RT Journal Article SR Electronic T1 Physics and Derivatives: On Three Important Problems in Mathematical Finance JF The Journal of Derivatives FD Institutional Investor Journals SP jod.2020.1.098 DO 10.3905/jod.2020.1.098 A1 Alexander Lipton A1 Vadim Kaushansky YR 2020 UL https://pm-research.com/content/early/2020/02/21/jod.2020.1.098.abstract AB In this article, we use recently developed extension of the classical heat potential method in order to solve three important but seemingly unrelated problems of financial engineering: (A) American put pricing; (B) default boundary determination for the structural default problem; and (C) evaluation of the hitting time probability distribution for the general time-dependent Ornstein–Uhlenbeck process. We show that all three problems boil down to analyzing behavior of a standard Wiener process in a semi-infinite domain with a quasi-square-root boundary.TOPICS: Derivatives, options, credit default swapsKey Findings• We introduce a powerful extension of the classical method of heat potentials designed for solving initial boundary value problems for the heat equation with moving boundaries.• We demonstrate the versatility of our method by solving several classical problems of financial engineering in a unified fashion.• In particular, we find the boundary corresponding to the constant default intensity in the structural default model, thus solving in the affirmative a long outstanding problem.