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, 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.
A note on market completeness with American put options / L. Campi - In: Inspired by Finance : The Musiela Festschrift / [a cura di] Y. Kabanov, M. Rutkowski, T. Zariphopoulou. - [s.l] : Springer International Publishing, 2014. - ISBN 9783319020686. - pp. 73-82 [10.1007/978-3-319-02069-3_4]
A note on market completeness with American put options
L. Campi
2014
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, 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.File | Dimensione | Formato | |
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AmericanPutCompleteness-3-submitted.pdf
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Campi2014_Chapter_ANoteOnMarketCompletenessWithA.pdf
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