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

Jiří Hozman, Tomáš Tichý, Miloslav Vlasák (2019)

Applications of Mathematics

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 activity....

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

Jiří Hozman, Tomáš Tichý (2017)

Applications of Mathematics

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 of European-style...

DGM for real options valuation: Options to change operating scale

Hozman, Jiří, Tichý, Tomáš (2023)

Programs and Algorithms of Numerical Mathematics

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 method...

Diagnosing corporate stability using grammatical evolution

Anthony Brabazon, Michael O'Neill (2004)

International Journal of Applied Mathematics and Computer Science

Grammatical Evolution (GE) is a novel data-driven, model-induction tool, inspired by the biological gene-to-protein mapping process. This study provides an introduction to GE, and demonstrates the methodology by applying it to construct a series of models for the prediction of bankruptcy, employing information drawn from financial statements. Unlike prior studies in this domain, the raw financial information is not preprocessed into pre-determined financial ratios. Instead, the ratios to be incorporated...

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