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

Amirul Hakam*, Endah R.M. Putri, Lutfi Mardianto

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationApplied and Computational Mathematics - ICoMPAC 2023
EditorsDieky Adzkiya, Kistosil Fahim
PublisherSpringer
Pages177-189
Number of pages13
ISBN (Print)9789819721351
DOIs
Publication statusPublished - 2024
Event8th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2023 - Lombok, Indonesia
Duration: 30 Sept 202330 Sept 2023

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume455
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference8th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2023
Country/TerritoryIndonesia
CityLombok
Period30/09/2330/09/23

Keywords

  • Better of options
  • Exchange options
  • Homotopy perturbation method
  • Rainbow options
  • Spread options

Fingerprint

Dive into the research topics of 'A General Solution of Black–Scholes Equations on Some Rainbow Options'. Together they form a unique fingerprint.

Cite this