, K., 2018, A Deep Learning Algorithm for Solving Partial Differential Equations, DGM: Journal of Computational Physics, Amsterdam, The Netherlands. [24] Shahrokhabadi, M.A., Neisy, A., Perracchione, E., Polato, M., 2019, Learning with reduced kernel-based methods: Environmental and financial applications, Dolomites Research Notes on Approximation, 12, 12-27. [25] Shidfar, A., Zakeri, A., Neisy, A., 2005, A two Dimension Inverse Heat Conduction Problem For Estimating Heat Source, International Journal of Mathematics and Mathematical Science, 10, 1633-1641. [26] Wilmott, P., Howison, S., Dewynne, J., 2012, The Mathematics of Financial Derivatives, Cambridge University Press, 312 pp. [27] Van der Meer, R., Oosterlee, C., Borovykh, A., 2020, Optimally weighted loss functions for solving PDEs with Neural Netwoks, arXiv, arXiv:2002.06269. [28] Yadav, N., Yadav, A., Kumar, M., 2015, Neural Network Methods for Solving Differential Equations, Springer, 114 pp. [29] Zurada, J.M., 1992, Introduction to Artificial Neural Systems, St. Paul : West, 812 pp. | ||
|
آمار تعداد مشاهده مقاله: 1,217 تعداد دریافت فایل اصل مقاله: 991 |
||