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Numerical analysis and simulation of option pricing problems modeling illiquid markets. (English) Zbl 1193.91152
Summary: This paper deals with the numerical analysis and simulation of nonlinear Black-Scholes equations modeling illiquid markets where the implementation of a dynamic hedging strategy affects the price process of the underlying asset. A monotone difference scheme ensuring nonnegative numerical solutions and avoiding unsuitable oscillations is proposed. Stability properties and consistency of the scheme are studied and numerical simulations involving changes in the market liquidity parameter are included.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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