Supervised Machine Learning with Control Variates for American Option Pricing

• Autorzy: Mu G. , Godina T. , Maffia A. , Sun Y. C.

Identyfikatory

DOI

10.1515/fcds-2018-0011

• Języki publikacji: EN

Abstrakty

EN

In this paper, we make use of a Bayesian (supervised learning) approach in pricing American options via Monte Carlo simulations. We first present Gaussian process regression (Kriging) approach for American options pricing and compare its performance in estimating the continuation value with the Longstaff and Schwartz algorithm. Secondly, we explore the control variates technique in combination with Kriging to further improve the estimation of the continuation value. This method allows to reduce dramatically the standard errors and to improve the stability of the Kriging approach. For illustrative purposes, we use American put options on a stock whose dynamics is given by Heston model, and use European options on the same stock as control variates.

Słowa kluczowe

EN

American option; Monte Carlo; Gaussian processes; Kriging; LSM; supervised learning; Heston Model; control variates

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2018
• Tom: Vol. 43, No. 3
• Strony: 207--217
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Mu G.

• School of Mathematical Sciences, Tongji University, 200092, Shanghai, China
• F. Hoffmann-La Roche AG, Grenzacherstrasse 124, 4070 Basel, Switzerland

autor

Godina T.

• F. Hoffmann-La Roche AG, Grenzacherstrasse 124, 4070 Basel, Switzerland

autor

Maffia A.

• F. Hoffmann-La Roche AG, Grenzacherstrasse 124, 4070 Basel, Switzerland
• Department of Mathematics and Computer Science, University of Basel

autor

Sun Y. C.

• Department of Mathematics and Computer Science, University of Basel

Bibliografia

• [1] Ackerer D. and Filipovic D. (2017), ’Option Pricing with Orthogonal Polynomial Expansions’, Swiss Finance Institute Research Paper No. 17-41.
• [2] Carr P. and Madan D. (1999), Option valuation using the fast Fourier transform’, New York, NY: John Wiley & Sons.
• [3] Glasserman P. (2003), Monte Carlo Methods in Financial Engineering’, Springer Science and Business Media New York.
• [4] Glasserman P. and Yu B. (2004). ’Number of paths versus basis functions in American option pricing.’ The Annals of Applied Probability, 14(4):2090-2119.
• [5] Gramacy R. and Ludkovski M. (2015), ’Sequential design for optimal stopping problems’, SIAM Journal on Financial Mathematics, p. 748-775.
• [6] Heston S. (1993), ’A closed-form solution for options with stochastic volatility with applications to bond and currency options’, Review of Financial Studies.
• [7] Li Y., Szepesvari C. and Schuurmans D. (2008), Learning an Exercise Policy for American Options’, Proceedings of the 12th AISTATS.
• [8] Longstaff F. and Schwartz E. (2001), ’Valuing American options by simulations: a simple least squares approach’, The Review of Financial Studies, 14 , pp. 113-148.
• [9] Kloeden P. and Platen E. (1992), ’Numerical Solution of Stochastic Differential Equations’. Berlin: Springer-Verlag.
• [10] Ludkovski M. (2016), Kriging Metamodels and Experimental Design for Bermudan Option Pricing’, arXiv preprint arXiv:1509.02179, pp. 748-775.
• [11] Pizzi C. and Pellizzari P. (2002) Monte Carlo Pricing of American Options Using Nonparametric Regression’, Rendiconti per gli Studi Economici Quantitativi, 75-91.
• [12] O’Sullivan C. and O’Sullivan S. (2013) Pricing European and American Options in the Heston Model with Accelerated Explicit Finite Differencing Methods’, International Journal of Theoretical and Applied Finance Vol. 16, No. 3
• [13] Rasmussen N.S. (2005) Control variates for Monte Carlo valuation of American options’, Journal of Computational Finance, vol. 9, no. 1, 09.
• [14] Rasmussen C.E. and Williams C.K.I. (2006), Gaussian Processes for Machine Learning’, MIT Press.
• [15] Tsitsiklis J. and Van Roy B. (2001), Regression methods for pricing complex American-style options’, IEEE Transactions on Neural Networks, 12 , pp. 694-703.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).