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
First version: December 17, 1999
Reference: Finance and Stochastics, Vol. 6 (2002) 143-172.
2010 Mathematics Subject Classification:
The paper (30 pages including 3 figures, revised version February 21, 2001) is available in:
Sponsors: National Science Foundation, Credit Suisse Group, Institute for Mathematics Research
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