Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, cadlag process S. Every option price is defined as the conditional expectation under a given equivalent martingale measure, the same for all options. We show that every contingent claim on S can be approximately replicated by investing dynamically in the underlying and statically in all American put options (of every strike price and with the same maturity), which are assumed to be optimally exercised by their respective holders. We also provide a counter-example to dynamic hedging with European call options of all strike prices and all maturities.
 
 
Market completeness with American put options
CAMPI Luciano
2007-44
04-09-2007
 
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