Option spanning beyond $$L_p$$-models

The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the results in Galvani (J Math Econ 45(1):73–79, 2009), Galvani and Troitsky (J Math Econ 46(4):616–619, 2010) and Nachman (Rev Financ Stud 1(3):311–328, 1988) for \(L_p\)-models. We also apply the spanning power properties to the pricing problem. In particular, we show that prices on call and put options of a limited liability asset can be uniquely extended by arbitrage to all marketed contingent claims written on the asset.