Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk
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Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk. / Mashayekhi, Sima; Hugger, Jens.
I: Acta Mathematica Universitatis Comenianae, Bind 84, Nr. 2, 08.09.2015, s. 255-266.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 84
SP - 255
EP - 266
JO - Acta Mathematica Universitatis Comenianae
JF - Acta Mathematica Universitatis Comenianae
SN - 0862-9544
IS - 2
ER -
ID: 161393684