Robustness of delta hedging for path-dependent options in local volatility models

A. Schied, M.A. Stadje

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)

    Abstract

    We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.
    Original languageEnglish
    Pages (from-to)865-879
    JournalJournal of Applied Probability
    Volume44
    Issue number4
    DOIs
    Publication statusPublished - 2007

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