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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.

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
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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
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[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
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