MATHEMATICAL PROPERTIES OF AMERICAN CHOOSER OPTIONS

Shi Qiu and Sovan Mitra
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Shi Qiu: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
Sovan Mitra: University of Liverpool, Brownlow Hill, Liverpool, L69 7ZX, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 08, 1-30

Abstract: The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

Keywords: American chooser options; American strangle options; change of variable; optimal stopping; free boundaries (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500620

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