When are static superhedging strategies optimal?

  • 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.

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Author:Nicole BrangerORCiDGND, Angelika Esser, Christian SchlagORCiDGND
Parent Title (English):Universität Frankfurt am Main. Fachbereich Wirtschaftswissenschaften: [Working paper series / Finance and accounting] Working paper series, Finance & Accounting ; No. 138
Series (Serial Number):Working paper series / Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften : Finance & Accounting (138)
Publisher:Univ., Fachbereich Wirtschaftswiss.
Place of publication:Frankfurt am Main
Document Type:Working Paper
Year of Completion:2004
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/10/06
Tag:Finanzderivat / Hedging / Strategie / Volatilität / Stochastischer Prozess / Theorie
Incomplete markets; stochastic interest rates; stochastic jumps; stochastic volatility; superhedging
GND Keyword:Derivat, Wertpapier; Hedging
Issue:Version: January 16, 2004
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht