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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:
91G60Numerical methods in mathematical finance
65M06Finite difference methods (IVP of PDE)
35Q91PDEs in connection with game theory, economics, social and behavioral sciences
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 · 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).
[4], New research trends in option pricing (2008)
[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)