PreprintCC BY 4.0arXiv
Derivation of the General Solution of the Black-Scholes Boundary-Value Problem
Abstract
There are infinitely many functions that satisfy the Black-Scholes partial differential equation and the terminal condition corresponding to the European call option. This means that the Black-Scholes formula, which led to the award of the 1997 Nobel Prize in Economic Sciences, is not the unique solution, as was once assumed. Consequently, it violates the law of one price, one of the fundamental laws of economics and finance. In this article, we present a rigorous derivation of these solutions to the Black-Scholes boundary value problem.
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BibTeX
@misc{choi2026derivation,
title = {{Derivation of the General Solution of the Black-Scholes Boundary-Value Problem}},
author = {ByoungSeon Choi and M. Y. Choi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36447},
eprint = {2609.36447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36447},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Derivation of the General Solution of the Black-Scholes Boundary-Value Problem
AU - ByoungSeon Choi
AU - M. Y. Choi
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36447
UR - https://arxiv.org/abs/2609.36447
AB - There are infinitely many functions that satisfy the Black-Scholes partial differential equation and the terminal condition corresponding to the European call option. This means that the Black-Scholes formula, which led to the award of the 1997 Nobel Prize in Economic Sciences, is not the unique solution, as was once assumed. Consequently, it violates the law of one price, one of the fundamental laws of economics and finance. In this article, we present a rigorous derivation of these solutions to the Black-Scholes boundary value problem.
ER -