Pricing American Put Option using RBF-NN: New Simulation of Black-Scholes

[1] Alanis, A. Y., Arana-Daniel, N., & Lopez-Franco, C. (Eds.). Artificial Neural Networks for Engineering Applications. Academic Press (2019). Search in Google Scholar

[2] Al-Aradi, A., Correia, A., Naiff, D., Jardim, G., & Saporito, Y. Solving nonlinear and high-dimensional partial differential equations via deep Learning. arXiv preprint arXiv:1811.08782 (2018). Search in Google Scholar

[3] Alqezweeni, M., & Gorbachenko, V. Solution of Partial Differential Equations on Radial Basis Functions Networks (No. 1964). EasyChair (2019). Search in Google Scholar

[4] Bennell, J., & Sutcliffe, C. BlackScholes versus artificial neural networks in pricing FTSE 100 options. Intelligent Systems in Accounting, Finance & Management: International Journal, 12(4), 243-260 (2004).10.1002/isaf.254 Search in Google Scholar

[5] Bhatia, G. S., & Arora, G. Radial basis function methods for solving partial differential equations-A review. Indian Journal of Science and Technology, 9(45), 1-18 (2016).10.17485/ijst/2016/v9i45/105079 Search in Google Scholar

[6] Black, F., & Scholes, M. The valuation of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654(1973).10.1086/260062 Search in Google Scholar

[7] Bollig, E. F., Flyer, N., & Erlebacher, G. Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs. Journal of Computational Physics, 231(21), 7133-7151 (2012).10.1016/j.jcp.2012.06.030 Search in Google Scholar

[8] Brennan, M. J., & Schwartz, E. S. Finite difference methods and jump processes arising in the pricing of contingent claims: A synthesis. Journal of Financial and Quantitative Analysis, 13(3), 461-474 (1978).10.2307/2330152 Search in Google Scholar

[9] Broomhead, D. S., & Lowe, D. Radial basis functions, multi-variable functional interpolation and adaptive networks (No. RSRE-MEMO-4148). Royal Signals and Radar Establishment Malvern (United Kingdom) (1988). Search in Google Scholar

[10] Chen, Y., & Wan, J. W. Deep neural network framework based on backward stochastic differential equations for pricing and hedging american options in high dimensions. arXiv preprint arXiv:1909.11532 (2019).10.1080/14697688.2020.1788219 Search in Google Scholar

[11] Clment, E., Lamberton, D., & Protter, P. An analysis of a least squares regression method for American option pricing. Finance and Stochastics, 6(4), 449-471 (2002).10.1007/s007800200071 Search in Google Scholar

[12] Cortese, A., De Martino, B., & Kawato, M. The neural and cognitive architecture for learning from a small sample. Current opinion in neurobiology, 55, 133-141 (2019).10.1016/j.conb.2019.02.01130953964 Search in Google Scholar

[13] Dumitrescu, R., Quenez, M. C., & Sulem, A. American options in an imperfect market with default. arXiv preprint arXiv:1708.08675 (2017).10.1137/16M1109102 Search in Google Scholar

[14] Ekstrm, E., & Tysk, J. The BlackScholes equation in stochastic volatility models. Journal of Mathematical Analysis and Applications, 368(2), 498-507 (2010).10.1016/j.jmaa.2010.04.014 Search in Google Scholar

[15] El Karoui, N., & Quenez, M. C. Non-linear pricing theory and backward stochastic differential equations. In Financial mathematics (pp. 191-246). Springer, Berlin, Heidelberg (1997).10.1007/BFb0092001 Search in Google Scholar

[16] El Karoui, N., Pardoux,., & Quenez, M. C. Reflected backward SDEs and American options. Numerical methods in finance, 13, 215-231 (1997).10.1017/CBO9781139173056.012 Search in Google Scholar

[17] Fu, M. C., Laprise, S. B., Madan, D. B., Su, Y., & Wu, R. Pricing American options: A comparison of Monte Carlo simulation approaches. Journal of Computational Finance, 4(3), 39-88 (2001).10.21314/JCF.2001.066 Search in Google Scholar

[18] Gurney, K. An introduction to neural networks. CRC press (2014). Search in Google Scholar

[19] Hackmann, D. Solving the Black Scholes equation using a finite difference method. Available online: math. yorku. ca/ dhackman/BlackScholes7. pdf (2009). Search in Google Scholar

[20] Hardy, R. L. Multiquadric equations of topography and other irregular surfaces. Journal of geophysical research, 76(8), 1905-1915 (1971).10.1029/JB076i008p01905 Search in Google Scholar

[21] Higham, D. J. An introduction to financial option valuation: mathematics, stochastics and computation (Vol. 13). Cambridge University Press (2004).10.1017/CBO9780511800948 Search in Google Scholar

