Valuation of exotic options under shortselling constraints

Uwe Wystup (), Uwe Schmock () and Steven E. Shreve ()
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Uwe Wystup: Commerzbank Treasury and Financial Products, Neue Mainzer Strasse 32-36, 60261 Frankfurtam Main, Germany Manuscript
Uwe Schmock: Department Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland
Steven E. Shreve: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Finance and Stochastics, 2002, vol. 6, issue 2, 143-172

Abstract: Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits super-replication of the option. We develop this idea for exotic options, in which case the pricing problem becomes one of stochastic control. Our motivating example is a call which knocks out in the money, and explicit formulas for this and other instruments are provided.

Keywords: Exotic options; super-replication; stochastic control (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2002-03-12
Note: received: January 2000; final version received: February 2001
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Citations: View citations in EconPapers (9)

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