When Are Static Superhedging Strategies Optimal?

Nicole Branger (), Angelika Esser () and Christian Schlag

No 138, Working Paper Series: Finance and Accounting from Department of Finance, Goethe University Frankfurt am Main

Abstract: 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.

Keywords: Incomplete markets; superhedging; stochastic volatility; stochastic jumps; stochastic interest rates (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2004-10
New Economics Papers: this item is included in nep-fin, nep-fmk and nep-rmg
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