Semi-nonparametric approximation and index options

In an arbitrage-free securities market, all state-contingent claims and the stochastic discount factors can be approximated appropriately by index options with a semi-nonparametric method. These index options are constructed by efficient algorithms and uniform approximation error under these efficient algorithms are derived. This paper suggests a method to examine state-contingent claims and stochastic discount factors using index options in financial market regardless the market is complete or not.