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The Use of Martingale Theory for the Superreplication of Exotic Options in Incomplete Markets

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  • Zimmer, Christian Johannes

Abstract

In this article we show the importance of modern martingale theory for the pricing and hedging of exotic options, especially in incomplete markets. When emitting an exotic option, the seller firstly has to ask himself whether there exists a hedging strategy for this title or not. Especially, when he wants to use a more realistic model than the simple Black-Scholes framework, the answer is not always obvious. We show in this article how to analyze this problem in the case of an exotic option, the Generalized Bermudian Option, which will turn out to be a generalization of the American option.

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  • Zimmer, Christian Johannes, 2003. "The Use of Martingale Theory for the Superreplication of Exotic Options in Incomplete Markets," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    • Handle: RePEc:sbe:breart:v:23:y:2003:i:2:a:2728
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    1. Neto, Cícero Augusto Vieira & Pereira, Pedro L. Valls, 2001. "Review of major results of Martingale theory applied to the valuation of contingent claims," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 21(2), November.
    2. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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