A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options

A. Galichon, P. Henry-Labordère, N. Touzi

    Research output: Contribution to journalArticle

    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 us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azéma-Yor solution of the sep for a certain class of lookback options. Unlike the sep technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques.

    Original languageEnglish (US)
    Pages (from-to)312-336
    Number of pages25
    JournalAnnals of Applied Probability
    Volume24
    Issue number1
    DOIs
    StatePublished - Feb 1 2014

    Keywords

    • Convex duality
    • Optimal control
    • Volatility uncertainty

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

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