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Abstract
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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US and Overseas: +1 646-931-9045
UK: 0207 139 1600