Article
Version 1
Preserved in Portico This version is not peer-reviewed
Multitouch Options
Version 1
: Received: 9 May 2023 / Approved: 11 May 2023 / Online: 11 May 2023 (04:42:23 CEST)
A peer-reviewed article of this Preprint also exists.
Guillaume, T. Multitouch Options. J. Risk Financial Manag. 2023, 16, 300. Guillaume, T. Multitouch Options. J. Risk Financial Manag. 2023, 16, 300.
Abstract
In this article, the multitouch option, also called the n touch option (or the “baseball” option when
n 3 ) is analyzed and valued in closed form. This is a kind of barrier option that sets a gradual knockout / knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. Unlike occupation time derivatives, the payoff at expiry does not depend on the amount of time spent outside the authorized range, but on the number of passages beyond the authorized range.
Keywords
multitouch option; n-touch option; baseball option; barrier option; step barrier option; first passage time; boundary crossing probability; dimension; multivariate gaussian integral
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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