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Numerical analysis and computing of a non-arbitrage liquidity model with observable parameters for derivatives. (English) Zbl 1219.91148
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.

91G60Numerical methods in mathematical finance
65M06Finite difference methods (IVP of PDE)
35Q91PDEs in connection with game theory, economics, social and behavioral sciences
Full Text: DOI
[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 · doi:10.1016/j.jedc.2004.11.004
[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, No. 8, 2964-2975 (2010) · Zbl 1193.91152 · doi:10.1016/j.camwa.2010.02.014
[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). · Zbl 1262.91146
[4] , New research trends in option pricing (2008) · 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.
[6] Howison, S.: Matched asymptotic expansions in financial engineering, Journal of engineering mathematics computers 53, 385-406 (2005) · Zbl 1099.91061 · doi:10.1007/s10665-005-7716-z
[7] Smith, G. D.: Numerical solution of partial differential equations: finite difference methods, (1985) · Zbl 0576.65089