On American Derivatives and Related Obstacle Problems

Jörg Kampen ()
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Jörg Kampen: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, University of Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 06, 565-591

Abstract: We derive obstacle problems for pricing of American derivatives with multiple underlyings heuristically using only a few postulates such that classical (Brownian motion) models as well as models based on Levy processes can be considered in our frame. For the classical models we define a "signed measure" which allows to compute the exercise region near maturity and obtain a generic condition for continuity of the free boundary and prove some more general features of exercise regions for classical models. Especially, we investigate the exercise regions of the most important American derivatives with one and multiple underlyings where we include dependence of volatility and interest rates on time and the underlyings extending and recovering some classical results. Further applications include stochastic volatility models. It is shown that in classical stochastic volatility models where volatility is driven by an Ornstein-Uhlenbeck process an American compound call has a nonempty exercise region and compute the exercise region near expiration in a typical situation.

Keywords: Viscosity solutions; continuity of free boundary; exercise regions; stochastic volatility (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0219024903002109

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