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June 2013 Root’s barrier: Construction, optimality and applications to variance options
Alexander M. G. Cox, Jiajie Wang
Ann. Appl. Probab. 23(3): 859-894 (June 2013). DOI: 10.1214/12-AAP857


Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root’s work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding problem. This construction has the remarkable property, proved by Rost, that it minimizes the variance of the stopping time among all solutions.

In this work, we prove a characterization of Root’s barrier in terms of the solution to a variational inequality, and we give an alternative proof of the optimality property which has an important consequence for the construction of subhedging strategies in the financial context.


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Alexander M. G. Cox. Jiajie Wang. "Root’s barrier: Construction, optimality and applications to variance options." Ann. Appl. Probab. 23 (3) 859 - 894, June 2013.


Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1266.91101
MathSciNet: MR3076672
Digital Object Identifier: 10.1214/12-AAP857

Primary: 60G40 , 91G20
Secondary: 60J60 , 91G80

Keywords: Root’s barrier , Skorokhod embedding problem , variance option , variational inequality

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.23 • No. 3 • June 2013
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