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A Note on Market Completeness with American Put Options

In: Inspired by Finance

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  • Luciano Campi

    (Université Paris 13, Département de Mathématiques, Institut Galilée)

Abstract

We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modeled by a suitably integrable, strictly positive, càdlàg process S on [0,T]. Every option price is defined as the conditional expectation under a given equivalent (true) martingale measure $\mathbb{P}$ , the same for all options. We show that every positive contingent claim on S can be approximately replicated in L 2-sense by investing dynamically in the underlying and statically in all American put options (of every strike price k and with the same maturity T). We also provide a counterexample to static hedging with European call options of all strike prices and all maturities t≤T.

Suggested Citation

  • Luciano Campi, 2014. "A Note on Market Completeness with American Put Options," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 73-82, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_4
    DOI: 10.1007/978-3-319-02069-3_4
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