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A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options

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  • Pierre Henri-Labordère
  • Nizar Touzi

    (Centre de Mathématiques Appliquées - Ecole Polytechnique)

  • Alfred Galichon

    (Département d'économie)

Abstract

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows to recover previously known results about Lookback options. In particular, our methodology induces a new presentation of the Azema-Yor solution of the SEP.

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Paper provided by Sciences Po in its series Sciences Po publications with number info:hdl:2441/5rkqqmvrn4tl22s9mc0ck8ecp.

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Date of creation: 2013
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Publication status: Published in Journal of Applied Probability, 2013
Handle: RePEc:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0ck8ecp

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  1. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
  2. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
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