Computing American option price under regime switching with rationality parameter

[EN] American put option pricing under regime switching is modelled by a system of coupled partial differential equations. The proposed model combines better the reality of the market by incorporating the regime switching jointly with the emotional behaviour of traders using the rationality parameter approach recently introduced by Tågholt Gad and Lund Petersen to cope with possible irrational exercise policy. The classical rational exercise is recovered as a limit case of the rational parameter. The resulting nonlinear system of PDEs is solved by a weighted finite difference method, also known as θ-method. In order to avoid the need of an iterative method for nonlinear system, the term with rationality parameter and the coupling term are treated explicitly. Next, the resulting linear system is solved by Thomas algorithm. Stability conditions for the numerical scheme are studied by using von Neumann approach. Numerical examples illustrate the efficiency and accuracy of the proposed method.This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P. The fourth author has been partially supported by MINECO Spanish grant MTM2013-47800-C2-1-P and Xunta de Galicia grant CN2011/004.Company Rossi, R.; Egorova, V.; Jódar Sánchez, LA.; Vázquez, C. (2016). Computing American option price under regime switching with rationality parameter. Computers and Mathematics with Applications. 72:741-754. https://doi.org/10.1016/j.camwa.2016.05.026S7417547

Positive Solutions of European Option Pricing with CGMYProcess Models Using Double Discretization Difference Schemes

[EN] This paper deals with the numerical analysis of PIDE option pricing models with CGMY process using double discretization schemes. This approach assumes weaker hypotheses of the solution on the numerical boundary domain than other relevant papers. Positivity, stability, and consistency are studied. An explicit scheme is proposed after a suitable change of variables. Advantages of the proposed schemes are illustrated with appropriate examples.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and by the Spanish M.E.Y.C. Grant DPI2010-20891-C02-01.Company Rossi, R.; Jódar Sánchez, LA.; El-Fakharany, M. (2013). Positive Solutions of European Option Pricing with CGMYProcess Models Using Double Discretization Difference Schemes. Abstract and Applied Analysis. 2013:1-12. https://doi.org/10.1155/2013/517480S1122013Kou, S. 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Z. (2000). OPTION PRICING FOR TRUNCATED LÉVY PROCESSES. International Journal of Theoretical and Applied Finance, 03(03), 549-552. doi:10.1142/s0219024900000541Matache *, A.-M., Nitsche, P.-A., & Schwab, C. (2005). Wavelet Galerkin pricing of American options on Lévy driven assets. Quantitative Finance, 5(4), 403-424. doi:10.1080/14697680500244478Poirot, J., & Tankov, P. (2007). Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes. Asia-Pacific Financial Markets, 13(4), 327-344. doi:10.1007/s10690-007-9048-7Fang, F., & Oosterlee, C. W. (2009). A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions. SIAM Journal on Scientific Computing, 31(2), 826-848. doi:10.1137/080718061Benhamou, E., Gobet, E., & Miri, M. (2009). Smart expansion and fast calibration for jump diffusions. Finance and Stochastics, 13(4), 563-589. doi:10.1007/s00780-009-0102-3Cont, R., & Voltchkova, E. (2005). 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Pricing options and computing implied volatilities using neural networks

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly