Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

Sima Mashayekhi; Jens Hugger

Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

Sima Mashayekhi, Jens Hugger

Department of Mathematical Sciences

6 Citations (Scopus)

Abstract

Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid market. In this paper, we compare several finite difference methods for the solution of this model with respect to precision and order of convergence within a computationally feasible domain allowing at most 200 space steps and 10000 time steps. We conclude that standard explicit Euler comes out as the preferred explicit method and standard Crank Nicolson with Rannacher time stepping as the preferred implicit method.

Original language	English
Journal	Acta Mathematica Universitatis Comenianae
Volume	84
Issue number	2
Pages (from-to)	255-266
Number of pages	12
ISSN	0862-9544
Publication status	Published - 8 Sept 2015

Keywords

Feedback and illiquidity
Finite difference schemes
Nonlinear black-scholes model
Transaction costs

Cite this

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KW - Feedback and illiquidity

KW - Finite difference schemes

KW - Nonlinear black-scholes model

KW - Transaction costs

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Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

Abstract

Keywords

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