Lower Precision calculation for option pricing

• Autorzy: Ścibisz-Mordelska K. , Nielek R.

Identyfikatory

DOI

10.7494/csci.2017.18.4.2361

• Języki publikacji: EN

Abstrakty

EN

The problem of options pricing is one of the most critical issues and fundamental building blocks in mathematical finance. The research includes deployment of lower precision type in two options pricing algorithms: Black-Scholes and Monte Carlo simulation. We make an assumption that the shorter the number used for calculations is (in bits), the more operations we are able to perform in the same time. The results are examined by a comparison to the outputs of single and double precision types. The major goal of the study is to indicate whether the lower precision types can be used in financial mathematics. The findings indicate that Black-Scholes provided more precise outputs than the basic implementation of Monte Carlo simulation. Modification of the Monte Carlo algorithm is also proposed. The research shows the limitations and opportunities of the lower precision type usage. In order to benefit from the application in terms of the time of calculation improved algorithms can be implemented on GPU or FPGA. We conclude that under particular restrictions the lower precision calculation can be used in mathematical finance.

Słowa kluczowe

EN

option pricing; lower precision; half-precision type; Monte Carlo; Black-Scholes formula

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2017
• Tom: Vol. 18 (4)
• Strony: 429--446
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr., tab.

Twórcy

autor

Ścibisz-Mordelska K.

• Polish-Japanese Academy of Information Technology, Koszykowa 86, 02-008 Warszawa, Poland

autor

Nielek R.

• Polish-Japanese Academy of Information Technology, Koszykowa 86, 02-008 Warszawa, Poland

Bibliografia

• [1] Abbas-Turki L.A., Vialle S., Lapeyre B., Mercier P.: Pricing derivatives on graphics processing units using Monte Carlo simulation, Concurrency and Computation: Practice and Experience, vol. 26(9), pp. 1679-1697, 2014.
• [2] Angerer C.M., Polig R., Zegarac D., Giefers H., Hagleitner C., Bekas C., Curio-ni A.: A fast, hybrid, power-e_cient high-precision solver for large linear systems based on low-precision hardware, Sustainable Computing: Informatics and Systems, vol. 12, pp. 72-82, 2015. http://dx.doi.org/10.1016/j.suscom.2015.10.001
• [3] Black F., Scholes M.: The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol. 81(3), pp. 637-654, 1973. http://EconPapers.repec. org/RePEc:ucp:jpolec:v:81:y:1973:i:3:p:637-54.
• [4] Boyle P.P.: Options: A Monte Carlo approach, Journal of Financial Economics, vol. 4(3), pp. 323-338, 1977. https://ideas.repec.org/a/eee/jfinec/ v4y1977i3p323-338.html.
• [5] Courbariaux M., Bengio Y., David J.: Training deep neural networks with low precision multiplications. In: CoRR, vol. abs/1412.7024, 2014. http://arxiv. org/abs/1412.7024.
• [6] Dang D.M., Christara C.C., Jackson K.R.: A parallel implementation on GPUs of ADI _nite diference methods for parabolic PDEs with applications in _nance, Canadian Applied Mathematics Quarterly, vol. 75(4), pp. 627{660, 2009. http://ami.math.ualberta.ca/CAMQ/pdf_files/vol_17/17_4/17_4b.pdf.
• [7] Fatica M., Phillips E.: Pricing American options with least squares Monte Carlo on GPUs. In: Proceedings of the 6th Workshop on High Performance Computational Finance, p. 5. ACM, 2013.
• [8] Ganesan N., Chamberlain R.D., Buhler J.: Acceleration of Binomial Options Pricing via Parallelizing along Time-axis on a GPU. In: Proceedings of Symposium on Application Accelerators in High Performance Computing. 2009.
• [9] Grauer-Gray S., Killian W., Searles R., Cavazos J.: Accelerating _nancial applications on the GPU. In: Proceedings of the 6th Workshop on General Purpose Processor Using Graphics Processing Units, pp. 127-136. ACM, 2013.
• [10] Gupta S., Agrawal A., Gopalakrishnan K., Narayanan P.: Deep Learning with Limited Numerical Precision. In: CoRR, vol. abs/1502.02551, 2015. http:// arxiv.org/abs/1502.02551.
• [11] Harris M.: New Features in CUDA 7.5, 2015. http://devblogs.nvidia.com/ parallelforall/new-features-cuda-7-5/.
• [12] Haug E.G.: The complete guide to option pricing formulas, McGraw-Hill Companies, 2007.
• [13] IEEE Task P754: IEEE 754-2008, Standard for Floating-Point Arithmetic, 2008. http://dx.doi.org/10.1109/IEEESTD.2008.4610935.
• [14] Joshi M.S.: Graphical Asian options, Wilmott Journal, vol. 2(2), pp. 97-107, 2010. http://dx.doi.org/10.1002/wilj.26.
• [15] Konsor P.: Performance Bene_ts of Half Precision Floats, Intel Developer Zone, 2012. https://software.intel.com/en-us/articles/ performance-benefits-of-half-precision-floats.
• [16] Liu L., Zhang Y., Yang G., Zheng W.: E_cient Monte Carlo-based options pricing on graphics processors and its optimizations, Science China Informa- tion Sciences, vol. 53(9), pp. 1703-1712, 2010. http://dx.doi.org/10.1007/ s11432-010-3109-7.
• [17] Los C.: Computational Finance: A Scientific Perspective. World Scienti_c Pub., 2001. https://books.google.ca/books?id=dLWmQgAACAAJ.
• [18] Lungu I., Petrosanu D.M., Pirjan A.: Solutions for optimizing the Monte Carlo option pricing method's implementation using the compute unifed device architecture, University Politehnica of Bucharest Scientific Bulletin, Series A: Applied Mathematics and Physics, vol. 75(3), pp. 105-112, 2013.
• [19] Polhill J.G., Izquierdo L.R., Gotts N.M.: The Ghost in the Model (and Other Efects of Floating Point Arithmetic), Journal of Artificial Societies and Social Simulation, vol. 8(1), pp. 1-5, 2004
• [20] Rau C.: Half: Half-precision oating point library, 2013. http://half.sourceforge.net/.
• [21] Sharpe W.F., Alexander G.J., Bailey J.V.: Investments, vol. 6. Prentice-Hall Upper Saddle River, NJ, 1999.
• [22] Suo S., Zhu R., Attridge R., Wan J.: GPU option pricing. In: Proceedings of the 8th Workshop on High Performance Computational Finance, WHPCF '15, pp. 8:1-8:6. ACM, New York, NY, USA, 2015. http://dx.doi.org/10.1145/2830556.2830564.
• [23] Zhang B., Oosterlee C.W.: Acceleration of option pricing technique on graphics processing units, Concurrency and Computation. Practice and Experience, vol. 26(9), pp. 1626-1639, 2014. http://dx.doi.org/10.1002/cpe.2825.