Company Rossi, R.; Egorova, V.; Jódar Sánchez, LA.; Vázquez, C. (2016). Finite difference methods for pricing American put option with rationality parameter: Numerical analysis and computing. Journal of Computational and Applied Mathematics. 304:1-17. https://doi.org/10.1016/j.cam.2016.03.001
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/87841
Title:
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Finite difference methods for pricing American put option with rationality parameter: Numerical analysis and computing
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Author:
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Company Rossi, Rafael
Egorova, Vera
Jódar Sánchez, Lucas Antonio
Vázquez, Carlos
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UPV Unit:
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Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports
Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària
Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses
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Issued date:
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Abstract:
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[EN] In this paper finite difference methods for pricing American option with rationality parameter are proposed. The irrational exercise policy arising in American options is characterized in terms of a rationality ...[+]
[EN] In this paper finite difference methods for pricing American option with rationality parameter are proposed. The irrational exercise policy arising in American options is characterized in terms of a rationality parameter. The model is formulated in terms of a new nonlinear Black Scholes equation that requires specific numerical methods. Although the solution converges to the solution of the classical American option price when the parameter tends to infinity, for finite values of the parameter the classical boundary conditions cannot apply and we propose specific ones. A logarithmic transformation is used to improve properties of the numerical solution that is constructed by explicit finite difference method. Numerical analysis provides stability conditions for the methods and its positivity. Properties of intensity function are studied from the point of view of numerical solution. Concerning the numerical methods for the original problem we propose the θ-method for time discretization, thus including explicit, fully implicit and Crank Nicolson schemes as particular cases. The nonlinear term is treated by a Newton method. The convergence rate is illustrated by numerical examples.
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Subjects:
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American option
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Irrational exercise
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Nonlinear Black Scholes equations
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Finite difference method
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Numerical analysis
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Copyrigths:
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Cerrado |
Source:
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Journal of Computational and Applied Mathematics. (issn:
0377-0427
) (eissn:
1879-1778
)
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DOI:
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10.1016/j.cam.2016.03.001
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.cam.2016.03.001
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Project ID:
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info:eu-repo/grantAgreement/EC/FP7/304617/EU
MINECO/MTM2013-41765-P
MINECO/MTM2013-47800-C2-1-P
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Thanks:
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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) ...[+]
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. Fourth author has been partially funded by grant MTM2013-47800-C2-1-P.
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Type:
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Artículo
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