@inproceedings{08e9af197a8244c4ba7b503b191afb85,
title = "A General Solution of Black–Scholes Equations on Some Rainbow Options",
abstract = "This study proposes a general solution of the Black–Scholes equation to determine some Rainbow options{\textquoteright} 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.",
keywords = "Better of options, Exchange options, Homotopy perturbation method, Rainbow options, Spread options",
author = "Amirul Hakam and Putri, {Endah R.M.} and Lutfi Mardianto",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.; 8th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2023 ; Conference date: 30-09-2023 Through 30-09-2023",
year = "2024",
doi = "10.1007/978-981-97-2136-8_14",
language = "English",
isbn = "9789819721351",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "177--189",
editor = "Dieky Adzkiya and Kistosil Fahim",
booktitle = "Applied and Computational Mathematics - ICoMPAC 2023",
address = "Germany",
}