Alternating Direction Explicit Methods for Linear, Nonlinear and Multi-Dimensional Black-Scholes Models

Bučková, Zuzana; Ehrhardt, Matthias; Günther, Michael; Pólvora, Pedro

doi:10.1007/978-3-319-61282-9_19

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Among them there are alternating direction explicit (ADI) methods for linear, nonlinear and multi-dimensional Black-Scholes models (c.f. (Bučková et al 2017) and references therein).…”

Section: Algorithmmentioning

confidence: 99%

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Pólvora

Ševčovič

2021

JRFM

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Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions solving the system of HJB equations. We introduce the transformation method for solving the penalized nonlinear partial differential equation. The transformed equation involves possibly non-constant the risk aversion function containing the negative ratio between the second and first derivatives of the utility function. Using comparison principles we derive useful bounds on the option price. We also propose a finite difference numerical discretization scheme with some computational examples.

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“…Among them there are alternating direction explicit (ADI) methods for linear, nonlinear and multi-dimensional Black-Scholes models (c.f. (Bučková et al 2017) and references therein).…”

Section: Algorithmmentioning

confidence: 99%

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Pólvora

Ševčovič

2021

JRFM

Self Cite

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“…Among them there are alternating direction explicit (ADI) methods for linear, nonlinear and multi-dimensional Black-Scholes models (c.f. [2] and references therein).…”

Section: −∆T Rβmentioning

confidence: 99%

Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Polvora,

Sevcovic

2021

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Alternating Direction Explicit Methods for Linear, Nonlinear and Multi-Dimensional Black-Scholes Models

Cited by 2 publications

References 11 publications

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

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