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Pi options

Guo, Xin and Zervos, Mihail ORCID: 0000-0001-5194-6881 (2010) Pi options. Stochastic Processes and Their Applications, 120 (7). pp. 1033-1059. ISSN 0304-4149

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Identification Number: 10.1016/


We consider a discretionary stopping problem that arises in the context of pricing a class of perpetual American-type call options, which include the perpetual American, Russian and lookback-American call options as special cases. We solve this genuinely two-dimensional optimal stopping problem by means of an explicit construction of its value function. In particular, we fully characterise the free-boundary that provides the optimal strategy, and which involves the analysis of a highly nonlinear ordinary differential equation (ODE). In accordance with other optimal stopping problems involving a running maximum process that have been studied in the literature, it turns out that the associated variational inequality has an uncountable set of solutions that satisfy the so-called principle of smooth fit.

Item Type: Article
Official URL:
Additional Information: © 2010 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 13 Jul 2010 10:10
Last Modified: 20 Oct 2021 01:48

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