Company Rossi, R.; Jódar Sánchez, LA.; Pintos Taronger, JR. (2012). A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets. Mathematics and Computers in Simulation. 82(10):1972-1985. https://doi.org/10.1016/j.matcom.2010.04.026
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/50301
Title:
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A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets
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Author:
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Company Rossi, Rafael
Jódar Sánchez, Lucas Antonio
Pintos Taronger, José Ramón
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction ...[+]
Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction costs or illiquid market effects are taken into account. This paper deals with the numerical analysis of nonlinear Black-Scholes equations modeling illiquid markets when price impact in the underlying asset market affects the replication of a European contingent claim. Numerical analysis of a nonlinear model is necessary because disregarded computations may waste a good mathematical model. In this paper we propose a finite-difference numerical scheme that guarantees positivity of the solution as well as stability and consistency. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.
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Subjects:
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Illiquid Markets
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Nonlinear Numerical Analysis
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Option Pricing
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Simulation
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Black Scholes equations
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Black-Scholes
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Contingent claims
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Financial risk management
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Finite difference
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Liquid markets
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Market effect
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Non-linear model
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Numerical scheme
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Option pricing models
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Price impacts
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Transaction cost
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Mathematical models
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Nonlinear equations
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Nonlinear systems
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Numerical analysis
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Risk management
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Commerce
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Mathematics and Computers in Simulation. (issn:
0378-4754
)
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DOI:
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10.1016/j.matcom.2010.04.026
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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.matcom.2010.04.026
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Project ID:
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info:eu-repo/grantAgreement/MEC//TRA2007-68006-C02-02/ES/DESARROLLO Y VALIDACION DE NUEVOS MODELOS 1D DE CAVITACION, MODELADO DEL CHORRO Y SUS INTERACCIONES/
info:eu-repo/grantAgreement/GVA//GVPRE%2F20081092/
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Thanks:
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This paper has been supported by the Spanish Department of Science and Education grant TRA2007-68006-C02-02 and the Generalitat Valenciana grant GVPRE/20081092.
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Type:
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Artículo
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