When Are Static Superhedging Strategies Optimal?
AbstractThis 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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Bibliographic InfoPaper provided by Department of Finance, Goethe University Frankfurt am Main in its series Working Paper Series: Finance and Accounting with number 138.
Date of creation: Oct 2004
Date of revision:
Incomplete markets; superhedging; stochastic volatility; stochastic jumps; stochastic interest rates;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-12-12 (All new papers)
- NEP-FIN-2004-12-12 (Finance)
- NEP-FIN-2004-12-15 (Finance)
- NEP-FMK-2004-12-12 (Financial Markets)
- NEP-RMG-2004-12-12 (Risk Management)
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