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When Are Static Superhedging Strategies Optimal?


  • Nicole Branger


  • Angelika Esser


  • Christian Schlag



This paper deals with the superhedging of derivatives and with the corresponding price bounds. A static superhedge results in trivial and fully nonparametric price bounds, which can be tightened if there exists a cheaper superhedge in the class of dynamic trading strategies. We focus on European path-independent claims and show under which conditions such an improvement is possible. For a stochastic volatility model with unbounded volatility, we show that a static superhedge is always optimal, and that, additionally, there may be infinitely many dynamic superhedges with the same initial capital. The trivial price bounds are thus the tightest ones. In a model with stochastic jumps or non-negative stochastic interest rates either a static or a dynamic superhedge is optimal. Finally, in a model with unbounded short rates, only a static superhedge is possible.

Suggested Citation

  • Nicole Branger & Angelika Esser & Christian Schlag, 2004. "When Are Static Superhedging Strategies Optimal?," Working Paper Series: Finance and Accounting 138, Department of Finance, Goethe University Frankfurt am Main.
  • Handle: RePEc:fra:franaf:138

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    Incomplete markets; superhedging; stochastic volatility; stochastic jumps; stochastic interest rates;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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