Deep Learning Application in Rainbow Options Pricing

الموضوعات :

Ali Bolfake ¹ (Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran)
Seyed Nourollah Mousavi ² (Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran)
Sima Mashayekhi ³ (Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran)

تاريخ الإرسال : 22 الثلاثاء , ربيع الأول, 1444 تاريخ التأكيد : 23 الإثنين , جمادى الثانية, 1444 تاريخ الإصدار : 13 السبت , ذو الحجة, 1444

الکلمات المفتاحية: Monte-Carlo simulation, descent gradient method, deep learning, European options, Asian options,

ملخص المقالة :

Due to the rapid advancements in computer technology, researchers are attracted to solving challenging problems in many different fields. The price of rainbow options is an interesting problem in financial fields and risk management. When there is no closed-form solution to some options, numerical methods must be used. Choosing a suitable numerical method involves the most appropriate combination of criteria for speed, accuracy, simplicity and generality. Monte Carlo simulation methods and traditional numerical methods have expensive repetitive computations and unrealistic assumptions on the model. Deep learning provides an effective and efficient method for options pricing. In this paper, the closed-form formula or Monte-Carlo simulation are used to generate data in European and Asian rainbow option prices for the deep learning model. The results confirm that the deep learning model can price the rainbow options more accurately with less computation time than Monte-Carlo simulation.

المصادر:

[1] Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., and Isard, M., TensorFlow: a system for large-scale machine learning, Oper. Syst, Des. Implement 2016, P. 265-283.

[2] Cao, J., Chen, J., and Hull, J., A neural network approach to understanding implied volatility movements, Quantitative Finance, 2020, 20(9), P. 1405-1413. Doi: 10.1142/9789811259142_0013

[3] Chen, W., and Wang, S. A., 2nd-order ADI finite difference method for a 2D fractional BlackScholes equation governing European two asset option pricing, Math. Comput. Simul., 2020, 171, P.279- 293.

Doi: 10.1016/j.matcom.2019.10.016

 

[4] Choe, G.H., Stochastic analysis for finance with simulations Berlin: Springer, 2016.

[5] Derman, E., Valuing and hedging outperformance options, Goldman Sachs, Quantitative Strategies Research Notes, 1992.

[6] Gan, L., Wang, H., and Yang, Z., Machine learning solutions to challenges in finance: An application to the pricing of financial products, Technological Forecasting and Social Change, 2020, 153, P.119928.
Doi: 10.1016/j.techfore.2020.119928

[7] Hozman, J., and Tich, T., DG Method for numerical pricing of multiasset Asian optionsThe case of options with floating strike, Applications of Mathematics, 2017, 62(2), P.171–195. Doi: 10.21136/AM.2017.0273-16

[8] Izadikhah, M. DEA Approaches for Financial Evaluation - A Literature Review. Advances in Mathematical Finance and Applications, 2022; 7(1), p. 1-36. doi: 10.22034/amfa.2021.1942092.1639

 [8] Ivascu, C.F., Option pricing using machine learning, Expert Systems with Applications, 2021, 163, P. 113799. Doi: 10.1016/j.eswa.2020.113799

[9] Jiang, L., Mathematical modeling and methods of option pricing, World Scientific Publishing Company, 2005.

[10] Jeong, D., Yoo, M., Yoo, C. and Kim, J., A hybrid Monte Carlo and finite difference method for option pricing, Comput. Econ., 2019, 53, P. 111-124. Doi: 10.1007/s10614-017-9730-4

[11] Khodayari, L. and Ranjbar, M., A computationally efficient numerical approach for multi-asset option pricing, Int. J. Comput. Math., 2019, 96, P. 1158-1168. Doi: 10.1080/00207160.2018.1458096

[12] Liang J., Xu Z., and Li P., Deep learning-based least squares forwardbackward stochastic differential equation solver for high-dimensional derivative pricing, Quantitative Finance, 2022, 21(8), P. 1309–1323.
Doi: 10.1080/14697688.2021.1881149

[13] Maas, A.L.; Hannun, A.Y., and Ng, A.Y., Rectifier nonlinearities improve neural network acoustic models, In Proc. icml, 2013, 30(1).

[14] Mashayekhi S., and Mousavi, S.N. A robust numerical method for single and multi-asset option pricing, AIMS Mathematics, 2022, 7(3), P. 3771–3787. Doi: 10.3934/math.2022209

 

[15] Mashayekhi, S., Alternating Direction Explicit Method for a Nonlinear Model in Finance, Advances in Mathematical Finance and Applications, 2021, 6(4), P.745-755. Doi: 10.22034/AMFA.2021.1918952.1540

[16] Rumelhart, D.E., Hinton, G.E., and Williams, R.J., Learning representations by back-propagating errors, nature, 1986, 323, P. 533–536.

 [17] Stulz, R. M., Options on the Minimum or the Maximum of Two Risky Assets, Journal of Financial Economics, 1982, 10, P. 161-185.

[18] Seifoddini, J., Stock Option Pricing by Augmented Monte-Carlo Simulation models, Advances in Mathematical Finance and Applications, 2021, 6(4), P.1-22. Doi: 10.22034/AMFA.2019.1879290.1297

[19] Zanjirdar, M., Overview of Portfolio Optimization Models. Advances in Mathematical Finance and Applications, 2020. 5(4), P.419-435. Doi: 10.22034/amfa.2020.674941.

 

[20] Zanjirdar, M., Kasbi, P., Madahi, Z., Investigating the effect of adjusted DuPont ratio and its components
on investor & quot; s decisions in short and long term, Management Science Letters, 2014, 4(3), P.591-596.
Doi: 10.5267/j.msl.2014.1.003

[21] Zhan, P. G., Exotic Options, a guide to second generation options, 2nd ed, 1998.

[22] Zohrabi, A., Tehrani, R., Souri, A., and Sadeghi Sharif, S.J., Provide an improved factor pricing model using neural networks and the gray wolf optimization algorithm, Advances in Mathematical Finance and Applications, 2023, 8(1). Doi: 10.22034/AMFA.2022.1942547.1641

 

 [23] West, G., Better approximations to cumulative normal functions, Wilmott Magazine, 2005, 9, P. 70–76.