Casabán, M.-C.; Company, R.; Jódar, L.; Pintos, J.-R. Numerical analysis and computing of a non-arbitrage liquidity model with observable parameters for derivatives. (English) Zbl 1219.91148 Comput. Math. Appl. 61, No. 8, 1951-1956 (2011). Summary: This paper deals with the numerical analysis and computing of a nonlinear model of option pricing appearing in illiquid markets with observable parameters for derivatives. A consistent monotone finite difference scheme is proposed and a stability condition on the stepsize discretizations is given. Cited in 3 Documents MSC: 91G60 Numerical methods (including Monte Carlo methods) 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35Q91 PDEs in connection with game theory, economics, social and behavioral sciences Keywords:nonlinear partial differential equation; numerical analysis; option pricing PDFBibTeX XMLCite \textit{M. C. Casabán} et al., Comput. Math. Appl. 61, No. 8, 1951--1956 (2011; Zbl 1219.91148) Full Text: DOI Link References: [1] Liu, H.; Yong, J., Option pricing with an illiquid underlying asset market, Journal of Economic Dynamics and Control, 29, 2125-2156 (2005) · Zbl 1198.91210 [2] Ballester, C.; Company, R.; Jódar, L.; Ponsoda, E., Numerical analysis and simulation of option pricing problems modeling illiquid markets, Computers and Mathematics with Applications, 59, 8, 2964-2975 (2010) · Zbl 1193.91152 [3] R. Company, L. Jódar, J.-R. Pintos, A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets, Mathematics and Computers in Simulation, 2010, in press (doi:10.1016/j.matcom.2010.04.026; R. Company, L. Jódar, J.-R. Pintos, A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets, Mathematics and Computers in Simulation, 2010, in press (doi:10.1016/j.matcom.2010.04.026 [4] (Ehrhardt, M., New Research Trends in Option Pricing (2008), Nova Science Publishers: Nova Science Publishers New York) · Zbl 1182.91002 [5] D. Bakstein, S. Howison, An arbitrage-free liquidity model with observable parameters for derivatives, Working paper, Mathematical Institute, Oxford University, 2004.; D. Bakstein, S. Howison, An arbitrage-free liquidity model with observable parameters for derivatives, Working paper, Mathematical Institute, Oxford University, 2004. [6] Howison, S., Matched asymptotic expansions in financial engineering, Journal of Engineering Mathematics Computers, 53, 385-406 (2005) · Zbl 1099.91061 [7] Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods (1985), Clarendon Press: Clarendon Press Oxford · Zbl 0576.65089 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.