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Tractable Hedging - An Implementation of Robust Hedging Strategies

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  • Nicole Branger

    ()

  • Antje Mahayni

Abstract

This paper analyzes tractable robust hedging strategies in diffusion-type models including stochastic volatility models. A robust hedging strategy avoids any losses as long as volatility stays within a given interval. It does not depend on the exact specification of the volatility process and therefore mitigates problems caused by model misspecification. A tractable hedging strategy is defined as the sum over Black-Scholes strategies. For a convex (concave) payoff, the cheapest robust hedge is given by a BS-hedge at the upper (lower) volatility bound. Thus, it is tractable. For all other payoffs, one has to solve a Black-Scholes-Barenblatt equation, and the cheapest robust hedge is not tractable. A tractable hedge can then be found by decomposing the payoff into a convex and a concave function, each of which is hedged separately. We first give the decomposition that minimizes the initial capital. Second, we show that it may be even cheaper to hedge a dominating payoff, and we show explicitly how to determine the optimal dominating payoff. We illustrate our results by two examples.

Suggested Citation

  • Nicole Branger & Antje Mahayni, 2006. "Tractable Hedging - An Implementation of Robust Hedging Strategies," Working Paper Series: Finance and Accounting 135, Department of Finance, Goethe University Frankfurt am Main.
  • Handle: RePEc:fra:franaf:135
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    File URL: http://www.finance.uni-frankfurt.de/wp/404.pdf
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    Keywords

    Stochastic volatility; robust hedging; tractable hedging; superhedging; model misspecification; incomplete markets;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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