Amirul Hakam, Endah R. M. Putri, Lutfi Mardianto
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. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
Department of Mathematics, Sepuluh Nopember Institute of Technology, Sukolilo, Surabaya, 60111, Indonesia; Department of Mathematics, Sumatera Institute of Technology, Lampung, Selatan, 35365, Indonesia
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