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 swaps Key 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.

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物理与导数：关于数学金融的三个重要问题

在本文中，我们使用最近开发的经典热势方法的扩展来解决金融工程学中的三个重要但看似无关的问题：（a）美国卖出定价，（b）结构性违约问题的违约边界确定，以及（ c）评估与时间有关的一般Ornstein-Uhlenbeck过程的命中时间概率分布。我们显示所有这三个问题归结为分析具有准平方根边界的半无限域中的标准Wiener过程的行为。主题：衍生工具，期权，信用违约互换主要发现•我们引入了经典的热势方法的强大扩展，该方法旨在解决带有移动边界的热方程的初边值问题。•通过以统一的方式解决金融工程的几个经典问题，证明了我们方法的多功能性。•特别是，我们在结构默认模型中找到了与恒定默认强度相对应的边界，从而肯定地解决了一个长期未解决的问题。