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Superreplication of Options on Several Underlying Assets

Part of: Parabolic equations and systems Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Erik Ekström ,
Svante Janson  and
Johan Tysk
Erik Ekström*
Affiliation:
Uppsala University
Svante Janson*
Affiliation:
Uppsala University
Johan Tysk*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
∗Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
∗Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
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Abstract

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We investigate the conditions on a hedger, who overestimates the (time- and level-dependent) volatility, to superreplicate a convex claim on several underlying assets. It is shown that the classic Black-Scholes model is the only model, within a large class, for which overestimation of the volatility yields the desired superreplication property. This is in contrast to the one-dimensional case, in which it is known that overestimation of the volatility with any time- and level-dependent model guarantees superreplication of convex claims.

Keywords

Parabolic equationsuperreplicationconvexityoption

MSC classification

Secondary: 60H05: Stochastic integrals 35K10: Second-order parabolic equations
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 27 - 38
Copyright
© Applied Probability Trust 2005 

Footnotes

∗∗∗

Partially supported by the Swedish Research Council.

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