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

TY - JOUR

T1 - Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

AU - Mashayekhi, Sima

AU - Hugger, Jens

PY - 2015/9/8

Y1 - 2015/9/8

N2 - 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.

AB - 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.

KW - Feedback and illiquidity

KW - Finite difference schemes

KW - Nonlinear black-scholes model

KW - Transaction costs

UR - http://www.scopus.com/inward/record.url?scp=84941003156&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:84941003156

SN - 0862-9544

VL - 84

SP - 255

EP - 266

JO - Acta Mathematica Universitatis Comenianae

JF - Acta Mathematica Universitatis Comenianae

IS - 2

ER -