A Black–Scholes option pricing model with transaction costs

Amster, Pablo; Averbuj, C.G.; Mariani, Maria C.; Rial, Diego

doi:10.1016/j.jmaa.2004.08.067

Cited by 45 publications

(46 citation statements)

References 2 publications

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“…We present an example of a realistic transaction costs function which is nonincreasing with respect to the amount of transactions as in model studied by Amster et al [1], Averbuj [4] Mariani et al [28]. The benefit is the elimination of the problem of negative values of the linear decreasing costs function.…”

Section: Piecewise Linear Nonincreasing Transaction Costs Functionmentioning

confidence: 99%

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Analysis of the Nonlinear Option Pricing Model Under Variable Transaction Costs

Ševčovič

Zitnanska

2016

Asia-Pac Financ Markets

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In this paper we analyze a nonlinear Black-Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price V is assumed to be a function of the underlying asset price and the Gamma of the option. We show that the generalizations of the classical BlackScholes model can be analyzed by means of transformation of the fully nonlinear parabolic equation into a quasilinear parabolic equation for the second derivative of the option price. We show existence of a classical smooth solution and prove useful bounds on the option prices. Furthermore, we construct an effective numerical scheme for approximation of the solution. The solutions are obtained by means of the efficient numerical discretization scheme of the Gamma equation. Several computational examples are presented.

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Section: Piecewise Linear Nonincreasing Transaction Costs Functionmentioning

confidence: 99%

“…A disadvantage of such a transaction costs function is the fact that it may attain negative values when the amount of transactions exceeds the critical value ξ = C 0 /κ. In the model studied by Amster et al [1] (see also Averbuj [4], Mariani et al [28]) volatility function has the following form:σ…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Nonlinear Option Pricing Model Under Variable Transaction Costs

Ševčovič

Zitnanska

2016

Asia-Pac Financ Markets

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“…If we assume the volatility σ > 0 is a function of the solution V then equation (1) with such a diffusion coefficient represents a nonlinear generalization of the Black-Scholes equation. In this paper we focus our attention to the case when the diffusion coefficient σ 2 may depend on the asset price S and the second derivative ∂ 2 S V of the option price.…”

Section: Introductionmentioning

confidence: 99%

“…Another important contribution in this direction has been presented by Amster, Averbuj, Mariani and Rial in [1], where the transaction costs are assumed to be a non-increasing linear function of the form C(ξ) = C 0 −κξ, (C 0 , κ > 0), depending on the volume of traded stocks ξ ≥ 0 that is needed to hedge the replicating portfolio. In the model studied by Amster et al [1] the volatility function has the following form:…”

Section: Introductionmentioning

confidence: 99%

Pricing Perpetual Put Options by the Black–Scholes Equation with a Nonlinear Volatility Function

Grossinho

Faghan

Ševčovič

2017

Asia-Pac Financ Markets

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We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation in which the volatility function may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.

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“…By doing that we know exactly when transaction costs have to be paid and moreover how much has to be paid. Several authors have attempted to model transaction costs, since the Black-Scholes approach, among which Amster [1] and Daamgard [2]. No one has though tried to link them to the time instants at which they occur.…”

Section: Introductionmentioning

confidence: 99%