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

By Alexander M. G. Cox, Jiajie Wang. 2011

92 citations recorded by the source corpus.

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.

Subfields: Finance, Management Science and Operations Research, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/aa592f9501db09ff356b38e23593519159858c22

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Citations in the corpus

The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, methodology): “The embedding construction was tailored as to provide a model in which the optimal super-hedge is in fact a perfect hedge, see Section 4 for details.”
Martingale optimal transport and robust hedging in continuous time (2012, methodology): “We refer to the recent paper by Cox and Wang [8] for more information and a discussion of various constructions of the Root’s solution of the Skorokhod embedding.”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “Brown, Hobson & Rogers [13], Madan & Yor [62], Cox, Hobson & Oblój [18], Cox & Oblój [19, 20], Davis, Oblój & Raval [23], Cox & Wang [22], Gassiat, Oberhauser & dos Reis [34], Cox, Oblój & Touzi [21], Hobson & Neuberger [51], and Hobson & Klimmek [47, 48, 49, 50].”
Model-independent bounds for option prices—a mass transport approach (2011, unknown): “In the continuous-time setting, the problem has been treated for instance in the case of lookback options [20], variance/volatility options [8, 13, 23] and double-(no) touch options [11, 12].”
Optimal transport and Skorokhod embedding (2013, background): “Other recent approaches to the Root and Rost embeddings can be found in [13,14,25,26].”