[22] Jacquier, A. Numerical Methods in Finance. Lecture Notes, Imperial College London. Retrieved from https://www.imperial.ac.uk/on 20th November (2016). Search in Google Scholar

[23] Janson, S., & Tysk, J. FeynmanKac formulas for BlackScholes-type operators. Bulletin of the London Mathematical Society, 38(2), 269-282 (2006).10.1112/S0024609306018194 Search in Google Scholar

[24] Kasabov, N. K. Time-space, spiking neural networks and brain-inspired artificial intelligence. Heidelberg: Springer (2019).10.1007/978-3-662-57715-8 Search in Google Scholar

[25] Kolesnikov, D. Numerical Methods for Pricing American Put Options (2015). Search in Google Scholar

[26] Liu, S., Oosterlee, C. W., & Bohte, S. M. Pricing options and computing implied volatilities using neural networks. Risks, 7(1), 16 (2019).10.3390/risks7010016 Search in Google Scholar

[27] Longstaff, F. A., & Schwartz, E. S. Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147 (2001).10.1093/rfs/14.1.113 Search in Google Scholar

[28] Malliaris, M., & Salchenberger, L. A neural network model for estimating option prices. Applied Intelligence, 3(3), 193-206 (1993).10.1007/BF00871937 Search in Google Scholar

[29] McNelis, P. D. Neural networks in finance: gaining predictive edge in the market. Academic Press, (2005). Search in Google Scholar

[30] Medvedev, A., & Scaillet, O. Pricing American options under stochastic volatility and stochastic interest rates. Journal of Financial Economics, 98(1), 145-159 (2010).10.1016/j.jfineco.2010.03.017 Search in Google Scholar

[31] Natenberg, S. Option volatility and pricing: Advanced trading strategies and techniques. McGraw-Hill Education (2014). Search in Google Scholar

[32] Oksendal, B. Stochastic differential equations: an introduction with applications. Springer Science & Business Media (2013). Search in Google Scholar

[33] Papanicolaou, A. Introduction to Stochastic Differential Equations (SDEs) for Finance. arXiv preprint arXiv:1504.05309 (2015). Search in Google Scholar

[34] Pham, H. Optimisation et contrle stochastique appliqus la finance (Vol. 61). Berlin: Springer (2007). Search in Google Scholar

[35] Racicot, F.., & Thoret, R. Finance computationnelle et gestion des risques. PUQ (2006).10.2307/j.ctv18ph6c6 Search in Google Scholar

[36] Roncalli, T. (2001). Introduction la gestion des risques. Cours ENSAI, France. World Wide Web: http://www.univ-evry.fr/modules/resources/download/default/m2if/roncalli/gdr.pdf. (Accessed September 5, 2013). Search in Google Scholar

[37] Rubinstein, R. Y., & Kroese, D. P. Simulation and the Monte Carlo method (Vol. 10). John Wiley & Sons (2016).10.1002/9781118631980 Search in Google Scholar

[38] Schwartz, E. S. The valuation of warrants: Implementing a new approach. Journal of Financial Economics, 4(1), (1977) 79-93.10.1016/0304-405X(77)90037-X Search in Google Scholar

[39] Smith, G. D., Smith, G. D., & Smith, G. D. S. Numerical solution of partial differential equations: finite difference methods. Oxford university press (1985). Search in Google Scholar

[40] Sodhi, A. American Put Option pricing using Least squares Monte Carlo method under Bakshi, Cao and Chen Model Framework (1997) and comparison to alternative regression techniques in Monte Carlo. arXiv preprint arXiv:1808.02791 (2018). Search in Google Scholar

[41] peranda, I. & Trinski, Z. Hedging as a business risk protection instrument. Ekonomski vjesnik: Review of Contemporary Entrepreneurship, Business, and Economic Issues, 28(2), (2015), 551-565. Search in Google Scholar

[42] Sundaram, R. K. Derivatives in financial market development. International Growth Centre London, September. Pobrano z: http://pages.stern.nyu.edu/ersundara (2012). Search in Google Scholar

[43] Statistiques, D. E. A. & Alatoires enEconomie, M.. Mthodes de Monte Carlo pour la finance (2004). Search in Google Scholar

[44] Wilmott, P. Derivatives: The theory and practice of financial engineering. Wiley (1998). Search in Google Scholar

[45] Wilmott, P. Paul Wilmott on quantitative finance. John Wiley & Sons (2013). Search in Google Scholar

[46] Xie, T., Yu, H. & Wilamowski, B. Comparison between traditional neural networks and radial basis function networks. In 2011 IEEE International Symposium on Industrial Electronics (2011) (pp. 1194-1199). IEEE.10.1109/ISIE.2011.5984328 Search in Google Scholar

[47] Yadav, N., Yadav, A. & Kumar, M.. An introduction to neural network methods for differential equations (pp. 13-15). Netherlands: Springer (2015).10.1007/978-94-017-9816-7_2 Search in Google Scholar