Option spanning beyond $L_p$-models

TL;DR

This paper investigates the ability of options to span and replicate assets in a static market with non-integrable assets, extending previous $L_p$-model results and applying these findings to option pricing and arbitrage extensions.

Contribution

It extends the theoretical understanding of option spanning power beyond $L_p$-models and applies these insights to the arbitrage-free extension of option prices.

Findings

Options can uniquely extend prices of contingent claims via arbitrage.

Spanning power applies to markets with non-integrable assets.

Results unify previous models and broaden applicability.

Abstract

\begin{abstract} 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 [8,9,18] 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.