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.
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Manuscript received: January 2000; final version received: February 2001
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Schmock, U., Shreve, S. & Wystup, U. Valuation of exotic options under shortselling constraints. Finance Stochast 6, 143–172 (2002). https://doi.org/10.1007/s007800100050
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DOI: https://doi.org/10.1007/s007800100050