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Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

  • Alexander Schied (a1) and Mitja Stadje (a2)

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.

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Copyright

Corresponding author

Postal address: Institut für Mathematik, TU Berlin, MA 7-4, Strasse des 17. Juni 136, 10623 Berlin, Germany. Email address: schied@math.tu-berlin.de
∗∗ Postal address: Department of Operations Research and Financial Engineering, Princeton University, Engineering Quadrangle, Princeton, NJ 08544, USA. Email address: mstadje@princeton.edu

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