A Note on Market Completeness with American Put Options

Luciano Campi ()
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Luciano Campi: Université Paris 13, Département de Mathématiques, Institut Galilée

A chapter in Inspired by Finance, 2014, pp 73-82 from Springer

Abstract: 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.

Keywords: Market completeness; American put; Tanaka formula; European call; Marginals; 91B28; 60G40; 60G44; 60G48 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_4

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DOI: 10.1007/978-3-319-02069-3_4

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