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Rodosthenous, Neofytos and Zervos, Mihail (2017) Watermark options. Finance and Stochastics, 21 (1). pp. 157-186. ISSN 0949-2984

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Identification Number: 10.1007/s00780-016-0319-x

Abstract

We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly non-linear first order ODEs that have the characteristics of a separatrix. The asymptotic growth of these free-boundary functions can take qualitatively different forms depending on parameter values, which is an interesting new feature.

Item Type: Article
Official URL: http://link.springer.com/journal/780
Additional Information: © 2016 The Authors
Divisions: Mathematics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Sets: Departments > Mathematics
Collections > Economists Online
Date Deposited: 26 Sep 2016 13:51
Last Modified: 20 Apr 2019 01:39
URI: http://eprints.lse.ac.uk/id/eprint/67859

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