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A variation of the Azéma martingale and drawdown options

Dassios, Angelos ORCID: 0000-0002-3968-2366 and Lim, Jia Wei (2019) A variation of the Azéma martingale and drawdown options. Mathematical Finance, 29 (4). pp. 1116-1130. ISSN 0960-1627

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Identification Number: 10.1111/mafi.12202


In this paper, we derive a variation of the Azéma martingale using two approaches—a direct probabilistic method and another by projecting the Kennedy martingale onto the filtration generated by the drawdown duration. This martingale links the time elapsed since the last maximum of the Brownian motion with the maximum process itself. We derive explicit formulas for the joint densities of (τ,W τ , M τ ), which are the first time the drawdown period hits a prespecified duration, the value of the Brownian motion, and the maximum up to this time. We use the results to price a new type of drawdown option, which takes into account both dimensions of drawdown risk—the magnitude and the duration.

Item Type: Article
Official URL:
Additional Information: © 2019 Wiley Periodicals, Inc.
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 19 Sep 2018 09:17
Last Modified: 15 May 2024 23:20

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