Abstract We specialize the results on characterization of arbitrage and valuation of European and American Contingent claims obtained in Londoño [7 Londoño , J.A. 2004 . State tameness: A new approach for credit constrains . Electronic Communications in Probability 9 : 1 – 13 .[Crossref] , [Google Scholar]] for a model that is computational friendly, and include those whose price processes are of Itô type with coefficients that are only Hölder continuous. A unified framework for valuation of financial instruments of both European and American type is presented under some technical conditions. Also valuation of European and American contingent claims where the matrix of volatilities does not have maximal rank is provided, and valuation of contingent claims with random expiration date is developed.