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Displaying similar documents to “DG method for the numerical pricing of two-asset European-style Asian options with fixed strike”

DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike

Jiří Hozman, Tomáš Tichý (2017)

Applications of Mathematics

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Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts...

DG method for pricing European options under Merton jump-diffusion model

Jiří Hozman, Tomáš Tichý, Miloslav Vlasák (2019)

Applications of Mathematics

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Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion model, when the evolution of the asset prices is driven by a Lévy process with finite...

DGM for real options valuation: Options to change operating scale

Hozman, Jiří, Tichý, Tomáš

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The real options approach interprets a flexibility value, embedded in a project, as an option premium. The object of interest is to valuate real options to change operating scale, typical for natural resources industry. The evolution of the project as well as option prices is decribed by partial differential equations of the Black-Scholes type, linked through a payoff function given by a type of the flexibility provided. The governing equations are discretized by the discontinuous Galerkin...

Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs

Rafael Company, Lucas Jódar, José-Ramón Pintos (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of...

Option pricing in a CEV model with liquidity costs

Krzysztof Turek (2016)

Applicationes Mathematicae

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The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques...

Option valuation under the VG process by a DG method

Jiří Hozman, Tomáš Tichý (2021)

Applications of Mathematics

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The paper presents a discontinuous Galerkin method for solving partial integro-differential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical...

Valuing barrier options using the adaptive discontinuous Galerkin method

Hozman, Jiří

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This paper is devoted to barrier options and the main objective is to develop a sufficiently robust, accurate and efficient method for computation of their values driven according to the well-known Black-Scholes equation. The main idea is based on the discontinuous Galerkin method together with a spatial adaptive approach. This combination seems to be a promising technique for the solving of such problems with discontinuous solutions as well as for consequent optimization of the number...