Abstract
We consider the pricing of American put options in a modelindependent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process.
Original language  English 

Journal  Mathematical Finance 
Volume  26 
Issue number  2 
Early online date  2 Dec 2013 
DOIs  
Publication status  Published  Apr 2016 
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Alex Cox
 Department of Mathematical Sciences  Deputy Head of Department
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
Person: Research & Teaching