Valuing American floating strike lookback option and Neumann problem for inhomogeneous Black-Scholes equation

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• 作者：Junkee Jeon ; ^{hollman@snu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Heejae Han ; Myungjoo Kang
• 关键词：Free boundary problem ; Integral equation ; American floating strike lookback option ; Perpetual American floating strike lookback option ; Neumann problem ; Mellin transform
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：218-234
• 全文大小：494 K

文摘

This paper presents our study of American floating strike lookback options written on dividend-paying assets. The valuation of these options can be mathematically formulated as a free boundary inhomogeneous Black–Scholes PDE with a Neumann boundary condition, which we, by using a Mellin transform, convert into a relatively simple ordinary differential equation with Dirichlet boundary conditions. We then use these results to derive an integral equation that can be used to calculate the price of American floating strike lookback options. In addition, we also used Mellin transforms to derive the closed-form of the perpetual case.