A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets

Rafael Company, Lucas Jódar and José-Ramón Pintos

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 10, 1972-1985

Abstract: 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.

Keywords: Nonlinear Numerical Analysis; Simulation; Option Pricing; Illiquid Markets (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:10:p:1972-1985

DOI: 10.1016/j.matcom.2010.04.026

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