Tractable Hedging With Additional Instruments

31 Pages Posted: 5 Mar 2007

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Antje Brigitte Mahayni

Mercator School of Management

Date Written: March 1, 2007


In an uncertain volatility model where only the stock and the money market account are traded, the upper price bound of a European claim is given by the solution of a Black-Scholes-Barenblatt equation. If an additional hedge instrument is available, the price bound can be tightened. This is also true if the set of admissible strategies is restricted to tractable strategies defined as sums of Black-Scholes strategies. By combining the approach for including additional instruments in the hedge and for finding the optimal tractable hedge, we are able to analyze the structure of the optimal superhedge. We compare both the general strategies and the tractable strategies when an additional call option is traded. The restriction to tractable strategies allows for economic arguments in finding the optimal position in the additional hedge instrument.

Keywords: Stochastic Volatility, Robust Hedging, Tractable Hedging, Uncertain Volatility Model, Additional Hedge Instrument

JEL Classification: G12, G13

Suggested Citation

Branger, Nicole and Mahayni, Antje B., Tractable Hedging With Additional Instruments (March 1, 2007). Available at SSRN: or

Nicole Branger

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)


Antje B. Mahayni (Contact Author)

Mercator School of Management ( email )

Lotharstra├če 65
Duisburg, Nordrhein-Westfalen 47057

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