The Annals of Applied Probability

Root’s barrier: Construction, optimality and applications to variance options

Alexander M. G. Cox and Jiajie Wang

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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.

Article information

Ann. Appl. Probab., Volume 23, Number 3 (2013), 859-894.

First available in Project Euclid: 7 March 2013

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91G20: Derivative securities
Secondary: 60J60: Diffusion processes [See also 58J65] 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Skorokhod embedding problem Root’s barrier variational inequality variance option


Cox, Alexander M. G.; Wang, Jiajie. Root’s barrier: Construction, optimality and applications to variance options. Ann. Appl. Probab. 23 (2013), no. 3, 859--894. doi:10.1214/12-AAP857.

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