Displaying similar documents to “DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike”

DG method for the numerical pricing of two-asset European-style Asian options with fixed strike

Jiří Hozman, Tomáš Tichý (2017)

Applications of Mathematics

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The evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and extends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution...

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...

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...

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 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...

A mathematical model of inflammation during ischemic stroke

Cristiana Di Russo, Jean-Baptiste Lagaert, Guillemette Chapuisat, Marie-Aimée Dronne (2010)

ESAIM: Proceedings

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In this article we propose a model to describe the inflammatory process which occurs during ischemic stroke. First, an introduction to some basic concepts about the biological phenomenon is given. Then, a detailed derivation of the model and the numerical scheme used are presented. Finally, the studies of the model robustness and sensitivity are showed and some numerical results on the time and space evolution of the process are presented...

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...