Symmetrization associated with hyperbolic reflection principle

In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which i...

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Bibliographic Details
Published inInternational journal of mathematics for industry (Online) Vol. 10; no. 1; pp. 1 - 8
Main Authors Ida, Yuuki, Kinoshita, Tsuyoshi, Matsumoto, Tomohiro
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 11.01.2018
World Scientific Publishing Co. Pte., Ltd
SpringerOpen
Subjects
Applications of Mathematics
Barrier option
Brownian motion
Euler-Maruyama scheme
Hyperbolic Brownian motion
Math Applications in Computer Science
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Original Article
Quantitative Finance
Reflection
Reflection principle
Symmetrization
Volatility
Symmetrization
Reflection principle
Barrier option
Euler-Maruyama scheme
Hyperbolic Brownian motion
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Summary:In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which imply the efficiency of the numerical scheme based on the symmetrization, are given.
ISSN:2198-4115
2661-3352
2198-4115
2661-3344
DOI:10.1186/s40736-017-0035-2