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2024 | OriginalPaper | Chapter

A General Solution of Black–Scholes Equations on Some Rainbow Options

Authors : Amirul Hakam, Endah R. M. Putri, Lutfi Mardianto

Published in: Applied and Computational Mathematics

Publisher: Springer Nature Singapore

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Abstract

This study proposes a general solution of the Black–Scholes equation to determine some Rainbow options’ prices, both analytically and semi-analytically. We formulate general analytical solutions in non-dimensional terms by appropriately treating the payoff conditions. In particular, we present analytical solutions for three types of rainbow options: Better of options, Exchange options and Spread options. Furthermore, as our second contribution, we propose a semi-analytic solution for these three types of Rainbow options, leveraging the Homotopy Perturbation Method (HPM). The simulation results demonstrate the remarkable proximity of the semi-analytic solution to the analytical solution, ensuring accurate option pricing approximations.

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Literature
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Jiang, L.: Mathematical Modeling and Methods of Option Pricing. World Scientific Publishing Company (2005)
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Panini, R.: Option Pricing with Mellin Transforms. State University of New York at Stony Brook (2004)
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Jódar, L., Sevilla-Peris, P., Cortes, J., Sala, R.: A new direct method for solving the Black-Scholes equation. Appl. Math. Lett. 18(1), 29–32 (2005)MathSciNetCrossRef
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Putri, E.R., Mardianto, L., Hakam, A., Imron, C., Susanto, H.: Removing non-smoothness in solving Black-Scholes equation using a perturbation method. Phys. Lett. A 402, 127367 (2021)MathSciNetCrossRef
Metadata
Title
A General Solution of Black–Scholes Equations on Some Rainbow Options
Authors
Amirul Hakam
Endah R. M. Putri
Lutfi Mardianto
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Applied and Computational Mathematics

Print ISBN: 978-981-9721-35-1

Electronic ISBN: 978-981-9721-36-8

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-2136-8_14

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